Is Consciousness Truly Outside the Physical Realm?

[Paul Martin]

Paul - I don’t claim that your ideas are nonsensical – they constitute (imho) just unnecessarily complex assumptions. Your ideas seem to wrap up a lot of complexity within their assumptions; complexity which I believe is emergent rather than primordial.

Well, if you don't think my ideas are nonsensical, then I don't think you will change my mind. As for complexity, I don't think my ideas are any more complex than yours. In fact, I don't think our views of cosmogony and cosmology are very far apart after all.

My philosophy is based on making the simplest and smallest number of assumptions possible, and deriving complexity as emergent phenomena from these simple assumptions. One such emergent phenomenon (imho) is consciousness. Consciousness is an exceedingly complex phenomenon, and knowledge is predicated on consciousness – your theory posits that this complexity is somehow “built-in” to the boundary conditions of our universe; my theory posits that the boundary conditions are exceedingly simple, and that both consciousness and knowledge emerge as natural but complex phenomena when the circumstances are right.

Our assumptions seem to be nearly the same: We both assume that the ultimate origin of reality was extremely simple. We both assume that all of reality came to be what it is by a process of relatively gradual evolutionary change. We both assume that consciousness is an emergent phenomenon resulting from this evolution. We both assume that the physical universe is evolving according to some precise laws of physics, of which we have discovered some very close approximations so far.

We both believe that the complexity is emergent and not primordial.

The only difference in our views seems to be that I think the emergence of consciousness occurred prior to the Big Bang, and you think it happened (at least) sometime during the biological evolution on earth. In the big picture, I don't think that is much of a difference.

In thinking about the relative advantages and disadvantages of each of our views, it seems to me that my view has only one disadvantage: It is dangerously close to positing a "God" (shudder). But, as I have pointed out many times, this incomplete, imperfect, evolving, learning, limited, finite, error-prone, albeit powerful PC is not recognizable as anyone's description of God since Homer. I think it shouldn't be tagged with this label nor be burdened by "God's" baggage.

As for advantages, it easily explains the Hard Problem (which I know you deny) and it easily explains the otherwise highly improbable initial conditions for the Big Bang. It also, IMHO, explains many mysteries associated with humans.

I admit that my scheme is more complex to the extent that it is more comprehensive and extensive (it extends well prior to the BB). But this same complaint (if you could call it that) would also apply to Newton's extension and refinements to Kepler, and Einstein's extensions and refinements to Newton. It seems the more we know, the more complex things get. We just need to get used to complexity and accept it.

The problem is, I have no idea how one can generate an infinite set of integers (ie a set with infinite cardinality) using this procedure. Do you? (see below)

I think we see exactly eye-to-eye on this problem.

I had a long battle with the Maths geniuses on this forum a couple of years ago, in which I was basically told that I was an ignoramus for suggesting such a thing as an infinite integer –

I don't know whether you looked at my thread from almost two years ago at https://www.physicsforums.com/showthread.php?t=49732 but I was essentially arguing the same thing with the same people and was also told (gently) that I was an ignoramus and needed to go back to school. That was when I decided to study Foundations, and I still plan to do so some day.

Axiom of Choice, or Axiom of Infinity?

When I finish taking that course, I will be able to answer you better. But, for now, I'll just give you my impressions which may be wrong.

In my view, you have to account for the existence of an infinite number of integers if you are going to depend on the infinite set in any of your arguments. The Axiom of Infinity (which according to Wikipedia seems to be included in ZF theory) allows for the definition and thus existence of the infinite set. But I have the same problem that you seem to have in that the mere acceptance of the axiom doesn't explain "how one can generate an infinite set of integers (ie a set with infinite cardinality) using this procedure."

In my studies, it was explained that the Axiom of Choice allowed some mechanism for producing the infinite set of integers, and the ZFC axiomatic system is formed by appending the Axiom of Choice (the "C") to the ZF theory. (I don't know whether the Axiom of Infinity is still included in ZFC theory or not. But it doesn't matter at my level of knowledge anyway. I am just giving impressions here.)

My position, and the one I will try to defend when I take a Foundations course, is that we should develop an axiomatic system in which each and every primitive, axiom, and definition is explicitly expressed, either by the mathematician, or by a machine. I would disallow mathematical induction, because the process can't be carried out indefinitely by any known processor, human or machine, and unless it can, no infinite set can be defined.

My position is similar to Leopold Kronecker's in his opposition to Georg Cantor in that we would both deny the definition of sets of infinite cardinality. But I differ with him in one important respect. Kronecker held that the integers come from God and all the rest is the work of humans. I deny that there is any God who gave us an infinite set of integers. (PC giving us a huge but finite set, though, is a possiblity that I consider.)

Russell’s paradox is not a consequence of infinity, it is a consequence of unrestrained self-referentiality. THIS is why I said that legislating against infinity does not make the problem go away.

