# Let's start at the beginning

1. Sep 9, 2006

### 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.

Language - 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

2. Sep 10, 2006

### 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?

3. Sep 10, 2006

### Paul Martin

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 don't think it would have been rude, but I'm glad you said what you did.
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.
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.
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.
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.)
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.
They are if and only if they have been explicitly defined by either man or machine or equivalent.
Yes. It has been defined explicitly.

Warm regards,

Paul

Last edited: Sep 10, 2006
4. Sep 10, 2006

### AKG

What are Type A and Type B differences?
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?).
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 langauge).

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.
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?
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.

5. Sep 11, 2006

### 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

6. Sep 11, 2006

### moving finger

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

Last edited: Sep 11, 2006
7. Sep 11, 2006

### 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.

8. Sep 11, 2006

### Paul Martin

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.
I think so. What part of it do you not understand?
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.
I agree completely.
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.
I agree. At least in the case where we are trying to understand something of reality. Pure mathematics is not such a case.
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.
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.
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.
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'.
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.

Warm regards

Paul

Last edited: Sep 11, 2006
9. Sep 11, 2006

### Paul Martin

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?
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.
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.
Yes.
I hope you are as interested as you seem to be. If you are, start here: https://www.physicsforums.com/showthread.php?t=49732
Yes, I think such "numbers" are non-existent and I disagree that the whole set of N has been defined.
No.
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.
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.
"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.
It is the difference between mind and matter. (In case you haven't already picked it up, I am a Cartesian Dualist of sorts.)
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.
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

10. Sep 11, 2006

### Paul Martin

Hi MF,

Thanks for coming over to this thread.
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.
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

11. Sep 11, 2006

### AKG

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?
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?
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.
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.
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".
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?
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?
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.

12. Sep 11, 2006

### moving finger

They don't (imho)

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.

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

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

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

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

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

Last edited: Sep 11, 2006
13. Sep 11, 2006

### moving finger

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 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

Last edited: Sep 12, 2006
14. Sep 12, 2006

### moving finger

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

15. Sep 14, 2006

### Paul Martin

Hi AKG,

I am not sure how to take your post.
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.
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.
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.
Yes. In typical keyboard design, the difference represents seven or eight bits of information.
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.
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."
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.
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.
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.
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.
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

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.
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

16. Sep 14, 2006

### Paul Martin

Hi MF,
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.
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.
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.
Neither. I am asking "what do you suppose we could infer if we took the definition of 'truth' to be such-and-such?"
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.)
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.
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.
With respect, I think that is a premature judgment.

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

Warm regards,

Paul

17. Sep 14, 2006

### AKG

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 any one 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.
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.
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 travelling 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.

18. Sep 14, 2006

### moving finger

Hi Paul

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?
.
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.

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 possess knowledge (here I define knowledge as JTB). The problem is that we simply cannot be absolutely certain whether we do possess knowledge or not (the best we can ever do is to believe that we possess 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 :
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.

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

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.

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

Best Regards

Last edited: Sep 15, 2006
19. Sep 17, 2006

### Paul Martin

Hi AKG,
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.
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.
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.
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.
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.
It seems to me that in light of this new awareness, it might be the proper time to consider divorcing knowledge from truth.
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.)
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 possess 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 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.
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.
By my definition, it would be "probably useful knowledge".
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?
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?
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.
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.
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?
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?
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.
By seeing it as an example of pattern recognition.
Can you give me an example of a concept which can't be expressed as a pattern of bits?
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.
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.
No. I'd say it is the system of the vacuum and the photon which knows the photon's position.
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.
I think you are referring to this:
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.
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.
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

20. Sep 17, 2006

### Paul Martin

Hi MF,

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.
Agreed.
I made no such premise. I took the Receptive Principle as a primitive. Axioms are premises; primitives are simply undefined terms.
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.
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.
Here again, "Physicalism is false" must be A, C, or D.
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.
If you mean that I agree with B or C above, you are correct. I agree with both.
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.
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).
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.
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.
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."
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