Defining Reality: A Scientific Approach to Truth, Knowledge, and Consciousness

[Paul Martin]

It seems to me that we too frequently use the terms 'truth', 'knowledge', 'belief', 'faith', 'reality', 'existence', and 'consciousness' without first defining them. It also seems to me that these terms could be defined in many different ways, but I doubt that very many such sets of definitions will remain consistent after close examination of their consequences.

In this post, I will attempt to make a reasonable set of definitions that I think might be useful in discussing and speculating on what is going on in reality. If this turns out to be useful to anyone, I will be delighted. If it only turns out to be useful to me as a result of your criticisms, I will be equally delighted. I am here to learn and I would like to learn what is wrong with my approach. If we can come to an agreement to adopt these definitions, either as they are or with some modifications, then maybe we can proceed to use them to describe our various ideas about what is going on in reality. I think it's worth a try.

I'll sort of follow the mathematical paradigm of setting out primitive terms without definition and follow those with some definitions.

My thanks in advance to anyone who gives this any thought at all.

Primitives:
Existence = reality
Receptive Principle (in the sense of Rosenberg)
Contain (in the mathematical sense of sets containing elements)
Correspond (in the mathematical sense of a function)
Change
Patterns

Definitions:

Thing - any part of existence.

Information - Any difference (Type A) which can make a difference (Type B) (in the sense of Shannon) to anything in existence.

Bit - One difference of Type A. (Shannon's fundamental unit of information.)

Effective Principle (in the sense of Rosenberg) - The ability to effect a difference (of Type B) to some part of existence. Hence, information acts via the effective principle to make a difference to something real.

Apprehend - To change from the state of not containing, to the state of containing, the thing apprehended.

Knowledge - Any bit or set of bits which is apprehended by the Receptive Principle.

Concept - A stable pattern of knowledge.

Symbol - A part of reality, which if somehow known, will be known to correspond to some concept.

Langauge - An algorithm for converting concepts to patterns of real symbols and back again.

Proposition - A language statement making an assertion.

Truth - An attribute of a proposition if and only if the assertion made by the proposition is consistent with reality.

Belief (in a proposition, A) - A proposition (B) asserting the knowledge of a range of probability that the assertion of proposition A is true. The strength of the belief is measured by the probability range - the higher the range, the stronger the belief.

Faith (in a proposition, A) - Sufficiently strong belief to take some risk depending on the truth of A. (I.e. if A is true, good and no harm will result; if A is false, harm and no good may result.) If action is not taken, faith is lacking.

Consciousness - The Receptive Principle, i.e. the ability to know.

I am eager to hear what you think.

Warm regards,

Paul

 

[AKG]

I guess now that you're no longer running a country, you have time to start at the beginning.

I came on this thread for that, but it'd be rude if I didn't say anything else.

Defining truth, knowledge, and reality are things people have been trying to do for millenia.

"Concept - a stable pattern of knowledge" is pretty vague.

"Proposition - A language statement making an assertion." What's a statement?

"Truth - An attribute of a proposition if and only if the assertion made by the proposition is consistent with reality." This could have serious problems. You make truth dependent on language here. This means either you're speaking of existing languages only, or you're speaking of languages in abstract, as per your definition (as an algorithm...). If there's something in space that no language-speaking being has seen, then by interpretation 1 of your definition, there's no truth corresponding to facts about that thing in space, although there should be. On the second interpretation, it means that any statement can be true, because for every string of symbols imaginable, there exists (in theory) a language which interprets that as a true statement.

"Thing - any part of existence." Are numbers things? Are sets and functions things? Is the gross national product a thing?

 

[Paul Martin]

I guess now that you're no longer running a country, you have time to start at the beginning.

I guess the problem/benefit of having a common name is that you can get the blame/credit for things done by people who share it. That wasn't me up there in Canada.

I came on this thread for that, but it'd be rude if I didn't say anything else.

I don't think it would have been rude, but I'm glad you said what you did.

Defining truth, knowledge, and reality are things people have been trying to do for millenia.

True. But it would seem to me that with the benefit of all that hindsight and with the benefit of new scientific knowledge, we should be in a position to do a better job of defining these terms than our predecessors, don't you think? After all we can stand on the shoulders of some pretty big giants.

"Concept - a stable pattern of knowledge" is pretty vague.

Maybe. But I don't think it should take much work to fix it up. I think I precisely defined 'knowledge'. I took pattern as a primitive because I think we already have a notion of what it means, however vague. And I mean pattern in the most general and unspecified sense, so vagueness sort of comes with it. As for 'stable' that might take a little work incorporating the notions of change and time. Maybe you can help me with this.

"Proposition - A language statement making an assertion." What's a statement?

Good point. I should have defined it. 'Assertion' also should be defined. I think that by working through these kinds of issues, we could begin to make the progress I am looking for. I'll have to think about this some more.

"Truth - An attribute of a proposition if and only if the assertion made by the proposition is consistent with reality." This could have serious problems. You make truth dependent on language here. This means either you're speaking of existing languages only, or you're speaking of languages in abstract, as per your definition (as an algorithm...). If there's something in space that no language-speaking being has seen, then by interpretation 1 of your definition, there's no truth corresponding to facts about that thing in space, although there should be. On the second interpretation, it means that any statement can be true, because for every string of symbols imaginable, there exists (in theory) a language which interprets that as a true statement,

Good comments. Yes, I do think truth depends on language. I think you gain nothing by making 'truth' a synonym for 'reality'. But as an attribute of a language statement, you are right that there are two types. The first one is the sense in which I defined the term. The idea is that a statement is deemed true if there is a mathematical-type correlation between the concepts represented in the statement and things in the world. The second type of truth is the mathematical tautology. This is interesting but, as you say, any statement can be seen as true in this sense as long as the right mathematical primitives, definitions, and axioms are chosen. In most people's opinions it seems that this type of truth can't tell us much about reality. But in my opinion, it can and does. I am referring to Dr. Dick's deduction that if reality is describable, any consistent explanation of it must obey the laws of physics. (That is a completely separate issue which has been debated elsewhere.)

"Thing - any part of existence." Are numbers things?

Good question. I think we really need to get specific here. And we have to be careful. My answer is, "Yes, but..." The only numbers I claim exist, and thus are things, are those which have been explicitly defined, either by humans, or some other equally conscious entity, or by machines designed and built by those entities. What I don't claim exists is some "infinite" set of numbers, or numbers claimed to be transcendental or even just irrational even though approximations to those "numbers" out to trillions of digits might exist. I differ with most mathematicians on this issue since Brouwer and Kronecker died. I don't know if philosophers agree with me or not, or whether they have even thought about the question.

Are sets and functions things?

They are if and only if they have been explicitly defined by either man or machine or equivalent.

Is the gross national product a thing?

Yes. It has been defined explicitly.

Thanks for your comments, AKG.

Warm regards,

Paul

 

[AKG]

What are Type A and Type B differences?

Maybe. But I don't think it should take much work to fix it up. I think I precisely defined 'knowledge'. I took pattern as a primitive because I think we already have a notion of what it means, however vague. And I mean pattern in the most general and unspecified sense, so vagueness sort of comes with it. As for 'stable' that might take a little work incorporating the notions of change and time. Maybe you can help me with this.

Well if you express "concept" in terms of your primitives, is it even something we can understand? To me, it seems so vague that I wouldn't be able to tell whether a given thing is knowledge or not. How can I tell if something is a stable pattern of units of Type A differences contained inside the Receptive Principle, (which is the ability to know?).

Good comments. Yes, I do think truth depends on language. I think you gain nothing by making 'truth' a synonym for 'reality'. But as an attribute of a language statement, you are right that there are two types. The first one is the sense in which I defined the term. The idea is that a statement is deemed true if there is a mathematical-type correlation between the concepts represented in the statement and things in the world. The second type of truth is the mathematical tautology. This is interesting but, as you say, any statement can be seen as true in this sense as long as the right mathematical primitives, definitions, and axioms are chosen. In most people's opinions it seems that this type of truth can't tell us much about reality. But in my opinion, it can and does. I am referring to Dr. Dick's deduction that if reality is describable, any consistent explanation of it must obey the laws of physics. (That is a completely separate issue which has been debated elsewhere.)

Prima facie, your definition of "truth" looks unproblematic, until one realizes that it is based on your definition of proposition. That itself doesn't look problematic, but then you realize that it relies on your definition of language, which in turn relies on concepts, which in turn relies on knowledge. One thing worth noting is that you shouldn't assign truth directly to propositions, if you are defining them as symbolic statements. The same string of symbols may be interpreted in different ways in different languages. You should only define the truth of a sentence in a language. A sentence s is true in language L iff L(s) is true, where L(s) is true iff it agrees with reality. At this point, we would have to clarify what type of thing L(s) is, and what it means for such a thing to "agree" with reality. You have L(s) being a concept, which you call a stable pattern of knowledge. At the heart of it, this is problematic because it makes truth depend on knowledge, whereas the classic relationship is the other way around (truth is a necessary, but insufficient condition for knowledge). But before we go there, how can a sentence not be true? A sentence s is not true in L iff L(s) doesn't agree with reality, that is, iff the corresponding stable pattern of knowledge doesn't agree with reality. But if x doesn't agree with reality, then what are we doing calling it knowledge in the first place? Indeed, that would be a mistake, so there is no knowledge that doesn't disagree with reality, so all concepts agree with reality, hence all sentences are true (in every language).

You need to either make L(s) something other than a concept or redefine "concept". Calling it a concept isn't so bad, but I don't think perfect. But note concepts can be wrong (we can have wrong conceptions) so if you are sticking with concept, it shouldn't only be knowledge.

L(s) should be what the sentence s means in language L. s is a syntactic object, and under L, L(s) is the corresponding semantic object. Whereas L(s) should be something our consciousnesses interact with (like a concept) it should not be something that depends on conscious beings in particular. For example, your definition of information does not rely on there existing, or ever have existing, some conscious beings, even though it is something conscious beings interact with (because information makes up knowledge which is apprehended by consciousness). L(s) could be something analogous.

That said, your definition of "information" is a little confusing, which is why I asked earlier about Type A and B differences.

The general impression I get is that your definitions don't fit together. I aksed earlier how you would reduce "concept" to primitives and still make sense of it. But I think with most of your definitions, if you try to replace each term in a definition with a more primitive definition, until you have your term purely in terms of primitives, you see that things really haven't been fitting together.

The only numbers I claim exist, and thus are things, are those which have been explicitly defined, either by humans, or some other equally conscious entity, or by machines designed and built by those entities. What I don't claim exists is some "infinite" set of numbers, or numbers claimed to be transcendental or even just irrational even though approximations to those "numbers" out to trillions of digits might exist. I differ with most mathematicians on this issue since Brouwer and Kronecker died. I don't know if philosophers agree with me or not, or whether they have even thought about the question.

So you don't think irrationals or transendentals exist, period? And no infinite sets exist? And the only numbers which exist are those that are defined? You definitely have to be more specific. In the finite history of the man, not every natural number has been said, or even thought about, so are such numbers non-existent even though the whole set of N has been defined? When people were searching for the simple groups, did the Monster group exist before it was "found" and/or defined? If not, then why were they looking for it? If so, then how did it do so without being defined? Before anyone thought to think of (Z, +) as a group, did it not satisfy the group axioms? Hence wasn't it "always" a group? Do the existence of groups depend on us deciding to think about groups? Note how sharply this differs from rocks on Pluto which are there whether we think of them, or whether we had ever discovered Pluto or not. Why this difference?

They are if and only if they have been explicitly defined by either man or machine or equivalent.

How does the existence of something depend on whether or not man (or equivalent) has defined it? I mean if something is a thing, i.e. if it is a part of existence, then it is a part of existence whether we have defined it or not.

 

[Paul Martin]

Hi AKG,

What a wonderful and thoughtful response! If those two blue-ribboned recognition medals by your name represent superior achievement, they are well deserved. Thank you again for your thoughts on my proposal.

I have to run off to the dentist right now, but when I get back I'll give your post the careful thought and response that it deserves.

Warm regards,

Paul

 

[moving finger]

It seems to me that we too frequently use the terms 'truth', 'knowledge', 'belief', 'faith', 'reality', 'existence', and 'consciousness' without first defining them. ...

Paul

Hi Paul

I'm not sure just what it is you are trying to achieve here. Your definitions seem very artificial to me - if you are trying to define a private language then that seems fine. Normally words take meaning from the way they are used in language; you seem to be doing it the other way around (defining special meanings without necessarily taking into account the way the words are used in reality). That's OK, as long as you recognise that you cannot then use these words in "normal language" arguments and expect people to necessarily agree with the arguments. And as long as you recognise that using these artificially defined words in an argument to "prove" anything at all will simply end up with you proving things in your own private language, which will not necessarily have relevance to the language that the rest of us speak.

In particular, I completely disagree (in normal English usage) with the notion that "consciousness" is simply defined as the ability to know, and to know is simply defined as "apprehending bits", which leads to the conclusion that anything which apprehends bits is conscious.

Best Regards

 

[AKG]

The definitions of consciousness, knowledge, etc. along with the constant emphasis that a conscious entity could be a man, machine, or equivalent gave me the initial impression that these definitions were just ad hoc constructions inspired by the desire to prove machine intelligence possible. However, there's no need to speculate on that at this time, as his definitions make metaphysical and epistemological claims that can be judged and discussed in their own right.

 

[Paul Martin]

What are Type A and Type B differences?

To define information I adapted a statement of Shannon's definition that says, "Information is a difference that makes a difference". I simply chose the symbols 'Type A' and 'Type B' to refer to those two mentions of 'difference' in his definition. This definition, together with the two differences seems to form a causal nexus where the first (Type A) difference causes the second (Type B). I think it is important to define 'information' to be as general as possible so it seems to me that these two types of differences can be different in kind. One is that the difference might be between "real", or tangible, or physical things, while the other might be a difference between symbols or concepts. You could think of those as being analog and digital respectively.

Considering the combinations, information defined in this way could inform any of these causations:

Analog difference causing an analog difference - (e.g. position and momentum of a billiard ball causing a change in the arrangement of balls on the table.)
Analog difference causing a digtal difference - (e.g. position and lighting of an object causing a difference in a digital photo of the object.)
Digital difference causing an analog difference - (e.g. signal from a thermostat causing a difference in the temperature of the room.)
Digital difference causing a digital difference - (e.g. computer GIGO, or a mind forming new concepts after reading written information.)

At any rate, it seems important to keep the two straight. 'Type A' and 'Type B' might not be the best choice of symbols so I am willing to exchange them for any others you might think are better. The main idea is that Type A is the informer while Type B is the informee.

Well if you express "concept" in terms of your primitives, is it even something we can understand?

I think so. What part of it do you not understand?

To me, it seems so vague that I wouldn't be able to tell whether a given thing is knowledge or not. How can I tell if something is a stable pattern of units of Type A differences contained inside the Receptive Principle, (which is the ability to know?).

Yes, it might seem vague and overwhelming. But your comment reminds me of my attempt long ago to try to understand some mathematical theorem by replacing all terms by their definitions, and then replacing all those terms by their definitions, and continuing until the entire theorem was stated using nothing but primitive terms. It gets overwhelming fast. When we use a number, like 4, it would be extremely clumsy and unworkable to think of the number as defined by set theoretic primitives and axioms. Instead, we convince ourselves that our definitions are consistent with what we have decided to accept so far, and then we draw inferences from them which form concepts that we use at that level from then on. That's the type of foundation I am trying to build here.

To answer your question using a specific example, let's say you just did an experiment that showed a particular photon going through a half-silvered mirror rather than being reflected. You say that you know that the photon was transmitted rather than reflected. Now you ask, "How can I tell if [knowing the photon was transmitted] is a stable pattern of units of Type A differences contained inside the Receptive Principle, (which is the ability to know?)" My answer would be that your apparatus contained a Receptive Principle that was part of an analog-to-digital causal nexus. That is, the information contained in the actual state and behavior of the photon caused a difference in some digital portion of your apparatus. Then, in a digital-to-digital causal nexus, the difference in your apparatus informed your sensory input system which in turn informed your mind and made a difference in what you knew prior to that experience.

Yes, it gets complicated. But so does almost everything we are interested in.

One thing worth noting is that you shouldn't assign truth directly to propositions, if you are defining them as symbolic statements. The same string of symbols may be interpreted in different ways in different languages. You should only define the truth of a sentence in a language.

I agree completely.

A sentence s is true in language L iff L(s) is true, where L(s) is true iff it agrees with reality.

Here I would have to disagree. If, for example, L is the language of Euclidean Geometry and s is the Pythagorean Theorem, L(s) is true whether or not it agrees with reality. The notion of 'truth' in Mathematics is not the same as the notion which equates truth with reality.

At this point, we would have to clarify what type of thing L(s) is, and what it means for such a thing to "agree" with reality.

I agree. At least in the case where we are trying to understand something of reality. Pure mathematics is not such a case.

You have L(s) being a concept, which you call a stable pattern of knowledge. At the heart of it, this is problematic because it makes truth depend on knowledge, whereas the classic relationship is the other way around (truth is a necessary, but insufficient condition for knowledge).

Exactly! It is this difference which is at the heart of the disagreement between MF and me that prompted me to start this thread.

I agree that "the classic relationship is the other way around". But my position is that the classic relationship might not be as fruitful. After all, as you pointed out, the questions about 'truth' 'knowledge' 'reality', etc. have been argued for centuries without yet having come to a resolution. It seems clear to me that using the classic approach, we are forced to conclude that knowledge is vacuous; that we know nothing about reality for sure; that truth is so elusive that we don't even know what it is (small wonder, we don't know anything at all). If truth is necessary for knowledge, it presents a requirement that is impossible to meet.

What I am trying to explore are the implications of taking them in a different order.

But before we go there, how can a sentence not be true? A sentence s is not true in L iff L(s) doesn't agree with reality, that is, iff the corresponding stable pattern of knowledge doesn't agree with reality. But if x doesn't agree with reality, then what are we doing calling it knowledge in the first place?

What we are doing by calling it knowledge is deliberately divorcing knowledge from knowledge of reality. Mathematics has already made a good start on this path starting in about 1900. Prior to that, most mathematicians thought they were talking about reality. Now, few if any of them do. Physicists a few decades later began to see that they too needed to divorce the concepts they used from reality and make fewer, or weaker, claims about what, exactly, reality was and what was going on in reality. I am only suggesting that we continue in this trend.

So, "how can a sentence not be true?" A sentence s in a language L is not true iff it is inconsistent with the rules in L establishing the criteria for truth in L. It is language dependent, as you have suggested earlier.

Indeed, that would be a mistake, so there is no knowledge that doesn't disagree with reality, so all concepts agree with reality, hence all sentences are true (in every language).

I don't think it is a mistake. To the contrary, I would say that there is no knowledge (at least not yet) that agrees with reality. But the good news is that we have a huge amount of knowledge of some conceptual systems and models which incidentally (miraculously?) seem to help us get along in this real world.

But note concepts can be wrong (we can have wrong conceptions) so if you are sticking with concept, it shouldn't only be knowledge.

This may be a quibble, but I don't think it makes sense to categorize concepts as 'right' or 'wrong', just as it makes no sense to label definitions as 'right' or 'wrong'. 'Useful' and 'useless' make sense, but not 'right' and 'wrong'.

your definition of information does not rely on there existing, or ever have existing, some conscious beings, even though it is something conscious beings interact with (because information makes up knowledge which is apprehended by consciousness).

Yes. You have ferreted out my motive here. My abiding interest is in consciousness. I question whether human consciousness is the best or ultimate example. I also question whether consciousness is dependent on live brains. So to probe these questions, I am proposing a change in how we define some terms which have carried limiting baggage with them for thousands of years.

Using my definitions, knowledge is not necessarily tied to human consciousness. And the type of "consciousness" that might be present in some primordial Receptive Principle, might be unimaginable to us using the traditional terminology of our inherited languages. I just want a language that opens up more possibilities for explanation than we currently have.

There is more coming, but this is getting too big so I'll post it now.