We may disagree here. I think the consequences of accepting infinity are fatal. I'm not sure about self-referentiality (Long ago when I read GEB I thought so, but now I'm not so sure. I need to take that course in Foundations.)

You say that the PC “does mathematics”, but then so do most humans. But humans do not create the laws of mathematics by “doing mathematics”.

But they do. See below.

Allow me to re-phrase the question. Given the choice by the PC to be consistent, did the laws of mathematics then follow as a necessary consequence of this (independently of the PCs wishes)? Or are the laws of mathematics contingent (the PC created the laws, and could have created different laws of mathematics if it had so wished)?

First of all, let me make sure you understand that when we talk about PC "doing mathematics" here, we don't mean PC in its primordial state. Instead it goes on much later after considerable mental capabilities have evolved but still before the Big Bang.

Next, there are many complex parts to "doing mathematics": There is the deductive process of proving propositions to be consistent within some system. There are some choices to be made in terms of which propositions are pursued, but for any particular proposition, its truth or falsity is a necessary consequence of the laws of that system.

But prior to that, there is the establishment of the "theory" or system itself, which consists of the primitives, the axioms, and some definitions. These are arbitrarily chosen, and different choices yield different theories or systems. These are not necessary consequences of anything and can be freely chosen.

But prior to that, there is the choice of rules of logic to be used in the manipulation of propositions and even expressing propositions. As Loseyourname has just taught some of us who weren't sure, there are several, or many, choices for the rules of logic (two-valued, many valued, etc). These too, seem not to be necessary consequences of anything and thus can be freely chosen.

But prior to that, there must be some equivalent of a natural language in which to express the choices made in the establishment of a mathematical system. People do mathematics in many different natural languages, so these seem to be arbitrary. Although it seems that the choice of natural language shouldn't affect the outcome of the mathematical system, who knows what kind of mathematics an extraterrestrial would really develop?)

And prior to that, there must be some minimal mental ability in order to even make sense of the above. After all parrots can become fairly proficient in language, but I doubt that they can develop axiomatic systems.

So, now, to your specific questions.

Given the choice by the PC to be consistent, did the laws of mathematics then follow as a necessary consequence of this (independently of the PCs wishes)?

No. The PC could still express whims and wishes in the choice of logic to use and then in the choice of primitives and axioms. (PC might choose ZF or maybe ZFC or some other.) The laws of mathematics follow from these arbitrary choices. I think the analogy of chess applies exactly here.

The analogy fails because the rules of chess are contingent, not necessary – they could have been different. But the laws of mathematics are not contingent, they are necessary.

No. The laws of mathematics are contingent on the logic system chosen and on the primitives and axioms chosen.

Or are the laws of mathematics contingent (the PC created the laws, and could have created different laws of mathematics if it had so wished)?

Yes. PC could have chosen a different logic system, and within that system, PC could have chosen from among many different sets of primitives and axioms. Many (but of course not infinitely many) different mathematical systems are possible.

We are quite fond of our mathematical system of analysis which contains the infinite set of real and imaginary numbers. It turns out that all (as far as I know) of our laws of physics fall within this system. (Loseyourname may be correct that QM does not need anything outside this system.) Dr. Dick, IMHO, has confirmed that our physical universe is built upon this familiar mathematical system since he deduces his result from its axioms and his result embodies the laws of physics.

In my view, however, which seems to resonate with some of what you wrote, the notion of infinite sets leads to contradictions and the axioms should be revised to disallow them. Whether this means dropping the Axiom of Choice, or the Axiom of Infinity, or some other I don't know. But I have sketched out a proposal for what I call Practical Numbers which are all finite. This is exactly the same set of numbers which each and every person or machine has ever used, or ever will use, to do any calculation whatsoever. Even the people who have computed the first trillion decimal digits of Pi have only produced a finite rational number and they only used finite rational numbers in all their calculations. Integers are naturally limited by virtue of the capability of the machine being used, or by the time, determination, will, and supply of paper and ink of a human calculator. The math I propose would be grainy, but then again, our universe seems to be grainy. But I digress.

Understood. But even in his [Dick's] formal development, it seems to me that an explanation is a mapping (a series of vectors if you like) which provides a translation from one set of points in his 3D space, to another set of points in the same space. Whether the points are more fundamental than the vectors which map between them, or vice versa, is arguable.

In Dick's formal development, 'explanation' is a definition he makes within the system of mathematical analysis. He starts with the assumption of that mathematical system which includes all the real and imaginary numbers as well as the notion of mapping, not to mention all the theorems that have been derived over the past several hundred years. IMHO he has proved a new theorem in that system and he has chosen his definitions so that they end up being ismomrphic to familiar entities.

I think we need to agree on a definition of “thought”. What do you mean by “thought”?

Mental activity of which the thinker can claim to be consciously aware.

Here I must be careful to avoid a mistake you taught me about. When we claim that "something exists", we might have in mind something primordial which accounts for everything else, or we might have in mind something that accounts for our present sense of the world. In our respective views of the evolution of reality, I think we agree that in the primordial state, any notion of 'thought' is far to complex to have existed. My attempts at reducing thought to its fundamental, and even primordial, essence have led me to use the notion of "the ability to know", or "the ability to realize", or the "receptive principle" as described by Gregg Rosenberg. So when I claim that "thought happens", I am referring to the present complex state of reality. When I claim that "there is something and not nothing", I am similarly referring to the present complex state of reality. In that context, I propose that the two claims are the same.

Have to stop. Warm regards,

Paul

 

[Canute]

I see the QM/logic question much more simply, in terms of the wave-particle duality.

The proposition: 'A quantum entity is a wave' is neither true nor false. Likewise, 'A quantum entity is a particle' is neither true nor false. 'A quantum entity is neither a wave nor a particle' is neither true nor false and so on. I mentioned the background-dependence problem because physicists seem to be reaching the same sort of conclusion about the fundamentality of spacetime. Some have proposed the hypothesis of duality as a solution, by which spacetime is fundamental or not depending on how we look at it. So the proposition 'spacetime is fundamental' would be neither true nor false.

The link with Brown (whose mathematics incorporates the idea of 'nonduality') is that spacetime is neither fundamental nor not-fundamental in the nondual view. If physicists were to rename their hypothesis the 'hypothesis of nonduality' the equivalence of this idea to the nonduality spoken of by the mystics would be more obvious. In this view spacetime has always been said to be fundamental or not depending on how we look at it. If this is a coincidence it would seem a very unlikely one.

Seeing as how this started out as a discussion of dualism it is worth noting that the statements 'spacetime is fundamental' and 'spacetime is not fundamental' would both be examples of dualism in the nondual view.

 

[Paul Martin]

Hi MF,

This comment had me lying awake early this morning.

Even in a finite number system, one can still ask “is the class of all classes that are not members of themselves a member of itself?”

Yes, one can ask the question, but I think the question is nonsense. I think the phrase "the class of all classes" cannot be consistently defined, even in a finite case.

Suppose the universe consisted of exactly 2 classes, say A and B. Then how could one define 'the class of all classes'? Since we are using the term 'class' in the phrase, to be consistent, we must mean the same thing by the term as we mean in the premise. In other words, the class of all classes must be a class. And since the universe consists of exactly two classes, A and B, the class of all classes must be either A or B. There are no other candidates. If the class of all classes is A, then it does not include B which is inconsistent with any reasonable meaning of 'all'. Similarly if it is B.

If we define 'the class of all classes' to be the class {A,B} then we are inconsistent with the premise because we now have a third class which is neither A nor B.

I think the problem is in the notion of "all". I think a consistent notion of "all" of anything must be time dependent. We must qualify 'all' by specifying "all at a point in time".

The problem is that the body of mathematics grows. What may be a proposition or a conjecture at one time becomes a theorem later as a proof is discovered. Similarly, if we consider a finite case, such as the existence of only A and B as above, we may introduce new concepts at a point in time which extend the "universe". So, if we have only A and B, and we form a new set with A and B as its members, we have extended the universe and from that point of time onward, 'all' has a new and different meaning.

Let's look at it in a different way. What does it mean for a set to be a member of itself? Well, let's look at an example.

Let A = {A,B}. The definition of A is recursive, but is it consistent? And does it make sense? Logically, it seems to me that there is no reason we can't define 'A' this way.

Now let's say the universe consists of exactly, and nothing but, the sets A and B and the set, C, which is defined as the set of all sets that are not members of themselves. At the time we define 'C', the only set which is not a member of itself is B. So at the time we define 'C' we have C = {B}. Then, and only after we have defined 'C', can we ask the question, "Is C a member of itself?" The answer is clearly "no" in this example.

I don't think this presents a contradiction or a difficulty. You might say that since C is a set and since C does not contain itself as a member, it must belong to the set of all sets that do not contain themselves as members. But I would say that you don't get a chance to refine, or redefine, your definitions as new concepts are added to your mathematical system. You have already defined 'C' once. That definition is consistent and you are not at liberty to change it later.

As I see it, the only problem presented is the interpretation of the word 'all' without considering the time-effectiveness of the concept. If I agreed to give you all the money in my checking account, I would reserve the right to specify exactly when the balance was going to be calculated.

Extending this notion of time dependency to the subject of this thread, I would say that time is a parameter which marks the progress of the mathematician's attention as he/she/it develops the theory by choosing primitives, choosing axioms, stating them in logical language, defining terms, and proving propositions to be consistent. The body of mathematics thus developed is time-dependent in that its state is not static but changes as concepts are added.

In other words, IMHO, you can't -- and don't -- have mathematics without a mathematician. Put another way, you can't have concepts in the total absence of a conscious mind. (The exception I have noted earlier would be if you define 'concepts' to include the symbolic representation of the mental concept as recorded on some physical medium to also be a concept, then that recorded concept may exist after the conscious originator has died and completely disappeared. In any case, a conscious mind was necessary for the concept to exist in the first place.)