Thanks again, AKG, for your interest, your thoughts, and your energy.

Warm regards

Paul

 

[Paul Martin]

The general impression I get is that your definitions don't fit together. I aksed earlier how you would reduce "concept" to primitives and still make sense of it. But I think with most of your definitions, if you try to replace each term in a definition with a more primitive definition, until you have your term purely in terms of primitives, you see that things really haven't been fitting together.

That's a fair and understandable general impression. I did not work through this before I sat down and composed it at my keyboard, so I am sure it needs a lot of correction and refinement. Comments like yours are exactly what I am looking for in order to either whip it into shape, or discover that it is nonsense and discard it. Your help is greatly appreciated regardless of the direction they take. In particular, how do you see that things really don't fit together?

So you don't think irrationals or transendentals exist, period?

Not as numbers, no. There are some numbers which are useful approximations, however. I think the concept of the length of the diagonal of a unit square exists. But I think that no extant number is consistent with that concept. Now, of course, you can choose a symbol, like 'pi', and define a number, which you will represent by that symbol, as the ratio of the circumference of a circle to its diameter, and after having done so, I guess it would be fair to say that "pi is a number". But in my humble opinion that is exactly the same as choosing a cardboard cutout, defining it to be a person, and then declaring that it is indeed a person.

It isn't exactly the same (upon reflection) because of the popular vote (which MF has just pointed out is important when it comes to language usage) you would get if you polled people on the questions of whether that cardboard cutout was a person and whether pi is a number. Most people would reject the former and accept the latter; I reject them both.

And no infinite sets exist?

No. I am unaware of any definition of them that satisfies me. All definitions I know of introduce inconsistencies, which I think should be disqualified based on the rules of mathematics and/or logic.

And the only numbers which exist are those that are defined?

Yes.

You definitely have to be more specific.

I hope you are as interested as you seem to be. If you are, start here: https://www.physicsforums.com/showthread.php?t=49732

In the finite history of the man, not every natural number has been said, or even thought about, so are such numbers non-existent even though the whole set of N has been defined?

Yes, I think such "numbers" are non-existent and I disagree that the whole set of N has been defined.

When people were searching for the simple groups, did the Monster group exist before it was "found" and/or defined?

No.

If not, then why were they looking for it?

Probably for the same reason Captain Cook spent all that time, money, and energy looking for another Pacific Continent. They both suspected there was such a thing. Cook was wrong, the mathematicians were right. Someone proved an existence theorem demonstrating that the concept of the monster group is consistent with the prior body of mathematics. As of yet, nobody has captured or displayed the monster, though.

Before anyone thought to think of (Z, +) as a group, did it not satisfy the group axioms?

I think not. What do you mean by 'satisfy' anyway? What I am fundamentally opposed to, which mathematicians seem to accept, is some process or algorithm which can be assumed to run by itself without any help from mind or matter. The Axiom of Choice and Mathematical Induction are examples which I don't think should be accepted beyond the explicit range that either a mind or a machine has achieved by cranking.

Do the existence of groups depend on us deciding to think about groups?

"Us"? I think any and all concepts depend on some sort of mind conceiving of them before they exist. I am very open to candidates for "some sort of mind". We now use vastly more numbers defined by machines than we do defined by human minds. In addition to human minds and human-built machines, there may be even more exotic possibilities which I think we should not rule out out of hand.

Note how sharply this differs from rocks on Pluto which are there whether we think of them, or whether we had ever discovered Pluto or not. Why this difference?

It is the difference between mind and matter. (In case you haven't already picked it up, I am a Cartesian Dualist of sorts.)

How does the existence of something depend on whether or not man (or equivalent) has defined it?

Well, how many different statues do you think were in that original block of marble that eventually became Michelangelo's "David"? An infinite number? None? I say none. I say that the existence of a statue depends on whether or not man (or equivalent, or superior even in the case of woman) goes ahead and chisels one out. Conceptually, I think it is no different with concepts. I don't think they can, or do, exist unless and until first conceived. Definition, IMHO is a more-or-less careful articulation of a concept in a language, so the thing defined actually exists a little before definition. It begins at conception.

I mean if something is a thing, i.e. if it is a part of existence, then it is a part of existence whether we have defined it or not.

Who's "we", white man? (Sorry. It's an old punch line I can't resist using.) When it comes to existence we are talking about something p r e t t y big. So I think it is presumptuous to think that we humans are all that critical or important in the big picture. My point is that there may be other definers and conceptualizers out there that we should allow for. So I would change your comment to say, if something is a thing, then it is part of existence. If that something is a concept, then it came into existence when it was first conceived.

(My remark about the size of reality reminded me of Woody Allen's assessment of the size of eternity. He said, "Eternity is a very long time, especially toward the end."

Good talking with you, AKG.

Warm regards,

Paul

 

[Paul Martin]

Hi MF,

Thanks for coming over to this thread.

Hi Paul

I'm not sure just what it is you are trying to achieve here. Your definitions seem very artificial to me - if you are trying to define a private language then that seems fine.

I trust that you have seen my responses to AKG, especially #8, and especially the last couple paragraphs of that. There I pretty much spell out what I am trying to achieve, and you are right, I am defining a private language. I hope that for normal vernacular usage the terms would end up having their same meanings. But I would like them to be grounded on a sensible foundation that wouldn't burden them with prior unwarranted assumptions. It may be an impossible task, but what the heck.

I completely disagree (in normal English usage) with the notion that "consciousness" is simply defined as the ability to know, and to know is simply defined as "apprehending bits", which leads to the conclusion that anything which apprehends bits is conscious.

You are jumping the gun a little by assuming that my definition of consciousness is simply the ability to know. I think that is a little like saying that a human body is simply quarks and leptons. Just as there is a lot of explaining to do in order to describe how quarks and leptons make a human body, I think it might be just as complex to explain how human consciousness is made up of complexes of interactions among Natural Individuals (as described by Gregg Rosenberg with their ability to know and to effect).

It seems to me that you would agree that we shouldn't even start such an adventure until we have precisely defined our terms. And it is just such a "private" set of definitions that I offer in order for you, me, and any other interested others to use in that discussion.

Warm regards,

Paul

 

[AKG]

"Information is a difference that makes a difference".

What are some differences that do make differences, and what are some that don't make differences? When a key on my keyboard goes from unpushed to pushed, the image on my screen is made different. Does that mean that the difference in position of a keyboard key is information?

To answer your question using a specific example, let's say you just did an experiment that showed a particular photon going through a half-silvered mirror rather than being reflected. You say that you know that the photon was transmitted rather than reflected. Now you ask, "How can I tell if [knowing the photon was transmitted] is a stable pattern of units of Type A differences contained inside the Receptive Principle, (which is the ability to know?)" My answer would be that your apparatus contained a Receptive Principle that was part of an analog-to-digital causal nexus. That is, the information contained in the actual state and behavior of the photon caused a difference in some digital portion of your apparatus. Then, in a digital-to-digital causal nexus, the difference in your apparatus informed your sensory input system which in turn informed your mind and made a difference in what you knew prior to that experience.

I don't understand what it even means for a difference to be contained in an ability. To me, it makes as much sense as talking about a process marrying an institution.

I might say something like "Tennessee can't finish their games," but this only makes sense because it is obviously short-form for "The Tennessee Titans can't finish their games." States don't play games, people do. Whereas we can get away with metonymy like this and still make sense, you seem to be doing it in a way that doesn't make sense. On it's own, it may be fair to equate a mind with a principle or an ability, because the ability in question occurs in a one-to-one correspondence with minds. But this is merely an ability unique to minds, the ability is not itself the mind. Similarly, I think there is some strong relation between certain differences and knowledge, but to define knowledge as differences seems to misinterpret figurative metonymy literally.

To the example in particular: I was asking about concepts, which are supposed to be stable patterns of differences of Type A contained in the ability to know. "Photons pass through a half-silvered mirror" might express a concept. In what sense is the concept expressed here a pattern of differences contained in an ability? Like what specifically are the differences, what specifically is the pattern, what is the ability, and in what sense is one contained in the other? Even if you don't want to reduce it fully, you still say that it is a stable pattern of knowledge. Well what stable pattern of knowledge does the above express? For each of the knowledges making up this pattern, could you then show how these are differences of Type A?

Here I would have to disagree. If, for example, L is the language of Euclidean Geometry and s is the Pythagorean Theorem, L(s) is true whether or not it agrees with reality. The notion of 'truth' in Mathematics is not the same as the notion which equates truth with reality.

Many mathematicians treat mathematical objects as real objects, part of reality, but not physical objects. To talk about physical objects, we normally use the English language. To speak of Euclidean geometries, we use the language of Euclidean geometry. Both physical objects and Euclidean geometries are real things, just very different in nature.

I agree that "the classic relationship is the other way around". But my position is that the classic relationship might not be as fruitful. After all, as you pointed out, the questions about 'truth' 'knowledge' 'reality', etc. have been argued for centuries without yet having come to a resolution. It seems clear to me that using the classic approach, we are forced to conclude that knowledge is vacuous; that we know nothing about reality for sure; that truth is so elusive that we don't even know what it is (small wonder, we don't know anything at all). If truth is necessary for knowledge, it presents a requirement that is impossible to meet.

The fact that knowledge is a true belief is almost never questioned. But there's more to knowledge than being a true belief. Some people say it must be justified. Some people say that it must be a belief that tracks the truth. The controversy is, for the most part, centered on what additional criteria make a true belief an instance of knowledge, not on whether knowledge is a true belief. Truth is not an elusive criteria. Blind guesswork gives you a 50-50 chance of believing the truth. Certainty, on the other hand, is quite hard to come by, but few people make certainty a criteria for knowledge. All the problems of us not knowing anything only come when certainty becomes a criteria for knowledge; these problems little to do with truth being a criteria for knowledge.

(Re: infinite sets)No. I am unaware of any definition of them that satisfies me. All definitions I know of introduce inconsistencies, which I think should be disqualified based on the rules of mathematics and/or logic.

I don't know of any such definitions that lead to contradictions.

Probably for the same reason Captain Cook spent all that time, money, and energy looking for another Pacific Continent. They both suspected there was such a thing. Cook was wrong, the mathematicians were right.

No, they weren't, not by your definition. Because prior to defining the Monster Group, there was no Monster Group, hence their suspicions that such a group might exist was wrong.

Also, what's the largest number? If it's n, then what of n+1? n and 1 are elements of your set of practical numbers, so do you just refuse to define n+1? You go on to say that we build bigger computers with greater number capacity. What greater numbers, you've refused to define any past n? Also, n+1 is defined as n U {n}. Note that n U {n} exists, and doesn't depend on time, or on you doing anything. There are no verbs in "n U {n}".

What do you consider a definition? Is "the largest root of x² - x - 1" a definition? How do you define 4, and what makes that a definition?

The fact that you don't regard irrationals as numbers suggests simply that you mean something totally abnormal by the word "number".

As of yet, nobody has captured or displayed the monster, though.

What would you even count as a display of this group? If someone printed an enormous Cayley table for you, would you accept the existence of the Monster Group?

I think any and all concepts depend on some sort of mind conceiving of them before they exist. I am very open to candidates for "some sort of mind". We now use vastly more numbers defined by machines than we do defined by human minds. In addition to human minds and human-built machines, there may be even more exotic possibilities which I think we should not rule out out of hand.

We can have concepts of groups, but groups are not concepts in the sense that they are objects solely of the mind. You can have a concept or thought about an apple, but apples exist even if no one is there to talk about them, perceive them, or call them "apples" or anything else. Why are groups any different?

Well, how many different statues do you think were in that original block of marble that eventually became Michelangelo's "David"?

Yes, the existence of the "David" statue depends on a man chiselling it out of marble, it doesn't depend on man defining "David". I asked how something's existence depends on someone defining it, not how it depends on someone fashioning it out of stone. I think you're confusing concepts of mathematical objects with mathematical objects themselves.

Anyways, I think this is getting too bogged down in the details. It also seems that the ideas you've introduced in this thread offer a position on a big handful of very tough, fundamental issues in metaphysics and epistemology. Maybe you could pick one main idea you'd like to elaborate on, and start other threads to deal with the other ideas.

 

[moving finger]

you are right, I am defining a private language. I hope that for normal vernacular usage the terms would end up having their same meanings.

They don't (imho)

But I would like them to be grounded on a sensible foundation that wouldn't burden them with prior unwarranted assumptions.

But you have unwarranted assumptions imho. Your "Receptive Principle" as an undefined primitive is one example. Rosenberg's philosophy and ideas (upon which you have based your "primitive") are imho unashamedly anti-physicalist, therefore (again imho) you are building unwarranted assumptions into the very foundations of your definitions.

You are jumping the gun a little by assuming that my definition of consciousness is simply the ability to know.

It is you, with respect, who is jumping the gun. That is exactly how you have defined consciousness, Paul, in your first post :

Consciousness - The Receptive Principle, i.e. the ability to know.

Not only does this build unwarranted assumptions (as explained above) into your definitions, it also clearly identifies consciousness as the ability to know.

I think that is a little like saying that a human body is simply quarks and leptons.

I agree completely - thus how can you define consciousness (as you do) as the ability to know?

Just as there is a lot of explaining to do in order to describe how quarks and leptons make a human body, I think it might be just as complex to explain how human consciousness is made up of complexes of interactions among Natural Individuals (as described by Gregg Rosenberg with their ability to know and to effect).

Another unwarranted assumption - you are packing all of Rosenberg's metaphysical anti-physicalist baggage into your definitions without qualification or discussion.

It seems to me that you would agree that we shouldn't even start such an adventure until we have precisely defined our terms.

Agreed. But as I said in my previous post, if you define a private language all you will end up with is arguments in terms of your own private language, the meaning of which the rest of us (in our everyday language) may or may not agree with.

Best Regards

 

[moving finger]

The fact that knowledge is a true belief is almost never questioned. But there's more to knowledge than being a true belief. Some people say it must be justified. Some people say that it must be a belief that tracks the truth. The controversy is, for the most part, centered on what additional criteria make a true belief an instance of knowledge, not on whether knowledge is a true belief. Truth is not an elusive criteria. Blind guesswork gives you a 50-50 chance of believing the truth. Certainty, on the other hand, is quite hard to come by, but few people make certainty a criteria for knowledge. All the problems of us not knowing anything only come when certainty becomes a criteria for knowledge; these problems little to do with truth being a criteria for knowledge.

I agree 100%. Claims to knowledge are not claims to certain knowledge. Claims to knowledge are both subjective and fallible, and this is why so many people have problems coming to grips with understanding the concept. It is also the reason why so many Gettier-style arguments proliferate in an attempt to show that knowledge is NOT JTB - all of which arguments can be shown to be unsound when the fallible and subjective nature of knowledge-claims is taken into account.

A "belief that tracks the truth" is (imho) just another way of saying the belief must be justified.

I don't know of any such definitions that lead to contradictions.

I have never understood how the notion that all natural numbers are finite could be consistent with the notion of the set of natural numbers of infinite cardinality. I've asked the question several times in the Number Theory forum and never received a coherent answer (the response from alleged mathematicians is usually along the lines of "well it just is consistent, so shut up and go away").

In other words :

(i) The cardinality of the set of natural numbers is infinite.
(ii) A natural number is defined as being a number which can be generated by adding 1 to itself a finite number of times.

From (ii) we can (in principle) generate the set of natural numbers, starting from 1. We can also order the elements of this set in ascending order. Since every member of this set is finite, how can there then be an infinite number of members of the set?

You might say we could never construct the complete set (it would take an infinite time). Not so. In principle (if not in practice) we could identify the first member of the set in 1/2 second, the second member in 1/4 second, the third member in 1/8 second, the fourth member in 1/16 second, etc. The total time required to generate a set of N numbers would then be less than 1 second, no matter what value we choose for N. Indeed, if we continue our set construction in this fashion for a full 1 second, we would have an infinite set of natural numbers. (yes, yes, I know that we could never do this in practice - but this is a thought-experiment, and there is nothing wrong in principle with the idea of adding 0.5 + 0.25 + 01.125 + ... over an infinite series to generate the sum 1).

But by definition (ii) we would hit a definitional obstacle if we continue this process for a full 1 second - because by definition (ii) we may add 1 to itself only a finite number of times - so what do we end up with if we continue adding 1 to itself in the manner described above for a full 1 second? It cannot be a natural number by definition (because there are an infinite, not a finite, number of steps in the process 0.5 + 0.25 + 0.125 +... to generate the sum 1, and natural numbers are generated only by adding 1 to itself a finite number of times).

The notion of an infinite set of finite natural numbers therefore seems totally incoherent to me. But then I'm not a mathematician, so I guess that according to the high priests of mathematics I don't know what I'm talking about.

Best Regards

 

[moving finger]

Well, how many different statues do you think were in that original block of marble that eventually became Michelangelo's "David"? An infinite number? None? I say none. I say that the existence of a statue depends on whether or not man (or equivalent, or superior even in the case of woman) goes ahead and chisels one out.

And what if the statue was chiselled out by a chimpanzee? Would you then say that the statue is not of David because it has not been created by man?

Existence (of a statue) is not dependent on a physical creation by man, it is only the naming of that statue which is dependent on man – and naming is purely subjective convention.

What would make a chimpanzee-produced statue a “statue of David” is not necessarily the artist who created it, but it is simply convention in the eyes of observers. If I believe the chimpanzee-produced statue resembles my Uncle George, I might claim “that’s a statue of my Uncle George!”, whereas another person might say “no, it’s my great grandfather Simon!”. In this sense there ARE a number of statues not just in one block of marble, but even within one statue – because naming and representation is governed simply by convention.

Best Regards

 

[Paul Martin]

Hi AKG,

I am not sure how to take your post.

Anyways, I think this is getting too bogged down in the details. It also seems that the ideas you've introduced in this thread offer a position on a big handful of very tough, fundamental issues in metaphysics and epistemology. Maybe you could pick one main idea you'd like to elaborate on, and start other threads to deal with the other ideas.

From this, it seems that you might not want to continue this discussion as I have started it. I feel sort of bad that I have sucked you into this (by using my real name, it seems) and gotten you more involved in details than you would like. If so, I apologize for the trick, and I thank you for the thought you have put into my proposal so far.

As for your suggestion that I fractionate my proposal and deal with individual pieces in different individual threads, I think it would defeat my purpose. Since my purpose was to go at the fundamental questions of philosophy (the "very tough, fundamental issues in metaphysics and epistemology"), using the techniques of mathematics, your suggestion would be equivalent to suggesting that mathematicians deal with individual primitive concepts, axioms, and definitions in isolation. Of course this would not be fruitful because it is the relationships among the various pieces that make up the useful body of a mathematical system.

As I have admitted and tried to make clear, I have not worked out the details, much less the implications, of my starting set of primitives and definitions. So I am not in a position to ask a simple yes or no question as to whether my system works or makes sense. Instead, I am looking for help in identifying where changes and improvements should be made in order to construct something that might be fruitful. I feel that your comments so far are exactly that kind of critique I need and they are exactly the sort of thing I am looking for. By discussing the type of issues you have raised, I can learn where my errors are and try to fix them.

So I hope I am wrong in interpreting your statement in the quote above as you wanting to back out of this project. But I won't twist your arm any more. If you want to stop, I understand and I sincerely thank you for your help to this point and for the time and energy you have put into it.

Now, if as I hope, my interpretation is wrong and you are still interested in my answers to the specific questions you asked, I'll try to answer them.

What are some differences that do make differences

If you recall, I gave five examples which I think cover four fundamentally different types:

1. A difference in the position and momentum of a billiard ball making a difference in the later arrangement of balls on the table.
2. A difference in the position or lighting of an object making a difference in a digital photo of the object.
3. The difference between a signal and no-signal from a thermostat making a difference in the temperature of the room.
4. A difference in the input to a computer making a difference in the output, or in computer lingo, Garbage In - Garbage Out (GIGO).
5. A difference in written information making a difference in the concepts in the mind of a reader of that information.

what are some that don't make differences?