I think this is the fundamental disagreement between you and me, MF. It is my conviction that "mind is necessary for concept" which compels me to accept the notion of PC existing and conceiving concepts prior to the existence of such events as the Big Bang, which very much seem to be dependent on a great many sophisticated concepts.

Warm regards,

Paul

 

[selfAdjoint]

Suppose the universe consisted of exactly 2 classes, say A and B. Then how could one define 'the class of all classes'? Since we are using the term 'class' in the phrase, to be consistent, we must mean the same thing by the term as we mean in the premise. In other words, the class of all classes must be a class. And since the universe consists of exactly two classes, A and B, the class of all classes must be either A or B. There are no other candidates. If the class of all classes is A, then it does not include B which is inconsistent with any reasonable meaning of 'all'. Similarly if it is B.

If we define 'the class of all classes' to be the class {A,B} then we are inconsistent

No your premise contradicts the definition of class. You can't restrict it that way; if you have two objects (including classes) you are free to form the class of their pair.

 

[Paul Martin]

No your premise contradicts the definition of class. You can't restrict it that way; if you have two objects (including classes) you are free to form the class of their pair.

What is the precise definition of 'class' that guarantees such freedom?

If you have the freedom to form new classes in such a way, then there can be no such thing as a finite system, as one can always extend it by forming new combinations of elements to form new sets or classes.

Paul

 

[moving finger]

In quantum theory this law ‘tertium non datur’ is to be modified. Against any modification of this fundamental principle one can of course at once argue that the principle is assumed in common language and that we have to speak at least about our eventual modification of logic in the natural language. Therefore, it would be a self-contradiction to describe in natural language a logical scheme that does not apply to natural language."

This seems clear and straightforward to me, but is there an objection I'm unaware of?

It may be clear and straightforward, but is it necessary? I could claim that we need a 7-valued logic (7 is my lucky number), but simply claiming it does not make it necessary (in the sense of being a necessary assumption to enable our understanding of the world). This seems to me like an expression of Heisenberg’s personal beliefs, but this doesn’t make such a belief necessary. Heisenberg (it seems) simply could not accept the notion of the excluded middle, therefore he chose to reject this premise. That’s an assumption of his. But does this make the assumption necessary? How could we tell?

Could you give an example where this “Heisenberg-modified tertium non datur” can be applied?

To see what he means here consider any metaphysical question. Take the something/nothing question of cosmogony for example. It contradicts reason that the universe arises from something or nothing.

Why do you say it contradicts reason? Please show that this follows. You are assuming first of all that the universe has “arisen” - presumably in time – which then assumes that time exists outside of the universe. Why can it not be the case that the universe has existed for all time (be careful how you define time)?

In other words, this question is undecidable in ordinary logic.

Not until you answer the question above. A meaningless question does not have a yes/no answer, but this does not mean we have rejected the law of the excluded middle.

The cause of the problem, according to Brown (and me) is that the universe did not arise from something or nothing. Rather, this distinction is ultimately innapropriate when considering such ontological questions.

Saying that “the universe arose” already presumes some backdrop of time against which it arose – what if time is an intrinsic part of the “creation” of the universe? If there is no background “time” before the “arising” then there can be background “time” against which the “arising” occurs (this should appeal to a mystical mind). One can expect yes/no answers only if one poses meaningful questions.

Would this not be a rather neat explanation of why metaphysical questions are undecidable?

It rather seems like a neat way of avoiding the question!

The whole reason why the possibility of a “third way” arises in quantum mechanics is precisely the same as the reason it arises in conventional logic – some questions are meaningless. To ask “is the King of France bald?” is a meaningless question, it has no true or false answer, because the object it refers to (the King of France) does not exist. In the same way to ask “what is the position and momentum of this quantum object” is also a meaningless question, it has no unique answer because the position and momentum of a quantum object cannot be simultaneously precisely specified (the concept of simultaneous position and momentum does not exist in QM).

Thus in both QM and logic there do indeed exist “true”, “false” and “meaningless” propositions, but there is no need to invoke a fourth class of “imaginary” propositions. This latter is imho simply mystical nonsense.

If you disagree, perhaps you could provide an example of a proposition which you believe is neither true, false nor meaningless, but is instead “imaginary”?

The properties of position and momentum are complementary. This means they cannot be measured at the same time.

Agreed – but this does not prevent us from measuring one property at a time (or assigning a probability to one property at a time).

If you pin down the position of something accurately, the momentum becomes completely undefined It doesn't have a probability distribution; it just doesn't exist as a measurable property.

If you pin down the position of something accurately, then the momentum becomes completely uncertain, but this is not the same as saying “it doesn’t exist as a measurable property”. I can choose to measure whatever I wish, but quantum mechanically I cannot measure both position and momentum simultaneously.

Well, if you don't think my ideas are nonsensical, then I don't think you will change my mind.

Paul – I know that I cannot change your mind, and I am not here for that reason. I am here simply to explore the limits of my own understanding of the world, to find out through test and experiment and discussion whether my beliefs are rational, coherent and sound, and to learn for myself whether I need to change any of those beliefs.

All I can do is to show you the water – it is your decision as to whether you drink from it or not. Changing your mind is under your control, not mine. (It’s like the old joke about “how many psychiatrists does it take to change a lightbulb?” – answer : “None – the lightbulb must want to change by itself”)

As for complexity, I don't think my ideas are any more complex than yours. In fact, I don't think our views of cosmogony and cosmology are very far apart after all.

I’m a great believer in the saying “one can lead a horse to water, but one cannot make him drink”. Your PC is inherently complex – it thinks, it knows, it understands, it perceives, it makes decisions, it is conscious, it has intentions and desires, and it seems to me that you feel you need to assume such properties as “a priori properties of the world” because you do not believe these properties could arise solely from complexity if they were not already somehow “built-in” to the boundary conditions. If you genuinely believe that the assumption of this primordial PC is a “simple assumption” then you and I are talking a fundamentally different language. (It’s similar to the theist idea that the assumption of God is a simple assumption).

In my view, you have to account for the existence of an infinite number of integers if you are going to depend on the infinite set in any of your arguments. The Axiom of Infinity (which according to Wikipedia seems to be included in ZF theory) allows for the definition and thus existence of the infinite set. But I have the same problem that you seem to have in that the mere acceptance of the axiom doesn't explain "how one can generate an infinite set of integers (ie a set with infinite cardinality) using this procedure."

My “solution” to the problem is that I reject the conventional mathematician’s dogma that an integer is a number generated by adding 1 to itself a “finite” number of times. Why does the conventional mathematician insist upon “finite”? To me, an integer is a number which is generated by adding 1 to itself an arbitrary (unlimited) number of times, and in the limit “unlimited” tends to infinity. Thus we arrive at the concept of an infinite integer, and thus no problem generating an infinite set of integers. I don’t see how the mathematics of integers can be claimed to be consistent otherwise. And incidentally the whole of Cantor’s ideas about different levels of infinity thereby goes out the window – the cardinality of the integers is just the same as the cardinality of the reals as soon as we acknowledge the existence of infinite integers (the only reason Cantor was able to show allegedly different levels of infinity was because of the incoherent notion of an infinite cardinality of finite integers).

Russell’s paradox is not a consequence of infinity, it is a consequence of unrestrained self-referentiality. THIS is why I said that legislating against infinity does not make the problem go away.

We may disagree here. I think the consequences of accepting infinity are fatal. I'm not sure about self-referentiality (Long ago when I read GEB I thought so, but now I'm not so sure. I need to take that course in Foundations.)

See below. Your evidence for the alleged contradictions inherent in the concept of an infinite set (the set of all logical possibilities for example) was Russell’s paradox. I have shown (and continue to explain below) that Russell’s paradox has nothing to do with infinity, it has to do with self-referentiality, and the paradox occurs even in finite sets.

The PC could still express whims and wishes in the choice of logic to use and then in the choice of primitives and axioms. (PC might choose ZF or maybe ZFC or some other.) The laws of mathematics follow from these arbitrary choices. I think the analogy of chess applies exactly here.

Pardon me, but it seems to me that you are avoiding the question. Yes of course one (whether “one” is the PC or a human agent) must choose axioms (how many times in how many threads have I said that we must make assumptions before we can arrive at any explanation or understanding of the world?) – and one is of course free to choose those axioms. But given the choice of axioms, the laws of mathematics then necessarily follow. Take again my example of Pythagoras’ theorem – given Euclid’s 5 postulates (axioms) then the theorem necessarily follows – neither the PC nor any human (given the assumptions) has any freedom at all to change this.

Humans are in exactly the same position. We can choose axioms, and the laws of mathematics follow from these axioms. There is nothing “special” about the PC in this respect – the PC is thus as powerful and as powerless as any human agent.

The laws of mathematics are contingent on the logic system chosen and on the primitives and axioms chosen.

Of course. But the PC has no more “power” to choose the laws of mathematics than do humans. We humans choose the axioms, then we deduce the laws which follow. How is the PC any different to this?

PC could have chosen a different logic system, and within that system, PC could have chosen from among many different sets of primitives and axioms. Many (but of course not infinitely many) different mathematical systems are possible.

Can you give an example of a choice that the PC could have made which a human is not capable of making?

The proposition: 'A quantum entity is a wave' is neither true nor false. Likewise, 'A quantum entity is a particle' is neither true nor false. 'A quantum entity is neither a wave nor a particle' is neither true nor false and so on. I mentioned the background-dependence problem because physicists seem to be reaching the same sort of conclusion about the fundamentality of spacetime. Some have proposed the hypothesis of duality as a solution, by which spacetime is fundamental or not depending on how we look at it. So the proposition 'spacetime is fundamental' would be neither true nor false.