Using the same examples,
1. A difference in the cue ball's position and momentum which causes it to miss all the other balls and return to its original position on the table.
2. A rotation of a shiny ball bearing making no difference in a digital photo of it if nothing else is changed.
3. A difference in the temperature of the bi-metal strip in a thermostat makes no difference to the furnace if both temperatures are, say, under the thermostat temperature setting.
4. The difference between a capital 'A' and a lowercase 'a' being input to a computer makes no difference to the computer output if the program is not case sensitive.
5. The difference between a particular word appearing in the text, and a synonym of that word appearing instead, may make no difference in the resulting concepts in the mind of a reader of that text.

When a key on my keyboard goes from unpushed to pushed, the image on my screen is made different. Does that mean that the difference in position of a keyboard key is information?

Yes. In typical keyboard design, the difference represents seven or eight bits of information.

I don't understand what it even means for a difference to be contained in an ability. To me, it makes as much sense as talking about a process marrying an institution.

That exactly illustrates the beauty and power of mathematics. That is, by basing all statements on primitives and rigorously defined terms, extremely complex concepts can be imagined and discussed at a high level without appealing to the horrendously complex structure of definitions at every turn.

For example, you have mentioned groups so I take it that you are familiar with the concept of group operation. And, of course I'm sure that you are familiar with the operations of addition and multiplication. 'Operation' is a mathematical concept which is fairly easy to grasp and use in our thinking, our calculations, and our conversations. But if we had to think and talk about the concept of 'operation' in primitive terms it would be difficult to understand. It would "make[] as much sense as talking about a process marrying an institution". It would end up being something like the last of these equivalent definitions:

1. An operation on a set A is a function on AXA to A.

2. An operation on a set A is a subset of AXA in which each member of A appears exactly once as a first member in the ordered pairs in AXA.

3. An operation on a set A is a set such that each element of the operation is also a member of AXA and in which each member of A appears exactly once as a first member in the ordered pairs in AXA.

4. An operation on a set A is a set such that each element of the operation is also a member of the set of all ordered pairs in which the first member is taken from A and the second member is taken from A and in which each member of A appears exactly once as a first member in the ordered pairs in the set of all ordered pairs in which the first member is taken from A and the second member is taken from A.

Even at this, we have not nearly reduced our definition to primitive terms. We still have the terms 'ordered', 'pair', 'first', 'second', and so on to define in terms of primitives. To continue this example, in order to define the term 'second' we need to define the ordinal number two. I just looked in my copy of Whitehead & Russell's "Principia Mathematica to *56" and found that it took 375 pages of the most horrendous logical complexity you can imagine to finally define the ordinal number 2.

It is interesting to note that the ordinal number 2 was used for millennia to great effect without anyone ever having rigorously defined it. Similarly, terms like 'truth', 'knowledge', 'infinity', and 'good' have also been used effectively in human affairs for millennia. But in the case of mathematics, a great deal is to be gained, and has been gained, by placing formerly non-rigorous, albeit useful, concepts on firmly rigorous foundations. What I am suggesting that we attempt to do is to try to place these elusive philosophical concepts on a similarly rigorous foundation. We can deal with the mathematical complexity, so I see no reason why we can't deal with the complexities that accompany these terms as well.

To the example in particular: I was asking about concepts, which are supposed to be stable patterns of differences of Type A contained in the ability to know. "Photons pass through a half-silvered mirror" might express a concept. In what sense is the concept expressed here a pattern of differences contained in an ability?

I'll reiterate my answer from a previous post:

"My answer would be that your apparatus contained a Receptive Principle that was part of an analog-to-digital causal nexus. That is, the information contained in the actual state and behavior of the photon caused a difference in some digital portion of your apparatus. Then, in a digital-to-digital causal nexus, the difference in your apparatus informed your sensory input system which in turn informed your mind and made a difference in what you knew prior to that experience."

Like what specifically are the differences,

There are three Type A differences in the causal chain in the example:
1. The difference in some value of some quantum number for the photon that caused it to be transmitted rather than reflected.
2. The difference between a spot appearing or not on some screen.
3. The difference between the experimenter seeing and not seeing a spot on some screen.
There are also three Type B differences:
1. The difference between a spot appearing or not on some screen.
2. The difference between the experimenter seeing and not seeing a spot on some screen.
3. The difference between the experimenter knowing and not knowing the outcome of the experiment.

what specifically is the pattern,

1. I'm not familiar enough with QED to be able to explain what these quantum numbers might be, but I would guess that the polarization of the photon might be one.
2. The pattern on the screen is a spot or no spot.
3. The pattern is a corresponding spot or no spot on the retina of the experimenter.
4. The pattern is a part of what is probably a very complex concept in the mind of the experimenter.

what is the ability,

1. The ability of the mirror to transmit or reflect photons depending on certain quantum numbers associated with the photon.
2. The ability to floresce when struck by a photon.
3. The ability to see the florescent spot.
4. The ability to interpret the presence/absence of the spot in the context of the experiment.

and in what sense is one contained in the other?

Your question might have uncovered a bad choice of terms on my part. I chose the term 'contained' in order to convey the same sort of relationship elements have to sets. So, applying it to the notion of ability, it does seem a little contrived. Let me suggest the sense in which I see it, and if this doesn't work well, I am open to alternative suggestions.

I would say that the notion of a "pattern of differences contained in an ability" is similar to the notion of water being contained in a pump, where 'pump' is defined as an ability to move water through pipes uphill. Yes, it's contrived, but so are all examples. The pattern of differences correspond to the water going into the pump, the pump is the ability, and the water is contained in the pump as it goes through.

Specifically,
1. The photon is contained in the apparatus, which is the ability to distinguish between transmission and reflection. (It occurs to me that 'capability' rather than 'ability' might be better.)
2. The florescent glowing is contained in the screen.
3. The difference between emitted photons and no emitted photons is contained in the retina amongst the rods and cones.
4. The pattern of difference between seeing a spot and not seeing a spot is contained in the concepts concerning the experiment in the mind of the experimenter.

Well what stable pattern of knowledge does the above express?

1. The apparatus knows which way the photon went.
2. The screen knows whether or not it was struck by a photon.
3. The retina knows whether or not it sees a spot
4. The experimenter knows a fact about this particular experiment.

Now, I admitted that 'stability' needs work. In these cases the stability is sometimes very brief. But I think the notion still applies. The stability must persist long enough for a Type B difference to be propagated on as a Type A difference down the chain.

For each of the knowledges making up this pattern, could you then show how these are differences of Type A?

I hope the foregoing has made that clear.

That is probably enough for now, especially since I am not sure how much more of this you are willing to stomach. My sincere thanks to everyone and anyone who has read this far.

Warm regards,

Paul

 

[Paul Martin]

Hi MF,

But you have unwarranted assumptions imho. Your "Receptive Principle" as an undefined primitive is one example.

Good point. All assumptions are unwarranted. Some, however, later become vindicated if they lead to valuable insights. But, note that in most of these cases, it took a lot of hard work to derive the insights. That work has not even begun for my proposal so I think it is too early to say whether it could be fruitful.

Rosenberg's philosophy and ideas (upon which you have based your "primitive") are imho unashamedly anti-physicalist, therefore (again imho) you are building unwarranted assumptions into the very foundations of your definitions.

It sounds like you don't hold Rosenberg in any higher esteem than you do Penrose. I don't think he is anti-physicalist so there is nothing to be ashamed of. I think that he only thinks it might be a mistake to rule out the possibility of some kind of non-physical existence. From what you say about your concept of 'concepts', it seems to me that you admit the existence of non-physical entities as well. We need to talk a lot more about this.

It is you, with respect, who is jumping the gun. That is exactly how you have defined consciousness, Paul, in your first post :

Consciousness - The Receptive Principle, i.e. the ability to know.

You got me, fair and square. I was wrong, and I'm glad you corrected me. As you know, I have a hunch that the fundamental essence of consciousness is something like the ability to know. And, it is obvious that I have chosen my primitive concepts with this in mind. But you are right: I have not done the hard work of connecting the dots and inferring that consciousness is really built on such a basis.

In fact, (I mean IMHO), that work can't be done without first choosing suitable primitive terms, and then precisely defining the terms needed to draw inferences. I am still in the starting gate.

Are you asking “what is truth?”, or “how do we decide what is true?”?

Neither. I am asking "what do you suppose we could infer if we took the definition of 'truth' to be such-and-such?"

At the end of the day, we are all fallible agents dependent on our beliefs. Nobody has access to absolutely certain knowledge (of truth and falsity) of the world, everything we think we know of the world is built upon our premises, and infallible (certain) knowledge of the external world is an impossible goal.

I agree with all those claims in vernacular English. The obvious implication is that knowledge is vacuous. This conclusion is not useful for any purpose that I can think of.

So, it seems to me that if we took different definitions for some fundamental concepts we might be able to construct a consistent structure of ideas that would (1) mean roughly the same as the same ideas expressed in English, and (2) provide inferences that can shed new light on millennia-old unresolved questions. (Exactly like Galois did in mathematics.)

Another unwarranted assumption - you are packing all of Rosenberg's metaphysical anti-physicalist baggage into your definitions without qualification or discussion.

Your comment prompted me to re-read the preface to a book on Differential Geometry ("Calculus on Manifolds", Spivak, 1965) which left a lasting impression on me when I first read it some 40 years ago. Spivak stated his intention to show how the proofs of complex theorems (in particular Stokes', Green's, and the Divergence Theorems) can be utterly simplified by the careful choice of definitions. In other words, if you do it right, the complexity shifts from the proofs to the definitions, but the definitions end up being much simpler than the classical proofs using classical definitions.

Yes, I have intentionally burdened my primitives with some of Rosenberg's concepts with the hope of being able to take Spivak's advice, and get his result. Again I would ask that you temper your views of Rosenberg's "anti-physicalist baggage" and open your mind to the possibility that there might be more going on in reality than mere physicality.

But as I said in my previous post, if you define a private language all you will end up with is arguments in terms of your own private language, the meaning of which the rest of us (in our everyday language) may or may not agree with.

You are absolutely right if nobody works with me and nobody reads anything I come up with. That is why I am looking for help from people like you. I think that if we are careful in choosing our definitions, we can end up with terms which have the same connotations as they do in ordinary English vernacular.

They don't (imho)

With respect, I think that is a premature judgment.

Thanks for your thoughts, MF. Looking forward to hearing more.

Warm regards,

Paul

 

[AKG]

You are trying to answer:

What is truth?
What is knowledge?
What is language?
What is consciousness?
What is existence?
What is reality?
What is belief?
How are truth and knowledge related?
How are language and knowledge related?
How are truth and language related?
How are belief and knowledge related?
How are consciousness and language related?
etc.

all in one thread. This is overly ambitious. It's not like a mathematician considering a bunch of axioms in one place, it's like a mathematician trying to solve all of Hilbert's problems in one place.

What's more, you bundle philosophical positions into your definitions themselves. For example, your definitions make truth contingent on linguistic beings of some sort, and divorce knowledge from truth.

Another thing: how does your definition of knowledge help? How does it clarify the notion of knowledge? I think I asked whether your definition of knowledge is something anyone could even recognize or understand. Take anyone of the Gettier problems, for example. How would you apply your definition of knowledge to decide whether the belief in question is an instance of knowledge or not, and how does it account for this answer? Consider the following particular example:

Smith walks into a room and seems to see Jones in it; she immediately forms the justified belief, "Jones is in the room." But in fact, it is not Jones that Smith saw; it was a life-size replica propped in Jones's chair. Nevertheless, Jones is in the room; she is just hiding under the desk reading comic books while her replica makes it seem as though she is in. (source)

Does Smith know that Jones is in the room? I can't make heads or tails of what your account would say about this. Maybe the light reflecting off the replica is information, and when Jones sees it, there's some pattern which is a subset of a principle, which supposedly means that he knows/believes that Jones/Jones' replica is in the room? If this were to, by your account, lead us to conclude that Smith knows that Jones is in the room, then your account is problematic, because Smith's belief here would be a fluke, and no one would really consider this knowledge. If, on the other hand, we would conclude that Smith knows that Jones' replica is in the room, you'd have another problem, because if you were to ask Smith if a replica of Jones is sitting in the room, he'd probably say, "A replica? What are you talking about?" The other option would be to say that Smith knows neither that Jones is in the room nor that Jones' replica is there, but surely seeing the replica caused some sort of pattern of information to enter his consciousness, so by definition this would be some sort of knowledge. If so, what is it?

You might answer that Smith knows that something that looks like Jones is in Jones' office, and nothing more. I would like to pre-empt such a response with the following. Earlier, you said:

To answer your question using a specific example, let's say you just did an experiment that showed a particular photon going through a half-silvered mirror rather than being reflected. You say that you know that the photon was transmitted rather than reflected.

You'd have to go back on this. You could not say that you knew that the photon was transmitted. You could only know what the experiment apparatus looked like. Although you wanted to escape global scepticism, which you mistakenly took to be characteristic of classical accounts of knowledge, your own account may have you returning to it anyways.

Regarding your differences that make no differences, it seems to subjective. A cue ball which hits the rail and returns to its original spot having touched no other ball still makes a difference. It likely imparted some tiny amount of energy to the felt and to the rail. The tiny fibers in the felt also probably changed position. In the thermostat example, even though the signal isn't toggled, the bimetallic strip will have changed shape, thus effecting the nearby air particles, and the region of space surrounding it in general. Although this would cause other problems, the following definition matches your examples better: "Information is a difference that causes a difference non-negligible to humans."

Regarding the keyboard key depression being information, this seems like another example of sloppy equivocation. Just as it is not that a mind is the ability to know, rather a mind has an ability to know, it's not that key depression is information, but rather, as you yourself put it, key depression represents information. X represents Y and X is Y are two different statements. If a sword represents violence, then you can say that violence is bad for society but you can't say that sword is bad for society. This is what I mean by things not fitting together.

We can deal with the mathematical complexity, so I see no reason why we can't deal with the complexities that accompany these terms as well

Because they aren't the same kind of complexity. We can think of real numbers just as numbers, or as equivalence classes of rational Cauchy sequences, or as Dedekind cuts, or points on a line, or as arrows. Whereas it makes sense to say that (3, 3.1, 3.14, 3.141, ...) is in \pi when we regard it as a Cauchy sequence, it doesn't make sense to say that this sequence is in an arrow. Nonetheless, we can take all these different definitions and realize that they are different ways at looking at the same thing. It's not clear that your definitions are likewise. The very fact that your relations between knowledge, truth, and belief are so different from the standard makes it hard to regard your definitions as simply a clearer way of looking at things we already talk about.

Moreover, if you take something in mathematics and reduce it to primitives, you get something that may be obtuse, but is still consistent and makes sense. If you boil a sentence down to set-theoretic terms, then any occurence of \in occurs with a set to the left and a set to the right. On the other hand, when you boil your definitions down, you get things like processes marrying institutions. Saying {{2}, {2,4}} is in x \mapsto x^2 doesn't make sense as is, but you can reduce it to primitives, and it will be an ugly string of brackets, commas, and an \in symbol, but it will be consistent. I don't see your definitions working that way.

"My answer would be that your apparatus contained a Receptive Principle that was part of an analog-to-digital causal nexus. That is, the information contained in the actual state and behavior of the photon caused a difference in some digital portion of your apparatus. Then, in a digital-to-digital causal nexus, the difference in your apparatus informed your sensory input system which in turn informed your mind and made a difference in what you knew prior to that experience."

No, I'm not talking about knowing that some photons really did pass through a half-silvered mirror. I'm just talking about the concept of photons passing through a mirror. A concept is just a thought. Think about someone planning to design a new kind of car. He has a concept for this concept car. Or going back to my previous example, someone is just thinking about photons passing through a half-silvered mirror, he isn't currently observing it in an experiment, indeed he may never have observed it. A concept is just an idea, or thought, how is it dependent on knowledge? Secondly, if it were to be dependent on knowledge (which it's not), what would make it a pattern of bits in an ability? How does your definition shed light on recognizing a concept? Personally, I think it might suffice to leave concept/idea a primitive term. I'm not sure that you can reduce it any further, and I don't think your attempts to do so clarify what a concpet is, or make concepts easier to identify.

In your final example, you in detail explain the differences, abilities, patterns etc. in an experiment. Many of the abilities are not abilities. Experimental apparati, retinae, and screens don't have abilities, they have tendencies. A half-silver mirror tends to transmit photons of a certain, I don't know, polarity? Screens tend to flouresce when hit by photons. Retina tend to send impulses to the brain when struck by photons. People, on the other hand, have abilities. And a pump is not an ability. A pump perhaps has an ability to move water, but it certainly isn't an ability to move water. However, I think even that is wrong. A person with a pump has the ability to move water, the pump itself has nothing.

All your examples of patterns shed no light on what you mean by pattern. If you entirely removed the reference to patterns in your definition of concept/knowledge, I can't see what difference it would make. Indeed, looking at your list of differences, the following causal chain seems to be implicit:

difference in quantum number of photon >
difference in spots on screen >
difference in what experimenter sees >
difference in what experimenter knows

As long as there's a difference in what the experimenter sees, there's a difference in what he knows, it doesn't matter if there's a pattern or not in what he sees. And what he sees differs as long as the screen differs, it doesn't matter if there's a pattern in the differences on the screen. And there's a difference on the screen if there's a difference in the photon, it doesn't matter if the photon's differences have any pattern.

A vacuum has the "ability" to transmit a photon traveling at constant speed v at position x to x+vt after an elapse of time t, and certainly this difference in photon position can cause differences in other things. Does the vacuum thus contain the difference in the photon's position, and thus know that different position of the photon? A vacuum is nothing, and does nothing, but does it know nonetheless?

You claimed there to be three instances of Type A information, but listed four instances of knowledge. How do you account for this inequality?

Next, if your definition of knowledge allows screens to know they are flourescing, doesn't this totally trivialize knowledge to the point that the case for AI which you might want to build from this definition for knowledge ends up proving nothing of consequence? That is, the current debate over whether machines do/can have knowledge is about knowledge of a kind seemingly much different from the kind you've defined, so even though your definition might conclude that machines have "knowledge", this in fact doesn't even come close to what's really being asked in the current debate over machine knowledge.

Also, you still haven't explained what knoweldge/concepts are. You keep telling me about patterns and changes that happen outside the mind, then at the end, you say, "and now the person knows the photon does this". How specifically, is this knowledge a pattern of bits? All you seem to be doing is telling me how a causal chain of events leads to a sequences of changing things, which corresponds to a sequence of differences, and eventually, one of the differences that occurs is that a subject goes from not-knowing to knowing. I still don't see how knowledge can, by definition, be a difference. Certainly, a difference occurs once a subject gains knowledge, but that can't possibly be what you're saying.

I think another reason why I felt this was getting bogged down in the details is that I have little idea what your pont is, or where you're going with this. All I can do is nitpick at little definitions and strange equivocations, it's hard to give suggestions because I don't know where you want to go with it. Since you don't want to solve a particular problem, but rather want to simultaneously solve all the biggest problems of philosophy in one thread, it's hard to give any underlying direction to the comments I make.

 

[moving finger]

Hi Paul

Good point. All assumptions are unwarranted. Some, however, later become vindicated if they lead to valuable insights. But, note that in most of these cases, it took a lot of hard work to derive the insights. That work has not even begun for my proposal so I think it is too early to say whether it could be fruitful.

Who is to judge what is “valuable” and what not? An unsound argument is misleading, not valuable, and by assuming false premises you end up with an unsound argument. On what basis can you validate your premise that the Receptive Principle is a correct and accurate notion?
.

It sounds like you don't hold Rosenberg in any higher esteem than you do Penrose. I don't think he is anti-physicalist so there is nothing to be ashamed of. I think that he only thinks it might be a mistake to rule out the possibility of some kind of non-physical existence. From what you say about your concept of 'concepts', it seems to me that you admit the existence of non-physical entities as well. We need to talk a lot more about this.