The issue here is that the question depends on the context. To ask “is the quantum entity a particle?” is a meaningless question outside of the context of a measurement. All propositions can be reduced to either true, false or meaningless.

This comment had me lying awake early this morning.

I’m not sure if I’m sorry or happy

Suppose the universe consisted of exactly 2 classes, say A and B. Then how could one define 'the class of all classes'? Since we are using the term 'class' in the phrase, to be consistent, we must mean the same thing by the term as we mean in the premise. In other words, the class of all classes must be a class. And since the universe consists of exactly two classes, A and B, the class of all classes must be either A or B. There are no other candidates. If the class of all classes is A, then it does not include B which is inconsistent with any reasonable meaning of 'all'. Similarly if it is B.

If we define 'the class of all classes' to be the class {A,B} then we are inconsistent with the premise because we now have a third class which is neither A nor B.

Artificially restricting the universe to 2 and only 2 classes is OK, and in this case it eliminates the concept of the additional third class of all classes that are not members of themselves, but this is hardly a realistic scenario, and it does not follow from this that the general solution in a universe with a finite number of classes avoids Russell’s paradox. If I have N classes (where N is a finite integer), I can always construct another class (numbered N+1) which is the class of all classes (selected from the original N classes plus the new N+1 class) which are not members of themselves. I still have a finite (N+1) number of classes, but I now also have Russell’s paradox – and no sign of infinity.

Think of it in terms of the Barber’s paradox – this is another variant. In Seville there is a barber who shaves everyone who does not shave himself. Now ask – does the barber shave himself? Clearly at anyone time there are a finite number of individuals in Seville – thus the paradox has nothing to do with either infinity or time.

The barber paradox is EXACTLY of the same form as Russell’s paradox of the class of all classes that are not members of themselves – and the paradox arises because of self-referentiality.

I think the problem is in the notion of "all". I think a consistent notion of "all" of anything must be time dependent. We must qualify 'all' by specifying "all at a point in time".

Nope – the problem is in self-referentiality. The “class of all classes that are not members of themselves” is class N+1, but it refers not only to all of the original classes N but also to ITSELF (class N+1). This has nothing to do with infinity, or with time. It has only to do with self-referentiality. This is precisely why Russell tried to get rid of the problem by eliminating self-referentiality through partitioning sets and classes – so that a class (ie the set N+1) could refer to a set (ie any of the sets N), but was not allowed to refer to itself (ie the set N+1). Infinity has absolutely nothing to do with it. Neither does time.

Paradox is inherent in self-referential systems – I think there is a warning there for our understanding of consciousness (which is also ultimately a self-referential system).

The problem is that the body of mathematics grows. What may be a proposition or a conjecture at one time becomes a theorem later as a proof is discovered. Similarly, if we consider a finite case, such as the existence of only A and B as above, we may introduce new concepts at a point in time which extend the "universe". So, if we have only A and B, and we form a new set with A and B as its members, we have extended the universe and from that point of time onward, 'all' has a new and different meaning.

It need not be connected with time (don’t forget that I don’t believe “the body of mathematics grows” in an ontic sense – all that grows is human knowledge of mathematics – the epistemic sense). You may see the paradox as a temporal progression, whereas I see it as a logical progression. Standing “outside of time” one can see the same atemporal paradox. The barber who shaves all those who do not shave themselves obviously has to shave one person at a time, but the paradox is not a time-dependent paradox – the barber may choose to decide whether he shaves himself or not before he decides whether to shave anyone else.

Let's look at it in a different way. What does it mean for a set to be a member of itself? Well, let's look at an example.

Let A = {A,B}. The definition of A is recursive, but is it consistent? And does it make sense? Logically, it seems to me that there is no reason we can't define 'A' this way.

Now let's say the universe consists of exactly, and nothing but, the sets A and B and the set, C, which is defined as the set of all sets that are not members of themselves. At the time we define 'C', the only set which is not a member of itself is B. So at the time we define 'C' we have C = {B}. Then, and only after we have defined 'C', can we ask the question, "Is C a member of itself?" The answer is clearly "no" in this example.

I don't think this presents a contradiction or a difficulty. You might say that since C is a set and since C does not contain itself as a member, it must belong to the set of all sets that do not contain themselves as members. But I would say that you don't get a chance to refine, or redefine, your definitions as new concepts are added to your mathematical system. You have already defined 'C' once. That definition is consistent and you are not at liberty to change it later.

What you have done is exactly what Russell did in his theory of types – he said that set C is in a different class to sets A and B, therefore set C cannot (= is not allowed to) refer to itself – thus eliminating the paradox.

Imagine that C is the barber, and A and B are two residents of Seville. A shaves himself, but B does not. Now we say that the barber (C) shaves all those that do not shave themselves – thus C shaves B. By your “rule” we are not allowed to ask if C shaves himself (thus avoiding the paradox) – and this is just what Russell tried to legislate against. But it has nothing to do with either time or infinity – it has to do with self-referentiality. Basically what you are saying is “we are not allowed to ask whether C shaves C – that is not a legitimate question”.

Indeed, I can reduce the set to 1. Imagine all the residents of Seville have left town, except for the barber. Once again, the barber shaves all those who do not shave themselves. But now there is only one person left in town to be shaved – the barber himself. We have a unique set, a single set. And we still have the paradox. Conclusion : Russell’s paradox has nothing whatsoever to do with infinity. It has to do with self-referentiality.

As I see it, the only problem presented is the interpretation of the word 'all' without considering the time-effectiveness of the concept. If I agreed to give you all the money in my checking account, I would reserve the right to specify exactly when the balance was going to be calculated.

Time is a red-herring (as time usually is – it is indeed strange how time figures in many false human intuitions). The issue is purely one of logical self-referentiality. In practice the barber could shave himself before he shaves anyone else – but you would still claim that the question “does the barber shave himself?” (ie “does C shave C?”) is a question which is not allowed.

Thus having rejected the idea that "Russell’s paradox is a contradiction entailed only by notions of infinite sets", we get back again to the question of why you think the notion of an infinite set involves contradiction. Over to you.

Best Regards

 

[Canute]

It may be clear and straightforward, but is it necessary? I could claim that we need a 7-valued logic (7 is my lucky number), but simply claiming it does not make it necessary (in the sense of being a necessary assumption to enable our understanding of the world). This seems to me like an expression of Heisenberg’s personal beliefs, but this doesn’t make such a belief necessary. Heisenberg (it seems) simply could not accept the notion of the excluded middle, therefore he chose to reject this premise. That’s an assumption of his. But does this make the assumption necessary? How could we tell?

I think you'd need to ask this question of a physicist. Heisenberg was quite a bright chap and a good physicist, and not in the habit of voicing his personal beliefs as if they were facts.

Could you give an example where this “Heisenberg-modified tertium non datur” can be applied?

A wave-particle seems a good example.

Why do you say it contradicts reason? Please show that this follows. You are assuming first of all that the universe has “arisen” - presumably in time – which then assumes that time exists outside of the universe. Why can it not be the case that the universe has existed for all time (be careful how you define time)?

Metaphysical questions are undecidable because both of their 'reasonable' answers give rise to contradictions. By 'reasonable' here I mean reasonable according to rules of ordinary logic. For example, the proposition that the universe arises ex nihilo is logically incoherent, the proposition that it arises from something pre-existent is logically incoherent, and therefore the question of how it arises is a metaphysical (undecidable) question. However, if we modify the tertium non datur rule this opens up a third possibility.

A meaningless question does not have a yes/no answer, but this does not mean we have rejected the law of the excluded middle.

Do you think Heisenberg didn't know this?

Saying that “the universe arose” already presumes some backdrop of time against which it arose –

Very true. Let us say then the the universe arises only in a particular sense.

If there is no background “time” before the “arising” then there can be background “time” against which the “arising” occurs (this should appeal to a mystical mind). One can expect yes/no answers only if one poses meaningful questions.

Exactly. To a mystic asking whether the universe arises from something or nothing is like me asking you whether you've stopped beating your wife. In Zen the repsonse may be 'Mu', a word meaning, roughly, there is nothing to say because the question embodies a false assumption and any answer would therefore be misleading.

The whole reason why the possibility of a “third way” arises in quantum mechanics is precisely the same as the reason it arises in conventional logic – some questions are meaningless. To ask “is the King of France bald?” is a meaningless question, it has no true or false answer, because the object it refers to (the King of France) does not exist. In the same way to ask “what is the position and momentum of this quantum object” is also a meaningless question, it has no unique answer because the position and momentum of a quantum object cannot be simultaneously precisely specified (the concept of simultaneous position and momentum does not exist in QM).

I gather that you're a logical positivist. I don't find that doctrine convincing, and it is now virtually dead.

Thus in both QM and logic there do indeed exist “true”, “false” and “meaningless” propositions, but there is no need to invoke a fourth class of “imaginary” propositions. This latter is imho simply mystical nonsense.

I know this is your opinion. However, I don't agree.

If you disagree, perhaps you could provide an example of a proposition which you believe is neither true, false nor meaningless, but is instead “imaginary”?

Light is a wave. Human being have freewill. Light is a particle. Human being do not have freewill. The universe arises ex nihilo. The universe arises from something. God exists. God does not exist. Bear in mind that the term 'imaginary' is used in its mathematical sense.

 

[Paul Martin]

I’m a great believer in the saying “one can lead a horse to water, but one cannot make him drink”.

I believe the same. I am eager to drink but sometimes I find it hard to swallow some of what is offered. I think the reciprocal is also true: it seems that you have a hard time swallowing some of what I offer to you. I think our objective should not so much be in the drinking, but in identifying those obstacles to swallowing.