Esteem for Rosenberg (the person) has nothing to do with it – I simply do not agree that physicalism is false. Before we can discuss existence of concepts, we need to agree what is meant by the term “existence”. To me, there are two very distinct “worlds” of existence, the physical world of our senses on the one hand, and Plato’s non-physical world of forms (wherein exists all logically possible forms, ideas and concepts). There is (imho) no causal connection between these two worlds (how can there be, since one is physical and one non-physical), and the physical world is entirely physical (ie physicalism is true in this world).
You may agree with Rosenberg that it is a mistake to rule out the possibility of non-physical existence in our world of the senses, but by adopting his RP as a premise you are thereby ruling out physicalism. Since I believe physicalism is true, we have a fundamental disagreement at the start.

I agree with all those claims in vernacular English. The obvious implication is that knowledge is vacuous. This conclusion is not useful for any purpose that I can think of.

Not quite (imho). “belief about knowledge” is fallible (I may be incorrect in believing that I know that X), but it does not follow from this that we cannot possesses knowledge (here I define knowledge as JTB). The problem is that we simply cannot be absolutely certain whether we do possesses knowledge or not (the best we can ever do is to believe that we possesses knowledge), because to be absolutely certain that my “belief that I know that X” is correct/true entails infinite regress (I would need to know that I know that I know that I know etc). Knowledge is attainable, but certainty of belief in knowledge is not. Whenever we say “I know X”, what we actually and strictly mean is “I believe that I know X” – but the “I believe that” qualification is usually dropped.

The issue (imho) is NOT whether this conclusion is “useful” in your eyes or not (this is a value judgement that you place on it), it is whether this conclusion is true or not. As with the above RP premise, we can delude ourselves into thinking something is valuable or useful because it gives us the answers that we want - ie assuming the premise that “physicalism is false” is true leads to the tautological conclusion that physicalism is false; assuming the premise that “knowledge is a fundamental essence of consciousness” is true (possibly) leads to the tautological conclusion that consciousness supervenes on knowledge, rather than the diametrically opposite conclusion (the one which I think is correct) that knowledge is an emergent property of consciousness.

I agree with AKG's above observation :

you bundle philosophical positions into your definitions themselves

So, it seems to me that if we took different definitions for some fundamental concepts we might be able to construct a consistent structure of ideas that would (1) mean roughly the same as the same ideas expressed in English, and (2) provide inferences that can shed new light on millennia-old unresolved questions. (Exactly like Galois did in mathematics.)

Sure we can. But that does not mean we arrive at true interpretations. You seem to be building your personal interpretation into your premises (ie that knowledge is somehow primal, and that physicalism is false), and I disagree with these premises.

Yes, I have intentionally burdened my primitives with some of Rosenberg's concepts with the hope of being able to take Spivak's advice, and get his result. Again I would ask that you temper your views of Rosenberg's "anti-physicalist baggage" and open your mind to the possibility that there might be more going on in reality than mere physicality.

Why? As far as I am concerned, I can explain everything based on physicalism. Therefore why should I assume physicalism is false?

You are absolutely right if nobody works with me and nobody reads anything I come up with. That is why I am looking for help from people like you. I think that if we are careful in choosing our definitions, we can end up with terms which have the same connotations as they do in ordinary English vernacular.

Then why define knowledge as “Any bit or set of bits which is apprehended by the Receptive Principle.” – how is this in any way related to the meaning of the word in ordinary English vernacular? 99.999% of people would look blankly at you if you defined knowledge this very artificial and contrived way.

They don't (imho)

With respect, I think that is a premature judgment.

With respect, I have just shown that it is a correct judgement (above reference to your definition of knowledge).

Best Regards

 

[Paul Martin]

Hi AKG,

You are trying to answer:

What is truth?
What is knowledge?
What is language?
What is consciousness?
What is existence?
What is reality?
What is belief?
How are truth and knowledge related?
How are language and knowledge related?
How are truth and language related?
How are belief and knowledge related?
How are consciousness and language related?
etc.
...Since you don't want to solve a particular problem, but rather want to simultaneously solve all the biggest problems of philosophy in one thread, it's hard to give any underlying direction to the comments I make.

Yes, I agree that it's hard. But you have proven yourself up to the task. I am impressed and grateful for the contributions you have made so far. I couldn't have asked for, or expected better.

All I can do is nitpick at little definitions and strange equivocations, it's hard to give suggestions because I don't know where you want to go with it.

What you call "nitpicking" I take as insightful analysis and criticism, and it has helped me sort out my own thoughts. It is my failing for not telling you clearly where I want to go with this. Hopefully in this post I can partially correct that.

This is overly ambitious. It's not like a mathematician considering a bunch of axioms in one place, it's like a mathematician trying to solve all of Hilbert's problems in one place.

Being the unqualified and tired old man that I am, my aims are not nearly that ambitious. Grand in scope maybe, but not ambitious in what I expect to achieve here.

Hilbert didn't set out to solve that list of problems. What he did was to recognize that the new approaches to mathematics that were developed around the turn of the century held the promise that some very tough problems could now be attacked. Instead of trying to solve all the problems on his list, he tried to encourage other people to attempt them using new tools. What had changed in mathematics was that it had been placed on completely new foundations. As I told MF in another post, some complex classical mathematical theorems can be greatly simplified by choosing slightly more complex, but vastly more robust, definitions. And these definitions turn out to have the same meanings in ordinary usage as their previous counterparts. That's roughly what I want to do for the hard philosophical problems. And, as my title indicates, I am only offering a starting point.

I like to imagine that one of the 10 or so people who have pushed the readership number of this thread up to 142, might be a brilliant young student who will become the next Francis Bacon or Evariste Galois. Maybe some ideas discussed here might inspire one of them to see the benefit in slightly changing the course of science by broadening, or changing some of their rules. Or it might inspire one of them to see how mathematics could be applied to the heretofore intractable philosophy problems you listed, just as Galois saw how abstract group theory could solve the centuries old problems of squaring the circle and trisecting an angle as trivial byproducts of a powerful and much more general new theory.

What's more, you bundle philosophical positions into your definitions themselves.

Yes, and deliberately so. This is exactly the technique that has proved to be so fruitful and powerful in mathematics, as I have tried to describe.

For example, your definitions make truth contingent on linguistic beings of some sort,

The traditional view that truth is synonymous with reality would be fine if we were able to discover it. But in the early 20th century it became evident that we didn't know exactly what is going on in reality and there are indications that we probably never will. This would mean that truth about reality is completely elusive. On the other hand, the tautological truths in mathematics, which are wholly linguistic forms, have been shown to have enormous explanatory power. It makes sense to me that we should forget about the putative truth about reality and concentrate on the linguistic truth of mathematics.

and divorce knowledge from truth.

It seems to me that in light of this new awareness, it might be the proper time to consider divorcing knowledge from truth.

Another thing: how does your definition of knowledge help?

If we can't know anything for sure about reality, as modern science seems to tell us, it means that either there is no such thing as knowledge, or at least that we can't have any. Either one is a useless notion inconsistent with ordinary usage of the term 'knowledge'. So, it seems to me that we should divorce knowledge from truth, if by 'truth' we mean agreement with reality, and let 'knowledge' mean something weaker. My proposal is to define knowledge as the possession of information and that seems to pretty well match ordinary English usage. (Possession is maybe a better way of saying "apprehended by a Receptive Principle", but I mean the same thing.)

How does it clarify the notion of knowledge?

I understand that epistemologists would like to make truth necessary for knowledge, but in ordinary usage, there are plenty of false claims to knowledge. On reflection, my proposal seems to be reducing knowledge to what you would call belief, but a weaker definition of 'knowledge' that is closer to 'belief' than to 'truth' might be more consistent with the ordinary connotation of the term. Maybe the problem is that we don't have enough words. We need words to differentiate among:

1. I know X.
2. I believe X.
3. I believe I know X.
4. I think I know X.
5. I possesses information that indicates X.

IMHO, 1. is always a false claim. 2. and 3. are of no use to anyone else. 4. may be true, but it is useless to anyone else. 5. may be useful to others if the information can be shared. It is for these reasons I propose that knowledge be defined as the possession of information.

I think I asked whether your definition of knowledge is something anyone could even recognize or understand.

I think so. I think people would take "I have information that says X" to mean the same thing as "I know X". It might be even better if we define 'fact' to mean reliable information. Then we could say, "I have facts indicating X". That would make it sound almost like "I can prove X.", which very nearly means the same as, "I know X." I think this notion could be very recognizable and understandable by ordinary people.

Does Smith know that Jones is in the room? I can't make heads or tails of what your account would say about this. ...Maybe the light reflecting off the replica is information, and when Jones sees it, there's some pattern which is a subset of a principle, which supposedly means that he knows/believes that Jones/Jones' replica is in the room?

Yes, something like that. Smith would say, "I think I saw Jones in the room.", or "I have information that indicates Jones is in the room." Now, I agree that this is not consistent with the JTB idea of knowledge, and in fact, Smith would say the same thing even if Jones weren't really in the room. But since we have to operate in the absence of real truth anyway, the fallible knowledge that we do have is still useful. I guess I am proposing to redefine knowledge from "certain or absolute knowledge" to "fallible or probable knowledge". It seems to me that is what MF has been saying too.

The other option would be to say that Smith knows neither that Jones is in the room nor that Jones' replica is there, but surely seeing the replica caused some sort of pattern of information to enter his consciousness, so by definition this would be some sort of knowledge. If so, what is it?

By my definition, it would be "probably useful knowledge".

You could not say that you knew that the photon was transmitted. You could only know what the experiment apparatus looked like. Although you wanted to escape global scepticism, which you mistakenly took to be characteristic of classical accounts of knowledge, your own account may have you returning to it anyways.

It is clear to me that I could learn a lot about classical epistemology from you. In particular, how is my conclusion of global scepticism mistaken? Can you tell me anything we know for sure?

Although this would cause other problems, the following definition matches your examples better: "Information is a difference that causes a difference non-negligible to humans."

I am willing to compromise. I would rather not tie the definition to humans, but also allow for machines, animals, and other possible agents. Thus, 'information' would be defined in the context of a particular agent; information for one might be inconsequential for another. Would that fix the problems you see?

Regarding the keyboard key depression being information, this seems like another example of sloppy equivocation. Just as it is not that a mind is the ability to know, rather a mind has an ability to know, it's not that key depression is information, but rather, as you yourself put it, key depression represents information. X represents Y and X is Y are two different statements.

Yes. That was sloppy of me. I should have said, the key depression is seven or eight (depending on your keyboard design) bits of information. My language might have been sloppy equivocation, but the design of keyboards makes them fairly reliable instruments for transmitting the information in a key depression to the computer. Even the depression of the key is designed to be unequivocal in the sense that it is mechanically either depressed or not depressed. There is almost always some sort of click mechanism built in which clearly makes the difference between "depressed" and "not depressed" distinct. Yes, you may push the key partway down, but you are either above the click threshold or below it, which corresponds to the information being present or not. It is unequivocal. If the key is depressed, information exists which is transmitted to the computer. If not, that information does not exist.

Moreover, if you take something in mathematics and reduce it to primitives, you get something that may be obtuse, but is still consistent and makes sense. ... I don't see your definitions working that way.

I agree that they aren't ready for publication quite yet. But I see no reason why the definitions of these terms can't be made with mathematical rigor. It will just take some work.

No, I'm not talking about knowing that some photons really did pass through a half-silvered mirror. I'm just talking about the concept of photons passing through a mirror. A concept is just a thought. Think about someone planning to design a new kind of car. He has a concept for this concept car. Or going back to my previous example, someone is just thinking about photons passing through a half-silvered mirror, he isn't currently observing it in an experiment, indeed he may never have observed it. A concept is just an idea, or thought,

With respect, "A concept is just a thought" and "A concept is just an idea" seem to be a sloppy equivocations. Using the word 'just' makes it sound as if these assertions are trivial or obvious. Yet the terms 'concept', 'thought', and 'idea' seem to me to denote profoundly mysterious ideas. I proposed a definition for 'concept' as a pattern of information. You have defined none of them and IMHO use them in a cavalier way. What exactly do you think a thought or an idea is, anyway?

how is it dependent on knowledge?

It makes intuitive sense to me to consider thoughts, ideas, and concepts as patterns in sets of known information. That is what my definitions say and it clearly shows how concepts are dependent on knowledge (i.e. known information). Does it make sense to you that you can have a concept which you do not know, or know about?

This brings up a related question, which MF and I still need to resolve: Does it make sense to you that a concept can exist without some agent first knowing it or knowing about it?

Now, even if you agree with MF that there are concepts existing in some Platonic reality which have never been conceived by any agent, do you think they consist of something other than patterns of information? If so, what would they consist of?

Secondly, if it were to be dependent on knowledge (which it's not), what would make it a pattern of bits in an ability?

You have almost convinced me that my construction of "in an ability" needs work. Neither my pump example, nor the set-theoretic notion of "contains" seems to capture the idea I am trying to get across. Let me try another approach.

For a concept to be formed, it seems necessary that some pattern of bits becomes known, or recognized. For example, the concept of a circle might be formed by seeing, or imagining, or otherwise apprehending an image formed by a set of pixels in a circular arrangement, or it might be an algebraic equation of a circle expressed in some symbolic form, such as chalk on a blackboard and seen and recognized by the agent forming the concept. So the agent forming or gaining the concept, must have the ability to apprehend the pattern in the set of bits making up the information content of the concept.

Now, it might be clumsy to talk about the "bits being in the ability", but the agent must have the ability to apprehend the bits, and when the bits are apprehended, then and only then is the concept formed and known.

How does your definition shed light on recognizing a concept?

By seeing it as an example of pattern recognition.

Personally, I think it might suffice to leave concept/idea a primitive term. I'm not sure that you can reduce it any further, and I don't think your attempts to do so clarify what a concpet is, or make concepts easier to identify.

Can you give me an example of a concept which can't be expressed as a pattern of bits?

Many of the abilities are not abilities. Experimental apparati, retinae, and screens don't have abilities, they have tendencies.

I don't think I would have any problem using the term 'tendency' rather than 'ability'. I can't see that it makes any difference to what I am trying to get across. I chose 'ability' partly because it seemed to parallel the classical definition of 'energy' as the ability to do work. It might make as much sense to say that energy is the tendency to do work. It doesn't seem to make much difference to me. And, there may be a more modern definition of 'energy' that I don't know about and which might suggest an even better choice. I'm open to suggestions.

As long as there's a difference in what the experimenter sees, there's a difference in what he knows, it doesn't matter if there's a pattern or not in what he sees. And what he sees differs as long as the screen differs, it doesn't matter if there's a pattern in the differences on the screen.

I disagree. I think there is something important added by the notion of pattern. Pattern recognition is something beyond the simple apprehension of the bits. Think of those 3-D random dot pictures. There is quite a difference between seeing the detail of all the dots, and seeing the 3-D image that is present in the pattern.

Does the vacuum thus contain the difference in the photon's position, and thus know that different position of the photon?

No. I'd say it is the system of the vacuum and the photon which knows the photon's position.

A vacuum is nothing, and does nothing, but does it know nonetheless?

I'd say it knows it is empty and that's all. It has (contains, owns, possesses, has apprehended, knows) exactly one bit of knowledge and that bit has the value of zero.

You claimed there to be three instances of Type A information, but listed four instances of knowledge. How do you account for this inequality?

I think you are referring to this:

There are three Type A differences in the causal chain in the example:
1. The difference in some value of some quantum number for the photon that caused it to be transmitted rather than reflected.
2. The difference between a spot appearing or not on some screen.
3. The difference between the experimenter seeing and not seeing a spot on some screen.

1. The apparatus knows which way the photon went.
2. The screen knows whether or not it was struck by a photon.
3. The retina knows whether or not it sees a spot
4. The experimenter knows a fact about this particular experiment.

It looks like I didn't separate out the retina from the experimenter in the list of differences. To be consistent, I should have inserted another difference between 2. and 3. that said, "The difference between some rods and cones in the retina being excited or not." Sorry for the confusion.

Next, if your definition of knowledge allows screens to know they are flourescing, doesn't this totally trivialize knowledge to the point that the case for AI which you might want to build from this definition for knowledge ends up proving nothing of consequence?

I don't think it "totally trivializes" knowledge but it does greatly increase the domain of knowledge from nothing (IMHO) to accepting such things as a thermometer "knowing" the temperature. I have no problem using the term to refer to machines, just as people do in ordinary conversation. I happen to be a strong disbeliever in strong AI, so I am not motivated to make a case for it. I say that machines can know, but I say that they can't be conscious.

Also, you still haven't explained what knoweldge/concepts are. You keep telling me about patterns and changes that happen outside the mind, then at the end, you say, "and now the person knows the photon does this". How specifically, is this knowledge a pattern of bits?

I think I have explained what knowledge and concepts are in my definitions and primitives. But let me summarize.

Bits are differences.
Information is bits.
Knowledge is apprehended information.
Concepts are patterns in knowledge.

Thanks for your thoughts and your help, AKG. It's good talking with you.

Warm regards,

Paul

 

[Paul Martin]

Hi MF,

Who is to judge what is “valuable” and what not?

People in the future who find it valuable can judge it to be so. People in the future who have not found it to be valuable should probably refrain from judging in case someone finds it to be valuable later on.

An unsound argument is misleading, not valuable, and by assuming false premises you end up with an unsound argument.

Agreed.

On what basis can you validate your premise that the Receptive Principle is a correct and accurate notion?

I made no such premise. I took the Receptive Principle as a primitive. Axioms are premises; primitives are simply undefined terms.

I simply do not agree that physicalism is false.

I don't know whether I agree or not. What do you mean by "Physicalism is false."?

A. Nothing physical exists.
B. Something exists which is not physical.
C. Something non-physical can effect the physical world.
D. ...?

I agree with B and C.

Before we can discuss existence of concepts, we need to agree what is meant by the term “existence”. To me, there are two very distinct “worlds” of existence, the physical world of our senses on the one hand, and Plato’s non-physical world of forms (wherein exists all logically possible forms, ideas and concepts).

Unless we disagree on the meaning of 'existence', it sounds like you agree with B. So your notion of "Physicalism is false" must be A, C, or D.

There is (imho) no causal connection between these two worlds (how can there be, since one is physical and one non-physical), and the physical world is entirely physical (ie physicalism is true in this world).

Here again, "Physicalism is false" must be A, C, or D.

You may agree with Rosenberg that it is a mistake to rule out the possibility of non-physical existence in our world of the senses

Let's leave Rosenberg out of it, since I can't speak for him. As for me, you are putting words in my mouth. I would "rule out the possibility of non-physical existence in our world of the senses" just as I would rule out the possibility of non-family members in my family. What I would not rule out is the possibility of non-physical existence outside our world of senses. And, with respect, it sounds as if you wouldn't either. You admit that there is a Platonic world existing outside our physical world. I don't think you and I are all that far apart. I think we might only disagree on the contents of that Platonic world, in the relative timing of a few physical events, and whether there is any causal connection between the physical and the non-physical.

by adopting his RP as a premise you are thereby ruling out physicalism.

If you mean that I agree with B or C above, you are correct. I agree with both.

Not quite (imho). “belief about knowledge” is fallible (I may be incorrect in believing that I know that X), but it does not follow from this that we cannot possesses knowledge (here I define knowledge as JTB). The problem is that we simply cannot be absolutely certain whether we do possesses knowledge or not (the best we can ever do is to believe that we possesses knowledge), because to be absolutely certain that my “belief that I know that X” is correct/true entails infinite regress (I would need to know that I know that I know that I know etc). Knowledge is attainable, but certainty of belief in knowledge is not. Whenever we say “I know X”, what we actually and strictly mean is “I believe that I know X” – but the “I believe that” qualification is usually dropped.

Even though our definitions of knowledge are different (I don't accept JTB), I still agree with everything you said here except for the "Not quite." (I think you were referring to my comment that knowledge is vacuous.) So I think our different definitions lead to essentially the same connotation. And, that is what I am trying to achieve.

The issue (imho) is NOT whether this conclusion is “useful” in your eyes or not (this is a value judgement that you place on it), it is whether this conclusion is true or not.

OK, I'll concede. I was wrong. Knowledge is not vacuous. I, at least, know one thing. I know that thought happens. I think, although I don't know, that you might know the same fact. But, with that one exception, let's examine the conclusion and see if we can figure out whether it is true or not that knowledge is otherwise vacuous.

I think we agree that one can't know for sure that one knows anything. But, could one could know something accidentally, i.e. without being sure about it? I don't think so because then you would be saying that a lucky guess amounts to knowledge.

If you disagree, then please produce one counter-example of something you know (other than thought happens).

Sure we can. But that does not mean we arrive at true interpretations.

I think true interpretations are too much to ask or expect. On the other hand if the interpretations turn out to be useful in solving some human problems, then they would have value for some humans and that would make the enterprise worth pursuing. That's exactly what science has done for the past couple hundred years.

Why? As far as I am concerned, I can explain everything based on physicalism.

Well, as far as you are concerned there is no reason for you to search further. If you are happy with your explanations that should be sufficient since you are the only one you need to satisfy.

Then why define knowledge as “Any bit or set of bits which is apprehended by the Receptive Principle.” – how is this in any way related to the meaning of the word in ordinary English vernacular? 99.999% of people would look blankly at you if you defined knowledge this very artificial and contrived way.

For the same reason it has been useful to define numbers based on set-theoretic primitives. "99.999% of people would look blankly at you if you defined [numbers] this very artificial and contrived way."

To me, there are two very distinct “worlds” of existence, the physical world of our senses on the one hand, and Plato’s non-physical world of forms (wherein exists all logically possible forms, ideas and concepts). There is (imho) no causal connection between these two worlds (how can there be, since one is physical and one non-physical), and the physical world is entirely physical (ie physicalism is true in this world).

I am interested in your view that there is no causal connection between the two worlds. As I think you know, I believe that there is causation in both directions. I think certain ideas influence our (human) actions, and I think certain (human) perceptions generate ideas and concepts which somehow end up in Plato's world.

It would seem to me that if there were no interaction between the worlds, the ideas and concepts generated in human brains would be totally separate and distinct from those in the Platonic world and there would be no way, even in principle, to compare them. In the other direction, it would seem that regardless of what forms, ideas, or concepts might be in Plato's world, they could have no influence on the ideas or thoughts which might go on in human brains. So, based on this, I don't see why you think a Platonic world exists. Why do you?

Good talking to you, MF.

Warm regards,

Paul

 

[AKG]

The traditional view that truth is synonymous with reality would be fine if we were able to discover it. But in the early 20th century it became evident that we didn't know exactly what is going on in reality and there are indications that we probably never will.

I think you're being a little extreme here. There may be some indeterminacy at a quantum level, but if Jones is hiding under a desk, she either is or she isn't, and the truth of the matter is not so elusive. It's certainly not elusive to Jones.

If we can't know anything for sure about reality, as modern science seems to tell us, it means that either there is no such thing as knowledge, or at least that we can't have any.

Remember, if truth is correspondence with reality, then "half" of the claims we can make will be true. Truth is not what stands in the way here, it is certainty. But certainty isn't really a condition for truth anyway. In JTB, J stands for Justified, not Certain. Even if we can't know anything for sure, it doesn't mean we can't know anything, and it doesn't mean we have to redefine knowledge.

I understand that epistemologists would like to make truth necessary for knowledge, but in ordinary usage, there are plenty of false claims to knowledge.

So? People make false claims to knowledge. This is hardly a reason to redefine knowledge.

Yes, something like that. Smith would say, "I think I saw Jones in the room.", or "I have information that indicates Jones is in the room." Now, I agree that this is not consistent with the JTB idea of knowledge, and in fact, Smith would say the same thing even if Jones weren't really in the room.

It seems you didn't get the point of my Gettier example. By your definition of knowledge, does Smith, after seeing the replica of Jones, have knowledge? I think it's safe to say that your accounts says that he does have knowledge, for the light that would reflect of Jones were she sitting at her desk can't be so much different from that reflecting off her replica that only the former leads to bits apprehendable by the Receptive Principle, while the latter does not. In light of this, what exactly does your account tell us that Smith knows? What, specifically, is the proposition P which satisfies, "upon seeing the replica, Smith knows (by Paul Martin's definition) that P."

But since we have to operate in the absence of real truth anyway, the fallible knowledge that we do have is still useful. I guess I am proposing to redefine knowledge from "certain or absolute knowledge" to "fallible or probable knowledge". It seems to me that is what MF has been saying too.

There is no absence of truth, maybe just an absence of certainty. But your proposed redefinition is in fact no redefinition at all, since certainty or absoluteness were never really requirements for knowledge.

In particular, how is my conclusion of global scepticism mistaken?

As I said, you mistakenly took it to be symptomatic of classical definitions of knowledge. But I've said more than once that certainty is not a traditional criterion.

Can you tell me anything we know for sure?

You know you exist, and you know that what you see looks like whatever it looks like to you. We can't derive empirical facts with certainty from foundational truths like those, but we don't need certainty.

I am willing to compromise. I would rather not tie the definition to humans, but also allow for machines, animals, and other possible agents. Thus, 'information' would be defined in the context of a particular agent; information for one might be inconsequential for another. Would that fix the problems you see?

For now, we can work with that.

With respect, "A concept is just a thought" and "A concept is just an idea" seem to be a sloppy equivocations. Using the word 'just' makes it sound as if these assertions are trivial or obvious. Yet the terms 'concept', 'thought', and 'idea' seem to me to denote profoundly mysterious ideas. I proposed a definition for 'concept' as a pattern of information. You have defined none of them and IMHO use them in a cavalier way. What exactly do you think a thought or an idea is, anyway?

Like I said, I think these are primitive terms, so no, I haven't provided a definition. If you look up "concept" on Merriam-Webster by the way, you get:

1: something conceived in the mind: THOUGHT, NOTION
2: an abstract or generic idea generalized from particular instances
synonym see IDEA (m-w.com)

And I don't think it's cavalier. You know what "seeing" is, don't you? I don't think you could put into words what "seeing" is in a way that would really explain it to someone else. Moreover, I can talk about "seeing" and you know exactly what I'm talking about, and neither of us need to be able to put into words what precisely we're talking about.

But that wasn't even my point. My point was that your definition of concept, aside from being slightly opaque, is too narrow. Knowledge and information are types of concepts, but musings, imaginings, plans, hypotheses, theories, etc. can also be concepts. Nobody might think about painting their walls with baby food, but we can talk about it as a concept. I mean, if someone were to say, "what if people started painting their walls with baby food," another person might say, "hey, that's a pretty weird concept." The idea that truth is correspondence with reality is a concept, even if no one believes it and even if no one knows it.

Roughly, asking whether there can be concepts that aren't known is like asking whether there are sentences that can be neither true nor false. Yes, of course there are sentences that can be neither true nor false - any question or command will do. "How are you today?" and "Pick that up now!" aren't true or false.

On the other hand, if you mean to ask, "can there exist concepts that haven't been thought about?" then you have a legitimate question. Concepts are like anything that can be thought about, and thinking about x can come in the form of knowing x, imagining x, etc. I emphasize "like" because I don't want to get into whether or not concepts exist in a platonic sense.

For example, the concept of a circle might be formed by seeing, or imagining, or otherwise apprehending an image formed by a set of pixels in a circular arrangement, or it might be an algebraic equation of a circle expressed in some symbolic form, such as chalk on a blackboard and seen and recognized by the agent forming the concept. So the agent forming or gaining the concept, must have the ability to apprehend the pattern in the set of bits making up the information content of the concept.

I think you have a problem here, for the "pattern" in "x² + y² = r²" that talks about a circle is not inherent in the symbols. That is, you can't get semantics from syntax. What is important is not so much the pattern of information, but the interpretation of information.

I wanted to bring this up earlier, but I thought it would be too much at that point, but now it seems fitting. Interpretation is key to calling something information and calling something knowledge. And interpretation requires reflection that things like sensors, vacuums, retinae and mirrors aren't capable of.

I don't think I would have any problem using the term 'tendency' rather than 'ability'. I can't see that it makes any difference to what I am trying to get across.

"Ability" is too anthropomorphic. Experimental apparati, vacuums, retinae, mirrors, and pumps don't have knowledge, and don't have abilities yet they may have tendencies. If you can recognize the qualitative difference between human ability and the tendencies of a pump, then you can understand why I wouldn't ascribe knowledge to a pump or anything else on that list above.

I disagree. I think there is something important added by the notion of pattern. Pattern recognition is something beyond the simple apprehension of the bits. Think of those 3-D random dot pictures. There is quite a difference between seeing the detail of all the dots, and seeing the 3-D image that is present in the pattern.

It isn't so much pattern recognition that happens, it's more of just squinting your eyes. Squinting your eyes makes the differences in light apprehended by your retina unlike the differences apprehended when viewing the picture normally. It really is just the data that's changed, not the pattern interpretation.

I don't think it "totally trivializes" knowledge but it does greatly increase the domain of knowledge from nothing (IMHO) to accepting such things as a thermometer "knowing" the temperature.

Why do we want to do this? In order to avoid one extreme where we must say that nothing knows anything, because certainty is too harsh a criterion, we go to the other extreme and start saying that thermometers know the temperature? Why not just stay near the middle, where we more or less have always been, ascribing knowledge to conscious, reflective beings capable of forming beliefs when said beings have true beliefs which aren't just believed at random and turn out luckily to be true, but are believed for some reasons which need not be certain but must be, in some way, good enough. The debate then centers on what counts as "good enough".

----------

I think I'm getting a clearer overall picture of what you're doing here, and this is a relief to me. Some things I'm noticing:

It appears you're unhappy with correspondence theories of truth and foundational theories of knowledge, largely because you feel they fall victim to skepticism. As a result, you offer up "new" definitions. However, I suggest you look into coherentism and pragmatism with respect to both truth and knowledge, because it appears you'd be quite at home here. See here, here, and here.

In addition, you seem to be defining information, concept, knowledge, etc. in excessively anthropomorphic ways. It's clear to me know that you define them so that when the bimetallic strip bends so much that it triggers the sensor, we can say that the strip informed the sensor, and now it knows something. Indeed, non-traditional accounts of truth and knowledge exist without such extreme redefinitions, so I don't know if you're redefinitions are just a result of your reaction to traditional accounts, coming part and parcel with the philosophical beliefs you bundle into your definitions, or whether they have some separate inspiration, perhaps in order to prove machine knowledge or something like that. Do you realize that we can define knowledge such that despite not having certain knowledge, we can claim to know things like that the photon was transmitted, without having to define knowledge such that we must ascribe knolwedge to the photon? If so, then why are your definitions so over-encompassing? If not, well, I hope it's clear now.

 

[moving finger]

Hi again Paul

I made no such premise. I took the Receptive Principle as a primitive. Axioms are premises; primitives are simply undefined terms.

Then I need to ask you to define exactly what you mean by “a primitive” in this context. To me, a primitive (fact) is one which is assumed to be beyond question, and is distinguished from derivative (facts) which are those discovered as a result of the attempt to answer, about its primitive facts, the kind of questions that distinguish an enterprise of the sort called scientific or philosophical from enterprises of other sorts.

Primitives therefore take the form of premises in logical argument, whilst derivatives take the form of assertions derived (inferred) from the premises.

If a primitive is to you simply an undefined term, and that’s it, then I must question what is the meaning of the alleged primitive “Receptive Principle” – since without defining this term its meaning is at best ambiguous.

I don't know whether I agree or not. What do you mean by "Physicalism is false."?

A. Nothing physical exists.
B. Something exists which is not physical.
C. Something non-physical can effect the physical world.
D. ...?

I agree with B and C.

Physicalism is the thesis that everything (in the world of our perceptions) supervenes on the physical.
To say that physicalism is false is to say that not everything (in the world of our perceptions) supervenes on the physical.
I believe everything (in the world of our perceptions) supervenes on the physical, therefore I do not agree that physicalism is false.

(A) Is inconsistent with physicalism if we are to accept that “something exists”
(B) Is not necessarily saying physicalism is false. It is simply saying that something exists which is not physical, which would still be consistent with physicalism as long as that “something” supervenes on the physical.
(C) Is inconsistent with physicalism.

Thus in my philosophy, (B) could be (but is not necessarily) true, but (A) and (C) are not true.

(NOTE : I use the qualification "in the world of our senses" to distinguish the world we are talking about here from the Platonic world of forms. The perfect representation of Pi exists in the Platonic world, but this Platonic Pi obviously does not supervene on the physical - it exists independently of the physical - but it does not exist in the world of our senses).

Unless we disagree on the meaning of 'existence', it sounds like you agree with B. So your notion of "Physicalism is false" must be A, C, or D.

I hope I have clarified that above.

You may agree with Rosenberg that it is a mistake to rule out the possibility of non-physical existence in our world of the senses

As for me, you are putting words in my mouth.

With respect, I have done nothing of the sort. I said “you may agree…….” – I did not say that you do agree, or that you have claimed to agree, or that you must agree. In normal English usage, in this context, “may” denotes the permissive, in the sense “you are free to….”. How is that putting words in your mouth?

I think we might only disagree on the contents of that Platonic world, in the relative timing of a few physical events, and whether there is any causal connection between the physical and the non-physical.

That last part makes a world of difference to our positions.

If you mean that I agree with B or C above, you are correct. I agree with both.

and I agree with the possibility of B, but not with C

Even though our definitions of knowledge are different (I don't accept JTB), I still agree with everything you said here except for the "Not quite." (I think you were referring to my comment that knowledge is vacuous.) So I think our different definitions lead to essentially the same connotation. And, that is what I am trying to achieve.

That different definitions lead to similarities in connotation may be fortuitous, but does not imply we are both talking of the same thing when we each talk of knowledge. Indeed, if you reject the JTB definition we definitely are not talking of the same thing. How would you define knowledge (apart from apprehending bits according to Receptive Principles, which is all Greek to me)?

Knowledge is not vacuous. I, at least, know one thing. I know that thought happens. I think, although I don't know, that you might know the same fact. But, with that one exception, let's examine the conclusion and see if we can figure out whether it is true or not that knowledge is otherwise vacuous.

Unfortunately, there is little point in me arguing with you on issues of knowledge, since we define the word differently. How can we have a meaningful discourse on what is known and what is not known when the word does not mean to you what it means to me?

I think we agree that one can't know for sure that one knows anything.

Yes, this conclusion follows logically from the JTB definition of knowledge. But how do you arrive at this conclusion? (since you reject the JTB definition)?

But, could one could know something accidentally, i.e. without being sure about it? I don't think so because then you would be saying that a lucky guess amounts to knowledge.

Again, what do you mean by knowledge?
According to JTB, no. If one does not justifiably believe that X, then one cannot know that X (knowledge entails justified belief). But since I don’t know how you define knowledge, I have no idea why you think one could not know something accidentally. According to your RP definition, I just need to “apprehend bits” in order to claim knowledge – so why couldn’t I know something accidentally? Where in your definition of knowledge does it say that I cannot acquire knowledge by a lucky guess? (JTB certainly implies that a lucky guess is not knowledge).

On the other hand if the interpretations turn out to be useful in solving some human problems, then they would have value for some humans and that would make the enterprise worth pursuing. That's exactly what science has done for the past couple hundred years.

No, that’s what technology and applied science has done. Pure science is not about “what is useful for humans”, it is about trying to understand and comprehend the world.

I am interested in your view that there is no causal connection between the two worlds. As I think you know, I believe that there is causation in both directions. I think certain ideas influence our (human) actions, and I think certain (human) perceptions generate ideas and concepts which somehow end up in Plato's world.

Certain ideas do influence our actions, but those ideas are present in the physical world and supervene on the physical; and human perceptions do indeed generate ideas (which again supervene on the physical). There may be a “mapping” between ideas in the physical world and ideas in Plato’s world of forms, but I see no causal connection between these two worlds.

It would seem to me that if there were no interaction between the worlds, the ideas and concepts generated in human brains would be totally separate and distinct from those in the Platonic world and there would be no way, even in principle, to compare them.

Correct.

In the other direction, it would seem that regardless of what forms, ideas, or concepts might be in Plato's world, they could have no influence on the ideas or thoughts which might go on in human brains. So, based on this, I don't see why you think a Platonic world exists. Why do you?

In your sense of exists, it probably does not exist, because it has no causal connection at all with our world. It exists in my sense of exists because certain rules of logic and mathematics are true regardless of human thought. The value of Pi is what it is regardless of whether man thinks about Pi or not, and regardless of the existence of, or the natural laws of, our physical world. Thus in a very real sense this value of Pi exists, always will exist, and has always existed, quite independently of our physical world. Of course I know you disagree – but that’s your choice.

Best Regards

 

[moving finger]

1. I know X.
2. I believe X.
3. I believe I know X.
4. I think I know X.
5. I possesses information that indicates X.

IMHO, 1. is always a false claim. 2. and 3. are of no use to anyone else. 4. may be true, but it is useless to anyone else. 5. may be useful to others if the information can be shared. It is for these reasons I propose that knowledge be defined as the possession of information.

Paul

Something is seriously wrong with your logic.

If (as you claim) knowledge is defined as the possession of information, and (1) is (as you claim) always false, this implies that I can never possesses information. How is this meaningful?

Further, if (1) is always false, and if (4) is true, it follows that what I think is false.

Best Regards

 

[Paul Martin]

Hi AKG,

I think I'm getting a clearer overall picture of what you're doing here, and this is a relief to me.

Good! And it is a great relief to me. In fact it is almost exhilarating. Your discussions, along with MF's, have helped me see how my ideas and my motives for my proposal relate to traditional ideas, of which I am woefully ignorant. Although I know how to swim, I feel as if I am in very deep water. I apologize for being such a slow student in catching on to my first exposure to such concepts as JTB, Gettier problems, pragmatism, and coherentism. But I guess you are here to teach, and I am definitely here to learn, so there may be no harm done.

As for the overall picture of what I'm doing here, I still have a few cards to lay on the table. It is probably the right time to come clean.

Over the course of my lifetime, I have formed an opinion about what is going on in reality. It all makes sense to me because my major, if not my only, criterion for acceptance of particular features in my model of reality is that they make sense to me. (To the extent that anyone is interested in my model, I am willing to explain it. I have made a few such attempts in PF. Readers familiar with my notion of "PC" will know part of what is in my model.)

In thinking about what I have learned in this thread so far, it occurs to me that what might set me apart from other thinkers is my different view of various mysteries. I think that my ranking of what I think are the most profound mysteries would differ significantly from other people's rankings. Maybe by listing some of those mysteries and explaining why I find them so interesting I can shed some light on my motivation for taking the approach to redefining terms that I did. Here they are:

1. My uniqueness. - It is very hard for me to articulate exactly what this mystery is to me, but it goes something like this: How can it be that my conscious experience is constrained to this tiny interval in such a vast expanse of time and to this tiny locality on this blue speck at the edge of the Milky Way which seems insignificant itself in the vastness of space? I think most people would brush this off and tell me, "Well, dummy, it's because that's where you happen to be. What's the mystery?" That doesn't satisfy me. What exactly is this thing you refer to as "you"?

2. The phenomenon of sleep. - There are two mysteries here, one more important to me than the other. The first is, How can we account for the fact that virtually all individual animals, of nearly all species, and nearly each and every day each one lives, and for a significant percentage of each day's duration, and for no plausible reason, and at significant risk to survival in most of these cases of sleep events (which IMHO should present nearly fatal blows to the theories of evolution), routinely, willingly, and even eagerly, lose consciousness? The second, and IMHO less important, mystery is, Why is it that in the face of the foregoing profound mystery, and the fact that we humans are among the vast majority of animals who sleep, and the inconvenience caused by sleep cutting into our work/play time, and the cost of furnishing bedrooms, and the in-your-face obvious necessity for sleep, do people take it so for granted and hardly question it or wonder about it? (This includes scientists who IMHO only dabble with the question.)

3. Contradictory notions of time. - We have two common notions of time: Our conscious experience of time (the subjective notion) and the parametric notion of time in physical theories (the objective notion). The mystery is, How can we account for the following contradictions between the two notions?:

a. The inescapable division of subjective time into past, present, and future do not appear and has no place in objective time.
b. The inescapable notion of 'now' in subjective time is not, and logically cannot be, defined for objective time.
c. The "arrow of time" which is so obvious in subjective time, hardly appears (except for the contrivance of the 2nd Law) in objective time. In most cases, the direction of objective time is reversible.

4. The seemingly narrow scope of consciousness. - How do we account for the seemingly improbable, but seemingly obvious, fact that conscious awareness is situated only in a small range in size (on the order of a meter) and not at all at the scale of intergalactic space or of subatomic particles?

Now let me try to very briefly summarize my personal model of reality. You can probably figure out how these mysteries played in the development of my model.

I think there is only and exactly one conscious entity in all reality (I have called it 'PC' for "Primordial Consciousness" but it probably should stand for "Primary Consciousness" since the universe is no longer in a primordial state and PC is still the only active conscious agent.) PC could be thought of as a mind, and as Gregory Bateson has speculated, the universe would then be nothing but PC and PC's thoughts (=concepts or ideas). The physical universe (that which is accessible to human bodies and instruments) is a structure composed of PC's thoughts (sort of as Berkeley proposed). Spatial dimensions are nothing but parameters involved in the algorithms which determine the behavior and evolution of the individual components of the physical universe. Temporal dimensions are nothing but parameters determining the position along the various world lines within the spatial structure of the physical universe at which position PC is exchanging information with components of the physical universe. (From PC's vicarious perspective from the brain of a human, the same parameter which appears to be temporal, would appear to be spatial from PC's perspective when not attending to a physical world line.) The exchange of information is both ways: PC accesses information from components in the physical universe at that point of space and time via such things as human eyes, human brain activity, etc. In the other direction, PC expresses certain intentions (exercises free will) by directly influencing the evolution of certain physical structures staying under the HUP and thereby not interfering with the operation of the algorithm (the laws of physics).

An even shorter summary is that "PC drives each living organism just as you drive each of the cars that you own."

Now, IMHO, this scenario satisfactorily explains all the above mysteries as well as all other mysteries I know of, including the mystery of quantum state reduction, quantum non-locality, Bell's inequality, the origin of life, the origin of consciousness, the meaning of life, the prevalence of all the goofy religious notions, etc., etc., etc.

Now, with these cards face up on the table, you might have a better idea of what motivates me. After reading the material which you suggested, and which I greatly appreciate, I can tell you that Pragmatism is not satisfactory to me. If "truth is the end of inquiry", exactly who or what is doing the inquiry? Leaving the "agent" unspecified is like ignoring the elephant in the room, IMHO. In my scheme, the agent is, of course, PC. And PC, being far from omniscient or omnipotent, does a lot of inquiring and most times gets it wrong.

Similarly, if "truth is satisfactory to believe", to whom or what is it satisfactory? In my scheme, of course, it can only be PC.

Coherentism is also unsatisfactory to me. "A seaworthy ship at sea" would imply a separate ship for each believer and no account of the sea itself. My scheme accounts for all of it and explains how each of these ships seems to be independent.

In reading the references you gave, I ran across a description of Tarski's theory of truth. Now that one I could buy into. He takes the logico-mathematical approach and ties truth to language, as I told you I prefer. I have a strong hunch that some intellectual giant, like Tarski or Goedel (providing they are still alive and willing) could take an approach along the lines I have been suggesting and develop a foundational theory which could provide the details to support the high-level hunches which have so far satisfied me. My hope is that the next Goedel or Schroedinger might be browsing this thread and get an inspiration to pursue my proposal.

I'm running short of time so I'll close this off now. If you are so inclined, we can resume our discussion later and I can address some of your detailed questions. Thank you once more for your thoughts, your energy, and your patience.

Warm regards,

Paul

 

[moving finger]

Hi Paul

IMHO, this scenario satisfactorily explains all the above mysteries as well as all other mysteries I know of

.
Explaining consciousness turns out to be a trivial exercise if one posits a primordial consciousness which is itself beyond explanation or investigation, but which in turn generates all other instances of consciousness. This is, with all due respect, not "starting at the beginning", it is assuming some things are beyond the beginning, hence beyond explanation.

One can explain any property of the world one wishes by positing that this property is somehow primordial and beyond explanation or investigation. Examples : "What is intelligence and how did it arise on earth? Oh, it didn't arise, it's just an instance of the continued existence of primordial intelligence in the universe, which has always existed". "How did living beings arise on earth? Oh, they didn't arise on earth, we are all just instances of the continued existence of life in the universe, which has always existed". "What is the soul (if such a thing exists), and how does it arise? Oh, the soul does not arise..." (I think you get the idea)

(The above "explanation" for the existence of life is not so far-fetched - this is one of the ID arguments!). You may consider such a thing qualifies as an "explanation" of mystery, but I don't.

In my last post I asked how does one arrive at the alleged conclusion that “one cannot know for sure that one knows anything”, if one rejects the JTB definition and defines knowledge simply as “apprehending bits according to the receptive principle”? I also asked how one arrives at the alleged conclusion (based on the same definition) that one cannot know something accidentally? If you believe that your scenario “satisfactorily explains…. all….. mysteries” as you claim, then you should have no trouble explaining how you arrive at these conclusions about knowledge?

Best Regards

 

[Paul Martin]

Hi MF,

Sorry it has taken so long for me to respond to you.

Then I need to ask you to define exactly what you mean by “a primitive” in this context. To me, a primitive (fact) is one which is assumed to be beyond question, and is distinguished from derivative (facts) which are those discovered as a result of the attempt to answer, about its primitive facts, the kind of questions that distinguish an enterprise of the sort called scientific or philosophical from enterprises of other sorts.

Primitives therefore take the form of premises in logical argument, whilst derivatives take the form of assertions derived (inferred) from the premises.

I was using the term 'primitive' in the mathematical sense of an undefined term. In this sense, what you called a "fact...which is assumed to be beyond question" is an axiom. (Prior to a hundred years or so ago, axioms were assumed to be obviously true while postulates were taken to be arbitrary assumptions. Nowadays axioms are what postulates used to be so the two terms are interchangeable.) What you called "derivatives" are theorems.

I am proposing an approach that is more mathematical than scientific. While I agree that the scientific approach has been unparalleled in its explanations for physical phenomena, I think a mathematical approach might open up some new possibilities in areas where science has provided no explanation, or where the explanations are incomplete or otherwise unsatisfactory. I know you disagree, but IMHO science has not satisfactorily explained consciousness and related phenomena like sleep. Keep in mind that new mathematical systems were required for the scientific breakthroughs of Newton and Einstein so maybe it can work here.

If a primitive is to you simply an undefined term, and that’s it, then I must question what is the meaning of the alleged primitive “Receptive Principle” – since without defining this term its meaning is at best ambiguous.

The nature of all primitives is that they are ambiguous. In a strange way, this is part of their power because it means that any mathematical system logically built on them applies to anything which can be consistently interpreted to be instances or models of the primitives, whether imagined ahead of time or not.

Physicalism is the thesis that everything (in the world of our perceptions) supervenes on the physical.

Please forgive my ignorance, but I am not comfortable using the word 'supervenience'. I don't quite know what it means. When I read Chalmers' "The Conscious Mind", I was sort of forced to learn what it meant in order to understand what he was saying. But, alas, I didn't learn it well enough for it to become a household word for me. Please be patient with me as I work my way back through it.

On page 39 Chalmers states what he calls a "revised definition" as, "B-properties are logically supervenient on A-properties if the B-properties in our world are logically determined on the A-properties in the following sense: in any possible world with the same A-facts, the same B-facts will hold."

Using that to interpret your definition of 'physicalism', we would have "everything (in the world of our perceptions) as the B-properties, and with "the physical" being the A-properties. Therefore, by definition, everything ( in the world of our perceptions) is logically determined on (by) the physical such that in any possible world with the same physical facts, the same phenomena will hold.

I disagree with this conclusion about our physical world. I'll try to explain why, but before I do, let me point out what I think are two basic disagreements between you and me.

The first is that I think that there is something non-physical going on in human consciousness and I think you do not agree. The second is that I think there is some transcendent part of reality which is not just the Platonic world of ideas, which you seem to acknowledge, but which, like our familiar physicality, also has structures with extension and duration. In other words, I think there are higher dimensions of physical reality which are inaccessible to us, and I don't think you do.

I don't think we can easily resolve our disagreement about whether consciousness involves something that transcends our physical world, so I won't try here. But I want to explain why I disagree with the proposition that everything in the world of our perceptions is logically determined by the physical. I'll use my well-worn radio analogy.

Suppose there were an undiscovered (by the people we know) continent in the Pacific Ocean whose inhabitants were extremely advanced in Chemistry but totally ignorant of electronics and electricity. Maybe they had evolved nanoscopic vision and had developed nanotechnology to a high degree, but, however they accomplished it, let's say that they could completely analyze any complex chemical sample, and not only that, they could completely reproduce it atom for atom.

Now, let's suppose that by some accident, one of our radios fell into their possession. They turned it on and discovered that it played music. (The signals from our radio stations could reach that continent.) Their scientists would try to understand where that music came from. The chemists among them would claim that it had to be purely physical, that is, it must be generated completely within the chemical structures of the radio itself. As a test, someone suggested reproducing the radio exactly atom for atom to see if the duplicate also played music. They did, and it did, so they concluded that the music must have come strictly from the physical arrangements and patterns and functions of the atoms in the radio. Of course, we know that is wrong.

I claim that there is a possibility that the same sort of thing holds true for the relationship between consciousness and brains. I think that if we could construct a duplicate brain, atom for atom, it might be just as conscious as the original. But just as in the case of the radio, it wouldn't prove that there wasn't something outside our physical world that is necessary for consciousness.

Physicalism is the thesis that everything (in the world of our perceptions) supervenes on the physical.
To say that physicalism is false is to say that not everything (in the world of our perceptions) supervenes on the physical.
I believe everything (in the world of our perceptions) supervenes on the physical, therefore I do not agree that physicalism is false.

I respectfully disagree and claim that consciousness does not supervene on the physical world of our perceptions. I would agree if we extended the notion of "physical" to include additional spatio-temporal dimensions.

With respect, I have done nothing of the sort. I said “you may agree…….” – I did not say that you do agree, or that you have claimed to agree, or that you must agree. In normal English usage, in this context, “may” denotes the permissive, in the sense “you are free to….”. How is that putting words in your mouth?

It's not. I am sorry. That was a sloppy mistake on my part. I must have been in a hurry, but that's no excuse.

That different definitions lead to similarities in connotation may be fortuitous, but does not imply we are both talking of the same thing when we each talk

I agree. And I think you would agree that the fortune doesn't accrue unless and until the hard work has been done to actually demonstrate those similarities. I am in no position to do that yet.

Indeed, if you reject the JTB definition we definitely are not talking of the same thing.

At least it definitely seems that way now.

How would you define knowledge (apart from apprehending bits according to Receptive Principles, which is all Greek to me)?

First, I would define 'information' as sets of bits. This is the same as in classical information theory so I don't think that part is Greek to you. If it is, let me know.

Next, I would define 'knowledge' as information that is gained, or acquired, or apprehended, by some knower where the process of gaining, acquiring, etc. is defined as 'learning' and the more-or-less steady state condition of holding or owning that knowledge is defined as 'knowing'. (If the information were somehow lost, that would be defined as 'forgetting'.) A 'knower' is some agent or entity which has the ability, or the capability, or the tendency, or the power, (or choose some other word if you prefer) to use that knowledge (i.e. the gained information) in some way. By 'use' I mean that the knowledge can effect the time evolution of the knower's environment.

The reason I reject JTB is that it is too anthropomorphic. By that definition, knowledge is a belief, held by a conscious human being, that is true and that is justified by that conscious human being. It is that conscious human being that I see as the undefined elephant in the room. In my definition, the 'knower' might be a human being but also might not be. The term 'conscious human being' doesn't play a part in my definition. On the other hand, if you take the knower to be a conscious human being, then I don't think my definition differs much from yours in terms of the actual information we would consider to be knowledge.

Unfortunately, there is little point in me arguing with you on issues of knowledge, since we define the word differently.

I don't think it is unfortunate. I don't think there is much point in arguing for any reason. I'd rather spend the energy in trying to understand one another.

How can we have a meaningful discourse on what is known and what is not known when the word does not mean to you what it means to me?

In the same way mathematicians do. Rather than argue about different definitions, the mathematical approach is to tentatively accept the definitions of someone whose ideas you are trying to understand. And, when presenting your own ideas, make sure to clearly define them so that others may understand your ideas the way you intended. In this way, the implications of different definitions can be explored without rancor.

I think we agree that one can't know for sure that one knows anything.

Yes, this conclusion follows logically from the JTB definition of knowledge. But how do you arrive at this conclusion? (since you reject the JTB definition)?

I'm not sure what you are asking. If you are asking how I personally came to the opinion that one can't know for sure that one knows anything, that's one case. But if you are asking me how my definition of knowledge formally and logically implies the conclusion that a knower can't know anything for sure, then that's another case.

In the first case, it came to me gradually as the result of applying Descartes' challenge of finding some proposition which was impossible to reasonably doubt. I came to the conclusion that "Thought happens" is the only such proposition, and which I still consider to be the single exception.

In the second case, using my definition, I don't know how it logically follows. I also don't see how it logically follows from the JTB definition. Maybe if you explained how it follows from JTB I could form an opinion on whether it follows from my definition, and if so, maybe show how.

But, could one could know something accidentally, i.e. without being sure about it? I don't think so because then you would be saying that a lucky guess amounts to knowledge.

According to JTB, no. If one does not justifiably believe that X, then one cannot know that X (knowledge entails justified belief). But since I don’t know how you define knowledge, I have no idea why you think one could not know something accidentally.

Sorry, I didn't make myself clear. I was using your definition of knowledge and asking about your point of view. From what I read about the Gettier problems, it seemed that the JTB definition didn't allow accidental knowledge.

According to your RP definition, I just need to “apprehend bits” in order to claim knowledge – so why couldn’t I know something accidentally? Where in your definition of knowledge does it say that I cannot acquire knowledge by a lucky guess? (JTB certainly implies that a lucky guess is not knowledge).

You are right. With my definition, knowledge can be gained by accidentally stumbling onto it.

No, that’s what technology and applied science has done. Pure science is not about “what is useful for humans”, it is about trying to understand and comprehend the world.

True. But applied science and technology not only draw deeply from what pure science has discovered, but they largely fund the effort as well.

Certain ideas do influence our actions, but those ideas are present in the physical world and supervene on the physical; and human perceptions do indeed generate ideas (which again supervene on the physical). There may be a “mapping” between ideas in the physical world and ideas in Plato’s world of forms, but I see no causal connection between these two worlds.

Here it sounds as if you have introduced yet another world. In addition to the physical world and Plato's world of forms, which does not supervene on the physical, you have introduced a world of ideas, separate and distinct from Plato's, which does supervene on the physical.

You can confirm or deny this, but I suppose that the ideas in that third world exist in patterns of brain states of various people, and/or in patterns of ink in books, patterns of bits in computers, or in patterns in some other physical medium.

Now if there is no causal connection between Plato's world and either of the other two worlds, why do you think Plato's world even exists? Doesn't that run afoul of Occam? What makes you think that there is an infinite expansion of the digits of Pi in Plato's world if it can't and doesn't influence any of the ideas in the third world? And, since thinkers who contribute ideas into that third world can't interject anything into Plato's world, that expansion of Pi must have been in there forever, even prior to the Big Bang. Doesn't that seem a little excessive?

Now as to whether there might be a "mapping" between elements of Plato's world and your third world, we would have to wonder "where" that mapping is. Since it is a concept, it must either be in Plato's world, or your third world, or Heaven forbid, in yet a fourth world.

Suppose there is such a "mapping" somewhere. We could reasonably expect there to be a mapping between that infinite expansion of Pi in Plato's world, and one of our finite expansions, say the one that only goes out a trillion digits. Would that particular correspondence have existed prior to the Big Bang? Or prior to the actual computer generation of the finite expansion? If yes, then that Platonic realm has some potent predictive power. If not, then it would seem that events in the physical world in conjunction with your third world do indeed influence Plato's world. It seems like it might be best to conclude that such a "mapping" doesn't exist, and let Plato's world float free and succumb to Occam's Razor.

In your sense of exists, it probably does not exist, because it has no causal connection at all with our world. It exists in my sense of exists because certain rules of logic and mathematics are true regardless of human thought. The value of Pi is what it is regardless of whether man thinks about Pi or not, and regardless of the existence of, or the natural laws of, our physical world. Thus in a very real sense this value of Pi exists, always will exist, and has always existed, quite independently of our physical world. Of course I know you disagree – but that’s your choice.

Yes, I do disagree. However I think our disagreement here stems not from our different notions of 'exist' but from our different notions of 'true'. With respect, I think you are mixing up two different notions of 'truth'. One is the correspondence with reality and the other is the tautological truth of mathematics and logic. If we take the former to be the "real sense" of truth, then the putative value of Pi may not exist in the real sense. Here's why.

The value of Pi is deduced from Euclidean geometry in which we have circles and their diameters in a plane. The definition of a Euclidean plane involves the definition of the Euclidean metric which is then used to derive the value of Pi. The end result is a complex tautology which tells us no more about reality than the statement, A = A.

As you know, if the Euclidean metric does not apply, as it does not on the surface of a sphere for example, then the ratio of a circle's circumference to its diameter will not give the customary value for Pi. (In the example, the diameters of the circle will be arcs of great circles of the sphere instead of being "straight" lines.) Since the metric of at least our physical world does not appear to be Euclidean, the value of Pi may not have its tautological value in reality.

As always, it's been good talking with you, MF

Warm regards,

Paul

 

[Paul Martin]

Hi again, MF

1. I know X.
2. I believe X.
3. I believe I know X.
4. I think I know X.
5. I possesses information that indicates X.

IMHO, 1. is always a false claim. 2. and 3. are of no use to anyone else. 4. may be true, but it is useless to anyone else. 5. may be useful to others if the information can be shared. It is for these reasons I propose that knowledge be defined as the possession of information.

Something is seriously wrong with your logic.

If (as you claim) knowledge is defined as the possession of information, and (1) is (as you claim) always false, this implies that I can never possesses information. How is this meaningful?

Once again, I apologize for not being clear. In my numbered statements I intended to use the JTB, or any other commonly used definitions for 'know', 'believe', 'think', etc. My point was that the first four statements, using conventional definitions, didn't seem to be very useful to me. Number 5, which also uses commonly used terms, with commonly understood definitions, seems to be useful. So it seems to provide a reason for preferring a definition of 'knowledge' along the lines I have been suggesting.

Explaining consciousness turns out to be a trivial exercise if one posits a primordial consciousness which is itself beyond explanation or investigation, but which in turn generates all other instances of consciousness.

I don't think it is trivial, but I do think it greatly simplifies the explanation of consciousness. I think that commends it as a choice.

This is, with all due respect, not "starting at the beginning", it is assuming some things are beyond the beginning, hence beyond explanation

Yes. I probably should have said "starting as near the beginning as we can". As you have frequently said, we have to start with some assumptions, and that is what I have done. You have also said that we have no way of knowing whether those assumptions are correct or not, and I agree. But I think that mathematics has shown that it can be useful to posit some assumptions which we can't know are correct or not, and see what we can deduce from them. That is what I am suggesting that some smart people do.

One can explain any property of the world one wishes by positing that this property is somehow primordial and beyond explanation or investigation. Examples : "What is intelligence and how did it arise on earth? Oh, it didn't arise, it's just an instance of the continued existence of primordial intelligence in the universe, which has always existed". "How did living beings arise on earth? Oh, they didn't arise on earth, we are all just instances of the continued existence of life in the universe, which has always existed". "What is the soul (if such a thing exists), and how does it arise? Oh, the soul does not arise..." (I think you get the idea)

Yes, I get the idea. But I still don't think you have quite gotten my idea. Intelligence, life, and whatever people mean by 'soul', are extremely complex entities or ideas and I am sure you agree with me that positing such a primordial complexity is not reasonable. You keep accusing me of positing the complexities of consciousness as primordial (undoubtedly because of my unfortunate choice of the 'PC' label) and I keep insisting that whatever was primordial was extremely rudimentary and simple, like nothing but the ability to acquire bits and with no bits around to acquire. But, I'm getting blue in the face.

As I tried to explain, mathematicians have shown us that if you choose the right definitions, even though they might be a little more abstruse and complex than customary definitions, they can lead to profoundly simpler implications for very powerful concepts. That's the paradigm I'm suggesting that someone follow.

(The above "explanation" for the existence of life is not so far-fetched - this is one of the ID arguments!). You may consider such a thing qualifies as an "explanation" of mystery, but I don't.

No, I am inclined to accept cosmological explanations only if they have extremely simple beginnings.

In my last post I asked how does one arrive at the alleged conclusion that “one cannot know for sure that one knows anything”, if one rejects the JTB definition and defines knowledge simply as “apprehending bits according to the receptive principle”?

I addressed this earlier. Sorry it took me so long to reply.

I also asked how one arrives at the alleged conclusion (based on the same definition) that one cannot know something accidentally? If you believe that your scenario “satisfactorily explains…. all….. mysteries” as you claim, then you should have no trouble explaining how you arrive at these conclusions about knowledge?

As I see it, whether one can know something accidentally is simply a matter of definition. I see no mystery in it. And, as I said, according to my proposed definition, accidental knowledge is possible, and I'd say it is very common. I'm surprised you didn't ask me about some real mysteries. You asked me once about sleep but you didn't comment much on my explanation. I guess different things mystify different people. How about, "Different mystification for different sophistication." to replace "Different strokes for different folks."? I'm starting to get giddy. I'd better quit.

As always, it's been good talking with you, MF

Warm regards,

Paul

 

[moving finger]

Hi Paul

I know you disagree, but IMHO science has not satisfactorily explained consciousness and related phenomena like sleep.

Yes, you know I disagree. I can explain consciousness and sleep based on a scientific, physicalist approach (whilst accepting that not all properties of the world are necessarily accessible from a 3rd person perspective). That you personally do not accept this explanation because it does not fit with your personal beliefs about consciousness does not lead to the conclusion that science cannot satisfactorily explain consciousness or sleep.

It doesn’t matter whether you call your primitives mathematical or scientific, at the end of the day they are assumed by you to be true. I am simply challenging your assumption that the Receptive Principle is true. Just as I may challenge the parallel postulate in geometry.

The nature of all primitives is that they are ambiguous.

Are you saying that you cannot offer any definition or meaningful interpretation of this thing you call the Receptive Principle? And you expect me to understand what you are talking about?

Using that to interpret ... the same phenomena will hold.

Yes, this is how I undertand “supervenience”.

The first is that I think that there is something non-physical going on in human consciousness and I think you do not agree.

Physicalism does not say that everything is physical (only that whatever those non-physical things might be, they supervene on the physical). Hence your belief that there is something non-physical going on in human consciousness is not inconsistent with the thesis of physicalism.

The second is that I think there is some transcendent part of reality which is not just the Platonic world of ideas, which you seem to acknowledge, but which, like our familiar physicality, also has structures with extension and duration. In other words, I think there are higher dimensions of physical reality which are inaccessible to us, and I don't think you do.

You have introduced a number of new terms into the discussion. Whether I think there are such other dimensions depends on what you mean by (a) transcendent part of reality (b) inaccessible to us and (c) higher dimension of physical reality. As you may have noticed from other threads in this forum, I do not believe that all properties of the world are necessarily accessible from the 3rd person perspective, for example. There is no way that moving finger (or anyone else) can have the same conscious experience (have access to exactly the same properties of phenomenal consciousness) that Paul Martin has access to, for example. Your phenomenal consciousness is accessible to you and you alone, by definition. In one sense this could be looked upon as a “higher” (I prefer to use the word different) dimension of physical reality.

But once again, the premise that there are other dimensions of physical reality is not inconsistent with the thesis of physicalism. To recap, physicalism does not say that everything in the world is physical, it also does not say that everything in the world is accessible from any particular perspective.

Hence thus far I do not understand why you say that you disagree with the thesis of physicalism – you have not so far provided a logical argument with a sound conclusion to the effect “these premises and inferences lead to the conclusion that physicalism is false”.

I claim that there is a possibility that the same sort of thing holds true for the relationship between consciousness and brains. I think that if we could construct a duplicate brain, atom for atom, it might be just as conscious as the original. But just as in the case of the radio, it wouldn't prove that there wasn't something outside our physical world that is necessary for consciousness.

Sorry, Paul, but this is argument is scientifically worthless. Absolutely no experiment can prove that there is no “inaccessible other dimension” which somehow non-physically determines or causes things in our dimension but which is completely inaccessible to us. The premise that there is such a dimension is thus a non-scientific premise, it is impossible to prove the premise false even if it is false. It’s rather like me suggesting that consciousness is caused by invisible fairies who live at the bottom of my garden, who sprinkle 7th-dimensional consciousness-dust over us while we sleep. Can you disprove that premise? No, of course you can’t, it’s impossible to disprove it.

In other words, if we are so inclined we can construct an unlimited number of different "theories" of the world using unscientific premises, each theory would agree with observation and none of them could be disproven. Whether one believes one of these theories in preference to another one of these theories is then a purely personal subjective judgement, a matter of faith, and beyond any means of rational, mathematical, philosophical, scientific or logical enquiry.

I respectfully disagree and claim that consciousness does not supervene on the physical world of our perceptions.

I understand that, but your claim is based on your personal subjective beliefs about how you want conscious to work, beliefs which are unverifiable either scientifically, rationally, logically or mathematically.

I would agree if we extended the notion of "physical" to include additional spatio-temporal dimensions.

Then I don’t understand why you think physicalism false. Physicalism does not say that the world is restricted to any particular spatio-temporal dimensions. You’ll need to elaborate.

First, I would define 'information' as sets of bits. This is the same as in classical information theory so I don't think that part is Greek to you. If it is, let me know.

Any “set of bits” (including a random set) qualifies as “information”?

Next, I would define 'knowledge' ... knower's environment.

Thus in your definition, knowledge does not entail either belief or truth?
Let X be a “knower” as defined by you, and let Y be a proposition about the world, which proposition is either true or false.
"X knows that Y" simply means (according to you) that X has apprehended some bits?
According to your definition, X can correctly claim to possesses knowledge that Y, even if X does not believe that Y, or even worse if X believes that ~Y? (ie Y is false)
According to your definition, X can correctly claim to possesses knowledge that Y, even if ~Y? (ie Y is false).

The reason I reject JTB is that it is too anthropomorphic. By that definition, knowledge is a belief, held by a conscious human being, that is true and that is justified by that conscious human being.

You seem to be making false assumptions. Knowledge is not defined in JTB in terms of “human beings”, it is defined in terms of an agent (your “knower” if you like) which is able to form beliefs about the world. Thus the JTB definition is no more anthropomorphic than your own definition (you posit the existence of a “knower” in order to have knowledge). The agent may be human, it may be an animal, it may be a machine. Knowledge does not exist except as a consequence of justified true beliefs, and only an agent able to form beliefs can claim to have justified beliefs.

The term 'conscious human being' doesn't play a part in my definition.

It doesn’t play a part in the JTB definition either, hence I cannot see what your objection is.

On the other hand, if you take the knower to be a conscious human being, then I don't think my definition differs much from yours in terms of the actual information we would consider to be knowledge.

Your definition seems to imply that one can know things which one does not believe, and even worse that one can know things which are false. Would you agree?

In the first case, it came to me gradually as the result of applying Descartes' challenge of finding some proposition which was impossible to reasonably doubt. I came to the conclusion that "Thought happens" is the only such proposition, and which I still consider to be the single exception.

Your definition entails that knowledge is simply the process of apprehending bits by a knower, there is no reference to the truth of a proposition, or necessity of truth of a proposition, in your definition. If a “knower apprehends bits” it follows necessarily that it possesses knowledge (ie it knows) according to your definition. There is no sense (from your definition) in which it makes any difference whether the information it knows represents either a true or false proposition; it simply knows, by definition, if it has apprehended bits. In what sense can you then claim that the knower “can’t know for sure” that it knows? Are you suggesting it might be mistaken in believing that it has indeed apprehended bits (but how can you, since according to you a knower need not have any beliefs)?

In the second case, using my definition, I don't know how it logically follows. I also don't see how it logically follows from the JTB definition. Maybe if you explained how it follows from JTB I could form an opinion on whether it follows from my definition, and if so, maybe show how.

By the JTB definition, I cannot 'know that X" if X is false (because knowledge entails truth), I also cannot know that X if I am not evidentially justified in believing that X (becasue knowledge entails justified belief). There is no rigorous way to prove that X is true except via an argument containing premises, and if those premises cannot be proven true then it follows that X may be false. If X may be false then any claim I have to know that X may also be false. Hence, claims to knowledge are fallible.

With my definition, knowledge can be gained by accidentally stumbling onto it.

Thus, you claim that a lucky guess amounts to knowledge?
If you guess the winning lottery number before the draw, are you saying that you knew before the draw what the winning lottery number would be?
I don’t think this is what most people mean by knowledge, hence again you are in danger of developing your own private language which has no relationship to the language used by everyone else.

Here it sounds as if you have introduced yet another world. In addition to the physical world and Plato's world of forms, which does not supervene on the physical, you have introduced a world of ideas, separate and distinct from Plato's, which does supervene on the physical.

This is not a separate world. I have never claimed that everything in the world of the senses is physical, only that everything in this world supervenes on the physical. There is a difference.

You can confirm or deny this, but I suppose that the ideas in that third world exist in patterns of brain states of various people, and/or in patterns of ink in books, patterns of bits in computers, or in patterns in some other physical medium.

It’s not a third world. It is part of the world of the senses.

why do you think Plato's world even exists? Doesn't that run afoul of Occam?

No, because Plato’s world has no explanatory purpose and can be quite easily discarded without affecting my understanding of the world of the senses in any way. From the perrspective of the world of the senses, it is simply a philosophical convenience to say that Plato’s world of forms exists, I don’t need to assume it exists in order to explain anything about the world of our senses. Occam’s razor applies to multiplying fundamental entities without cause, and Plato’s world of forms is not a fundamental entity as far as the world of the senses is concerned, simply because there is no causal connection.

What makes you think that there is an infinite expansion of the digits of Pi in Plato's world if it can't and doesn't influence any of the ideas in the third world?

What logical reason would there be for thinking that Pi does not have an infinite expansion?

that expansion of Pi must have been in there forever, even prior to the Big Bang. Doesn't that seem a little excessive?

Plato’s world does not have any physical attributes such as spacetime, so the question is meaningless.

We could reasonably expect there to be a mapping between that infinite expansion of Pi in Plato's world, and one of our finite expansions, say the one that only goes out a trillion digits. Would that particular correspondence have existed prior to the Big Bang?

At what point in time are you suggesting that this particular finite expansion of ours is generated in the world of the senses?

Or prior to the actual computer generation of the finite expansion? If yes, then that Platonic realm has some potent predictive power.

Indeed it does have predictive power, if we could tap into it (which we cannot) in the sense that all logical possibilities exist in Plato’s world..

If not, then it would seem that events in the physical world in conjunction with your third world do indeed influence Plato's world. It seems like it might be best to conclude that such a "mapping" doesn't exist, and let Plato's world float free and succumb to Occam's Razor.

There is no third world, as explained above. Also as explained above, since there is no causal connection between Plato’s world and the world of the senses you are quite free to cut it loose if you so desire, it makes no difference to anything in the world of the senses. It is purely a personal philsophical convenience on my part to assume that it exists. Whether you cut it free or not makes absolutely no difference to anything I have said about the world of our senses, so I fail to see why we are wasting time arguing this point unless it is simply an intellectual exercise on your part.

The value of Pi is deduced from Euclidean geometry in which we have circles and their diameters in a plane. The definition of a Euclidean plane involves the definition of the Euclidean metric which is then used to derive the value of Pi. The end result is a complex tautology which tells us no more about reality than the statement, A = A.

Pi may be defined via a number of different mathematical formulae, in which case it is a very definite and unique real number. It makes no diference whether one calls such a definition tautological or not, the fact is that using the definition leads to a very definite and unique real number. Correspondence with (physical) reality is irrelevant in this context, we are talking pure maths. In my view, the number represented by Pi exists (in Plato’s world of forms) independently of human thought about the number. I know you disagree, but it has nothing to do either with correspondence with reality or tautology.

1. I know X.
2. I believe X.
3. I believe I know X.
4. I think I know X.
5. I possesses information that indicates X.

My point was that the first four statements, using conventional definitions, didn't seem to be very useful to me.

Your original claim was that (2) and (3) are of no use to anyone else, not that they are of no use to you. Perhaps they don’t seem useful to you because your analysis in terms of JTB is flawed.
Using JTB,
(1) May be either true or false (it is not always false as you claim)
(2) May be true or false (if it is false then I cannot know that X)
(3) May be true or false (but if one does not believe that one knows that X, I don’t see how one can simultaneously claim that one knows that X)
(4) Is a variation of (3), depending on how one defines “think”
(5) May be either true or false (if it is false then it is hard to see how one can justify a belief that X, in which case one could not claim to know that X)

When it comes to "usefulness", your definition of knowledge in terms of apprehending bits doesn't seem very useful to me.
If an agent apprehends bits, it possesses knowledge according to your definition. Knowledge about what? About bits of course. And how is this useful? Do those bits correspond to any true or false proposition about the world? Not necessarily. Do those bits correspond to any true or false beliefs the agent has about the world? Not necessarily. What do those bits correspond to then? Well, perhaps nothing but bits...

I don't think it is trivial, but I do think it greatly simplifies the explanation of consciousness. I think that commends it as a choice.

Whereas I think it is very trivial. As I said, I can explain anything I wish by positing a primordial essence. What could be easier? Positing the existence of God explains absolutely anything everything in the world – by your logic this commends it as a choice (which is precisely why theology has so many followers – it explains everything)..

I think that mathematics has shown that it can be useful to posit some assumptions which we can't know are correct or not, and see what we can deduce from them. That is what I am suggesting that some smart people do.

By definition no assumption is known to be correct or not – otherwise it wouldn’t be an assumption would it?
A smart person should choose her assumptions wisely.

Intelligence, life, and whatever people mean by 'soul', are extremely complex entities or ideas and I am sure you agree with me that positing such a primordial complexity is not reasonable.

Consciousness is imho the most complex entity we are aware of! And you want to sweep that complexity under the rug, claim it is not an emergent complexity, but instead primordial? If your reason for rejecting primordial intelligence is because intelligence is a complex entity then the same logic applies to consciousness.

You keep accusing me of positing the complexities of consciousness as primordial (undoubtedly because of my unfortunate choice of the 'PC' label) and I keep insisting that whatever was primordial was extremely rudimentary and simple, like nothing but the ability to acquire bits and with no bits around to acquire. But, I'm getting blue in the face.

Thus you would agree that consciousness is not primordial after all, has not existed since before the Big Bang, but is instead a complex emergent property of the physical world, supervening on the physical, and arising only in certain circumstances when the required conditions for development of that complexity are just right?

if you choose the right definitions, even though they might be a little more abstruse and complex than customary definitions, they can lead to profoundly simpler implications for very powerful concepts. That's the paradigm I'm suggesting that someone follow.

That’s the paradigm followed by theism also. Does that make the premise of theism true?

You asked me once about sleep but you didn't comment much on my explanation.

Because I have an alternative physicalist explanation which I prefer, which does not entail needlessly multiplying fundamental entities in order to arrive at an explanation of the world.

Best Regards

 

[Paul Martin]

Hi MF,

I must admit that when I first read your latest response, I decided to concede defeat and walk away from PF. But rather than post a simple "I give up.", I decided to sleep on it.

Now I realize that such a concession might be interpreted to mean that I see that my ideas are wrong and that I have abandoned them. What I really meant was that it seems hopeless that you will ever be able to understand my ideas. After re-reading your post, it seems as if you told me exactly why you are having such difficulty understanding me. You said,

It doesn’t matter whether you call your primitives mathematical or scientific

From this, it seems to me that you don't understand enough mathematics to understand my proposal.

I can understand why my example of Galois might have gone over your head. I doubt that one can grasp the significance of the power of abstract mathematics to solve, in this example, problems of squaring the circle and trisecting an angle with ruler and compass, unless one has done the hard work of studying and understanding enough Galois Theory.

The "scientific" approach is to work with tangible, real, substantive entities such as rulers, compasses, sheets of paper, and pencils, forming hypotheses about how to go about squaring the circle, experimenting with actual real instruments, abandoning those approaches that don't work, trying more, and, literally for millennia, getting nowhere.

By contrast, Galois, in the few remaining hours before his death, hastily jotted down the framework of the Galois Theory, and in footnotes to his scribbling, noted that, Oh, by the way, notice that as rather trivial byproducts of this general theory, the solutions to the millennia old geometrical construction problems, as well as the centuries old problem of solving the quintic algebraic equation, among others, just pop out as obvious.

With respect, I suspect that the power of the mathematical approach can't be fully appreciated unless and until you study enough math to be able to follow Galois' proofs of the solutions to these problems. Sorry.

Of course, this forum is not the place for the teaching of math, so I will give up any thoughts of trying. I will, however, point out some errors you have made so you can get an idea of what I mean.

It doesn’t matter whether you call your primitives mathematical or scientific, at the end of the day they are assumed by you to be true.

You evidently don't understand the concept of a mathematical primitive. They cannot be said to be either true or false because those notions simply don't have any meaning for primitives. Even if there were a notion of a "true primitive" (which there is not, at least in mathematics) I made no such assumption.

I am simply challenging your assumption that the Receptive Principle is true.

I make no such assumption because the notion of a primitive being true (or false) has no meaning, and such a construction is not used in mathematics.

Just as I may challenge the parallel postulate in geometry.

You may, but such a challenge has no place in mathematics. Postulates may be accepted or not by a group of people who agree to pursue a particular mathematical system, but "challenging" the truth of a postulate would be like challenging the truth of the rules for the moves of a rook in the game of chess.

Are you saying that you cannot offer any definition or meaningful interpretation of this thing you call the Receptive Principle?

Of course I could offer a definition or interpretation. But if I did I would be violating a fundamental rule of mathematics. It is strictly forbidden in mathematics to define or describe or interpret any primitive. That's the whole idea. Primitives are undefined.

And you expect me to understand what you are talking about?

My expectations may have been too high. I thought you understood more math.

Any “set of bits” (including a random set) qualifies as “information”?

No. In a mathematical development you must remain consistent with all previously taken definitions, axioms, and primitives. It is not permitted to simplify the definition of a defined term later on.

In this case, according to my definition, 'information' is not "Any "set of bits"". Information is any difference which can make a difference to anything in existence. A 'bit' is defined as a single instance of a difference of the first kind (i.e. the first of the two kinds referred to in the definition of 'information').

"X knows that Y" simply means (according to you) that X has apprehended some bits?

No. Not "simply". The bits need to carry information.

According to your definition, X can correctly claim to possesses knowledge that Y, even if X does not believe that Y, or even worse if X believes that ~Y? (ie Y is false)

Yes.

According to your definition, X can correctly claim to possesses knowledge that Y, even if ~Y? (ie Y is false).

Yes.

That is consistent with ordinary usage. Think of the generations of scientists and technologists prior to Einstein who did exactly that with respect to Newton's "Laws". Take 'Y' to be 'F = ma'. Y is extremely useful knowledge in spite of its being false.

Your definition seems to imply that one can know things which one does not believe, and even worse that one can know things which are false. Would you agree?

Yes, I agree, except that I would get rid of the word 'worse'. I don't think it is bad at all.

Your definition entails that knowledge is simply the process of apprehending bits by a knower,...

It entails more than that, as I pointed out above.

there is no reference to the truth of a proposition, or necessity of truth of a proposition, in your definition.

That is correct. In mathematics the only reference to truth is tautological. There is certainly no claim of truth whatsoever regarding anything physical or even real for that matter.

If a “knower apprehends bits” it follows necessarily that it possesses knowledge (ie it knows) according to your definition.

No, it doesn't follow. The bits must carry information in order to be knowledge.

There is no sense (from your definition) in which it makes any difference whether the information it knows represents either a true or false proposition; it simply knows, by definition, if it has apprehended bits.

Since a requirement of knowledge, in my system, is that it must make a difference, it could very well be that the truth or falsity of the proposition will influence whether or not the bits make a difference. But that is not necessary.

Using the 'F = ma' example again, the knowledge of that formula made a big difference in the technological world. Learning later that it was not "true" after all, didn't change its usefulness very much. That is consistent with my system: in terms of usefulness, there is no sense in which it makes any difference whether the formula is true or false.

In what sense can you then claim that the knower “can’t know for sure” that it knows?

In the sense of your statement three quotes earlier: "[T]here is no reference to the truth of a proposition, or necessity of truth of a proposition, in [my] definition.

Are you suggesting it might be mistaken in believing that it has indeed apprehended bits...?

I didn't suggest that. I haven't defined 'mistaken'.

I defined 'belief' (in a proposition, A) as a proposition (B) asserting the knowledge of a range of probability that the assertion of proposition A is true. The strength of the belief is measured by the probability range - the higher the range, the stronger the belief.

If, using my definition of 'belief', 'mistaken' means that the probability is not equal to 1, then all beliefs are mistaken (with one exception, IMHO). On the other hand, if we define 'mistaken' to mean a probability of < 0.5, then one could have some beliefs which are mistaken and some which are not.

So, with a suitable definition of 'mistaken', we could indeed claim that some beliefs are mistaken.

(but how can you, since according to you a knower need not have any beliefs)

Only by first defining 'mistaken' and than attributing it to some beliefs. And, yes, a knower need not have any beliefs and in that case logically couldn't be mistaken.

I claim that there is a possibility that the same sort of thing holds true for the relationship between consciousness and brains.

Sorry, Paul, but this is argument is scientifically worthless.

I agree. And once again I would like to stress the fact that I am not proposing a scientific approach. I am suggesting a mathematical approach. You seem to miss the difference. Let me try to clear it up for you.

You have too narrow a view of my proposed project. I don't propose that any but tautological truths be revealed by mathematical reasoning. No truths about the nature of reality can be discovered this way.

What I am proposing is that we (1b) develop a mathematical structure which can be interpreted to encompass some of the features of mind by (1a) starting with a set of primitives and proceeding with mathematical definitions and inference. (This involves no science and little if any observation.) THEN, (2) I propose that science abandon their prejudices against the possible existence of large, nearly flat, extra dimensions of both space and time. (I am encouraged that this is beginning to happen.) THEN, (3) Draw inferences from the mathematical structure and use them to form hypotheses which can be experimentally verified or falsified. and finally, (4) Conduct scientific experiments in the traditional way testing these hypotheses.

In this thread I have only suggested a preliminary starting point for the first part of step (1a) by offering a list of some primitives and definitions for consideration. This has only scratched the surface of (1a) much less made a dent in the entire project. The hard work of completing (1a), and (1b), will have to be done by people a lot younger, smarter, and more energetic than I. And parts (2) through (4) will take completely different sets of people yet.

In a way, your impatience flatters me. You seem to expect that my proposal should yield understandable explanations for the mysteries of life at once and in this thread. Alas, at this point I can only give you hunches and guesses. And that is the best I can do. Sorry if that disappoints you.

We could continue discussing the mathematical meaning and implications of hyper-dimensionality, and other issues, but I think I'll stop here instead.

As always, it's been fun talking with you, MF.

Warm regards,

Paul

 

[AKG]

How can it be that my conscious experience is constrained to this tiny interval in such a vast expanse of time and to this tiny locality on this blue speck at the edge of the Milky Way which seems insignificant itself in the vastness of space? I think most people would brush this off and tell me, "Well, dummy, it's because that's where you happen to be. What's the mystery?" That doesn't satisfy me. What exactly is this thing you refer to as "you"?

You're saying: "This is how I am (a limited consciousness). Why? How did this happen?" Nothing wrong with that question. Of course, you cannot expect answers if you ask "why?" ad infinitum, but it's only one question, so it seems legitimate. The emphasis in your question does seem a little strange, however, because you ask it in a way that suggest there's something unnatural about a limited consciousness, and that consciousness should, by default, encompass everything. I can't think of any reason why this would be. Moreover, I don't see how your PC explanation of the origin of our limited consciousnesses is at all a satisfactory explanation.

The first is, How can we account for the fact that virtually all individual animals, of nearly all species, and nearly each and every day each one lives, and for a significant percentage of each day's duration, and for no plausible reason, and at significant risk to survival in most of these cases of sleep events (which IMHO should present nearly fatal blows to the theories of evolution), routinely, willingly, and even eagerly, lose consciousness? The second, and IMHO less important, mystery is, Why is it that in the face of the foregoing profound mystery, and the fact that we humans are among the vast majority of animals who sleep, and the inconvenience caused by sleep cutting into our work/play time, and the cost of furnishing bedrooms, and the in-your-face obvious necessity for sleep, do people take it so for granted and hardly question it or wonder about it?

Is there really no plausible reason? Animals are made of natural materials and work by natural processes, why does it surprise you that they have natural limitations? If you run some things non-stop, you will get less total usage time out of them than if you give them breaks to rest. If you work out, you know that it's not only the exercise that's necessary to build muscles, but the rest time that gives your body time to rebuild and grow them. That is, the process of improving muscles is a two-part process: part 1) work the muscle, part 2) rest it so the body has time to rebuild it stronger and bigger. Why does this seem implausible to you? Why does it seem more natural to you that a body should be able to build muscle without resting? The body needs to be at rest for the rebuilding subprocess to take place. This is a natural condition on a natural process. Indeed, it could be otherwise, and we can ask why it is this way and not the other, but you seem to suggest that it should be otherwise, and that existing natural conditions are unnatural. And again, we can't ask "why" ad infinitum so if we ask why the body needs to rest to rebuild, we can look at the rebuilding process in detail, and see where rest comes in. We can then ask why the process is the way it is, and perhaps we'll find that the chemistry of the human body makes that process more efficient, say. Maybe we can then ask why the chemistry of the body is the way it is, but we can't go on forever. And again, how does PC explain sleep?

The seemingly narrow scope of consciousness. - How do we account for the seemingly improbable, but seemingly obvious, fact that conscious awareness is situated only in a small range in size (on the order of a meter) and not at all at the scale of intergalactic space or of subatomic particles?

Why improbable? How did you calculate this probability?

According to your definition, X can correctly claim to possesses knowledge that Y, even if X does not believe that Y, or even worse if X believes that ~Y? (ie Y is false)

Yes.

Well you definitely aren't defining "knowledge" to mean anything any other English speaker means by that word. If you know Y, then you believe Y. If someone knows Y, and you ask them, "Is Y the case," and they respond "I don't know" (because they have no believe that Y is the case) or respond "no, it's not" (because they believe ~Y) then they don't know Y. This is what any person who understand the English word "know" will tell you. You're defining something totally that you're calling "knowledge" but has nearly nothing to do with.

According to your definition, X can correctly claim to possesses knowledge that Y, even if ~Y? (ie Y is false).

Yes.

That is consistent with ordinary usage.

No, it's not. His claim to knowledge that Y was incorrect if Y is false.

Think of the generations of scientists and technologists prior to Einstein who did exactly that with respect to Newton's "Laws". Take 'Y' to be 'F = ma'. Y is extremely useful knowledge in spite of its being false.

It was a useful belief, it was not knowledge of any sort if it is false. Assuming F=ma is false, people in the past might have said that "Newton can correctly claim to know F=ma" but they'd be wrong, and anyone today will tell you that if something is false, then even if everyone used to believe it, none of them would be said to have had knowledge. People didn't know that the Earth was flat, they thought, incorrectly, that it was.

You almost seem to be confusing knowledge with evidence, but you're not even doing that. Newton had evidence that F=ma, but he also believed F=ma. You say that someone can know something they don't believe. If your mistake was simply calling evidence "knowledge", then you would think still that even if truth weren't a requirement, belief would be, for if you have evidence that Y, then you would believe Y.

It seems you mean, by knowledge of X, "uninterpreted data (like sensory data) that could be interpreted to imply X". This way, you could even attribute "knowledge" to mirrors and vacuums because whereas knolwedge in real life requires interpretation, under your "definition" it doesn't.

 

[moving finger]

Hi Paul

The first words at the start of this thread were :

It seems to me that we too frequently use the terms 'truth', 'knowledge', 'belief', 'faith', 'reality', 'existence', and 'consciousness' without first defining them.

I agree 100% with this statement. What I have been trying to do since then is to understand your own definitions of these very terms. “Knowledge” for example you define in terms of something you call the Receptive Principle, but you refuse to define what you mean by the Receptive Principle. This seems to me simply to be replacing one undefined term (“Knowledge”) with another (“the Receptive Principle”), thus I cannot see how it is supposed to be a step forward.

it seems to me that you don't understand enough mathematics to understand my proposal.

It may indeed be the case that I don’t understand enough mathematics, since I am not a mathematician like yourself. However I do not believe there is much in the way of mathematics in your proposal, and I see your response here (with the greatest respect) as simply a possible attempt at evading the real issue, which is the meaning of the term “knowledge”.

I doubt that one can grasp the significance of the power of abstract mathematics to solve, in this example, problems of squaring the circle and trisecting an angle with ruler and compass, unless one has done the hard work of studying and understanding enough Galois Theory.

Forgive me, but I simply don’t see what relevance this has to understanding the meaning of English language terms such as “Knowledge” and “Consciousness”.

Are you saying that you cannot offer any definition or meaningful interpretation of this thing you call the Receptive Principle?

Of course I could offer a definition or interpretation. But if I did I would be violating a fundamental rule of mathematics. It is strictly forbidden in mathematics to define or describe or interpret any primitive. That's the whole idea. Primitives are undefined.

It seems to me that you are adopting mathematical conventions to suit your philosophical argument (and then accusing anyone who does not understand enough maths as being unable to understand your argument). The assertion that knowledge is to be defined in terms of the receptive principle (which is your assertion) is not a definition in terms of a mathematical primitive (no matter how much you would like it to be), it is a definition of one concept in terms of another concept. If you wish to present a true mathematical argument then I would probably not attempt to enter into any discussion with you because I freely admit that my maths is appalling, but you have not presented a mathematical argument.

Calling “the receptive principle” a mathematical primitive is thus (it seems to me) simply a convenience in this case, so that one may avoid giving any further explication of what one means by “the receptive principle”. I have no idea what you mean by the term “receptive principle”, and when asked to explain what it is supposed to mean you then seem to hide behind your “mathematical primitive” excuse in order to avoid further explication, hence your argument is totally unintelligible to me.

I thought you understood more math.

Understanding math has nothing to do with understanding what the term “receptive principle” is supposed to mean.

Any “set of bits” (including a random set) qualifies as “information”?

No. In a mathematical development you must remain consistent with all previously taken definitions, axioms, and primitives. It is not permitted to simplify the definition of a defined term later on.

My question was in response to your definition in post #26 :

First, I would define 'information' as sets of bits.

I was simply asking a question regarding your claimed definition.
Are you now saying that your definition is incorrect?

According to your definition, X can correctly claim to possesses knowledge that Y, even if ~Y? (ie Y is false).

Yes.

As AKG has also pointed out, this leads to the absurd notion that X can know something which is false, such as for example “Paul knows that Hitler won the 2nd World War”. You may believe this statement makes sense, but most users of the English language would agree that in this case Paul does not in fact possesses knowledge, instead he is simply mistaken in believing that Hitler won the 2nd World war.

That is consistent with ordinary usage. Think of the generations of scientists and technologists prior to Einstein who did exactly that with respect to Newton's "Laws". Take 'Y' to be 'F = ma'. Y is extremely useful knowledge in spite of its being false.

It is most certainly not consistent with ordinary usage. You seem to have adopted a private meaning for the word “knowledge”. I might claim (based on my belief that Y) that I know that Y, but if Y is in fact false (ie if ~Y) then I do not in fact know that Y (I simply believe that I do). Just as you claim that I am ignorant of mathematics and therefore cannot understand your argument based on mathematical primitives, I respectfully suggest that you need to study a little more epistemology so that you can understand your mistake regarding the meaning of knowledge.

Your definition seems to imply that one can know things which one does not believe, and even worse that one can know things which are false. Would you agree?

Yes, I agree, except that I would get rid of the word 'worse'. I don't think it is bad at all.

Then I must conclude that you and I have fundamentally different understandings of the word “knowledge” – which gets right back to the first sentence of your first post in this thread - that we too frequently use the terms 'truth', 'knowledge', 'belief', 'faith', 'reality', 'existence', and 'consciousness' without first defining them. Your suggested definition of “knowledge” in terms of “apprehending bits” (with respect) is not a definition that makes sense on its own, and it is only when we try to understand just what it is you are trying to say (via the discourse we have just had) that we realize that you have a very peculiar and personal interpretation of just what you think “knowledge” means.

Best Regards

 

[Tournesol]

1. My uniqueness. - It is very hard for me to articulate exactly what this mystery is to me, but it goes something like this: How can it be that my conscious experience is constrained to this tiny interval in such a vast expanse of time and to this tiny locality on this blue speck at the edge of the Milky Way which seems insignificant itself in the vastness of space? I think most people would brush this off and tell me, "Well, dummy, it's because that's where you happen to be. What's the mystery?" That doesn't satisfy me. What exactly is this thing you refer to as "you"?

That is easily explained by the physicalist assumption that
your consciousness i sgenrated by your brain.

2. The phenomenon of sleep. - There are two mysteries here, one more important to me than the other. The first is, How can we account for the fact that virtually all individual animals, of nearly all species, and nearly each and every day each one lives, and for a significant percentage of each day's duration, and for no plausible reason, and at significant risk to survival in most of these cases of sleep events (which IMHO should present nearly fatal blows to the theories of evolution), routinely, willingly, and even eagerly, lose consciousness? The second, and IMHO less important, mystery is, Why is it that in the face of the foregoing profound mystery, and the fact that we humans are among the vast majority of animals who sleep, and the inconvenience caused by sleep cutting into our work/play time, and the cost of furnishing bedrooms, and the in-your-face obvious necessity for sleep, do people take it so for granted and hardly question it or wonder about it? (This includes scientists who IMHO only dabble with the question.)

To save energy.

3. Contradictory notions of time. - We have two common notions of time: Our conscious experience of time (the subjective notion) and the parametric notion of time in physical theories (the objective notion). The mystery is, How can we account for the following contradictions between the two notions?:

There isn't a single theory of time in physics

c. The "arrow of time" which is so obvious in subjective time, hardly appears (except for the contrivance of the 2nd Law) in objective time. In most cases, the direction of objective time is reversible.

The arrow of time doesn't exist in micrphysics, but emerges in co,mplex systems.

4. The seemingly narrow scope of consciousness. - How do we account for the seemingly improbable, but seemingly obvious, fact that conscious awareness is situated only in a small range in size (on the order of a meter) and not at all at the scale of intergalactic space or of subatomic particles?

It's generated by the brain.

Now, IMHO, this scenario satisfactorily explains all the above mysteries
as well as all other mysteries I know of, including the mystery of quantum state reduction, quantum non-locality, Bell's inequality, the origin of life, the origin of consciousness, the meaning of life, the prevalence of all the goofy religious notions, etc., etc., etc.

I don't see how it addresses the time issue at all. And it addreses
the localisation of copnscuousness much less naturally than
the physicalist alternative. And you didn't even
mention the most mysterious aspect of consciousness, qualia.

 

[moving finger]

you didn't even mention the most mysterious aspect of consciousness, qualia.

Mystery? What mystery?

ohhhh, you mean the "hard problem"

Understanding consciousness (and qualia) is quite elementary, once one understands that phenomenal consciousness is a uniquely 1st person perspective emergent property of the physical world, which property by definition is inaccessible from any other (literal or metaphorical) perspective.

The so-called "hard problem" is a non-problem which is created within the minds of those who insist on clinging on to the notion that 3rd person perspective access to 1st person perspective properties is always possible.

As with many concepts in science, philosophy and mathematics, once one looks at it in the right way there is no problem, and no mystery.

Best Regards

 

[Tournesol]

Now, let's suppose that by some accident, one of our radios fell into their possession. They turned it on and discovered that it played music. (The signals from our radio stations could reach that continent.) Their scientists would try to understand where that music came from. The chemists among them would claim that it had to be purely physical, that is, it must be generated completely within the chemical structures of the radio itself. As a test, someone suggested reproducing the radio exactly atom for atom to see if the duplicate also played music. They did, and it did, so they concluded that the music must have come strictly from the physical arrangements and patterns and functions of the atoms in the radio. Of course, we know that is wrong.

But it could have been right. The claim that the music
was being gerneatd internally is simpler than the claim
that is coming from elsewhere, and the scientists
were right to adopt that approach as the initial hypothesis.
They were right to abandon it when it didn't work.

I claim that there is a possibility that the same sort of thing holds true for the relationship between consciousness and brains. I think that if we could construct a duplicate brain, atom for atom, it might be just as conscious as the original. But just as in the case of the radio, it wouldn't prove that there wasn't something outside our physical world that is necessary for consciousness.

Not being false isn't the issue. The issue is whether
the radio analoguy is the simplest and best explanation.
For instance, the claim that qualia are no-physical
properties of brains also explains conciousness,
and it gives a natural explanation of the localisation
of consciousness ina way that the PC theory doesn't.

I respectfully disagree and claim that consciousness does not supervene on the physical world of our perceptions.

So why is it affected by drugs, sugery and injuries ?

First, I would define 'information' as sets of bits. This is the same as in classical information theory so I don't think that part is Greek to you. If it is, let me know.

Bits do not need to be true of even meaningful. But any
definition of knowledge emust say someing about
truth.

The reason I reject JTB is that it is too anthropomorphic. By that definition, knowledge is a belief, held by a conscious human being, that is true and that is justified by that conscious human being.

I don't know where you got that idea. The definition doesn't say anyhting about
human beings at all.

 

[Tournesol]

Understanding consciousness (and qualia) is quite elementary, once one understands that phenomenal consciousness is a uniquely 1st person perspective emergent property of the physical world, which property by definition is inaccessible from any other (literal or metaphorical) perspective.

Doesn't work. Metaphorical perspective (subjective bias)
is not a necessary entailment of literal
perspective (geometry).

The so-called "hard problem" is a non-problem which is created within the minds of those who insist on clinging on to the notion that 3rd person perspective access to 1st person perspective properties is always possible.

It may not be possible as a matter of fact,
but it is entailed by physicalism in
the sense that Chalmers uses the word, so his
claim that there is a HP is entirely consistent.

 

[moving finger]

Doesn't work. Metaphorical perspective (subjective bias)
is not a necessary entailment of literal
perspective (geometry).

I never said it was. I said

inaccessible from any other (literal or metaphorical) perspective

If I claimed that "A is neither B nor C", does that imply I am claiming that B entails C, or that C entails B? No, I don't think so.

It may not be possible as a matter of fact,
but it is entailed by physicalism in
the sense that Chalmers uses the word, so his
claim that there is a HP is entirely consistent.

That must be some kind of "private meaning" of physicalism then. Physicalism is simply the thesis that everything supervenes on the physical, this thesis does not entail that all properties of the world are accessible from all perspectives.

It is only because some people seem to believe that all properties of the world must be accessible from all perspectives (which is in fact not entailed by physicalism) that they then create the HP for themselves (ie qualia are then mysterious and inexplicable). Accept the truth that not all properties of the world are accessible from all perspectives and the HP doesn't exist (ie qualia are trivially explained as 1st person perspective properties of the world) - and all still consistent with physicalism.

Best Regards

 

[Evo]

Thank you all that participated, but the thread has been allowed to remain open too long. Paul's "personal theory" claims fall outside the bounds of what is allowed here.