Your PC is inherently complex – it thinks, it knows, it understands, it perceives, it makes decisions, it is conscious, it has intentions and desires, and it seems to me that you feel you need to assume such properties as “a priori properties of the world” because you do not believe these properties could arise solely from complexity if they were not already somehow “built-in” to the boundary conditions.

What you say here is true about me and my ideas as long as it is interpreted correctly. You seem to gloss over two important points of interpretation which makes me think that you still misunderstand me. I have elaborated on these two points several times in our conversations, but I don't recall you ever acknowledging them, much less confirming or denying either of them.

Point number one is that I regrettably use the term 'PC' to refer to two separate and distinct entities: first is the truly primordial entity, about which we can say very little if anything, and which existed only as prior to and until the first change of anything occurred. From that point on, what was initially this truly primordial PC evolved into the second entity, which I also refer to as PC.

This evolving PC has undergone enormous change since primordial times, and I (again regrettably) use the term sometimes to refer to the conscious entity that is driving organisms on Earth now in the 21st century, sometimes to refer to the conscious entity which I think might have consciously interfered with the otherwise unitary evolution of our physical universe, sometimes to refer to the conscious entity which I think might have been involved in the establishment or choice of the boundary conditions for our BB, and at other times to refer to the evolving conscious capabilities which I think developed over an extended period of time "prior" to the BB itself.

So, when you claim that my notion of PC is "inherently complex", I agree only as long as you mean PC in the second sense above. It was not complex at the outset.

The second point of interpretation, which I think you gloss over, is in your use of the term 'world' as in " it seems to me that you feel you need to assume such properties as “a priori properties of the world” because you do not believe these properties could arise solely from complexity if they were not already somehow “built-in” to the boundary conditions."

You would be correct in suspecting that I feel that need as long as you interpret the term 'world' to mean our familiar 4D physical space-time continuum which began its existence with the BB. In this case, I do feel the need to assume such properties as being extant sometime prior to the BB in order to adequately explain the high improbability of the BB's initial boundary conditions and to adequately explain other phenomena such as the origin of life and the origin of consciousness in living organisms.

On the other hand, if you interpret 'world' to mean all of reality, then I think you and I are pretty much in agreement. We both think things (the world of reality) started out extremely simple, and that all complexity emerged as a result of recombinant changes over long periods of time. We disagree on some details, like the lengths of time involved (my estimate being vastly longer than yours), or the sequence of appearance of various specific phenomena (e.g. consciousness vs. organisms, concepts vs. mind).

Probably the most contentious of these details is whether there is some fundamental constituent of consciousness (whatever that is) which was primordial. I say "yes" and I think you say "no". But in my view, whatever that fundamental constituent is (was), it is not at all the complex entity or idea we refer to as consciousness (whatever it is). I have speculated that the fundamental constituent is something like a rudimentary ability to know, or ability to realize, or as Lars suggested, an ability to experience, or as Gregg Rosenberg has suggested, a receptive principle.

Now to figure out whether such a primordial ability or principle can give rise to consciousness as we know and experience it, it seems to me, would take the same sort of investigation Goethe and Beethoven went through trying to identify the same thing for music (as the two of us imagined it).

But to draw a comparison, you can have vibrations without a mind, but you can't have music without both vibrations and a mind. I'd say that a similar thing is true for concepts: you can have entities or things without a mind, but you can't have concepts without a mind. And, further, I'd say that you can't have consciousness without a mind. These, of course are only my opinions, and even though I have poured them into your water glass, I don't expect that you will easily swallow them. That's fine. I just wanted to offer them to you and get your response.

you do not believe these properties could arise solely from complexity if they were not already somehow “built-in” to the boundary conditions.

Yes, you have that right except that in this case, I claim that the boundary conditions we are talking about are the truly primordial conditions, which greatly precedes the BB. And, the "somehow 'built-in'" is the "fundamental constituent of consciousness" I talked about above. I believe there was such a constituent and you evidently don't.

I should point out that I do believe in emergent phenomena. Moire patterns, and the Mandelbrot Set are examples of emergent phenomena. So is the wetness of water. But it is my opinion that conscious experience is different in kind from all emergent phenomena and that it requires something more to get it to happen or exist. I think that "something more" is ontologically fundamental. And, it seems that you can't swallow that.

If you genuinely believe that the assumption of this primordial PC is a “simple assumption” then you and I are talking a fundamentally different language.

I don't think it is that drastic. I think we are talking the same language, but that we have been using different connotations of the words 'PC' and 'world'. Hopefully, we can get over that misunderstanding. As I said before, I think our respective views of what actually happened at the ultimate "beginning" are not all that different.

(It’s similar to the theist idea that the assumption of God is a simple assumption).

I was going to categorically deny this by saying that the theists have never defined their notion of 'God'. But I realized that I have never really defined my notion of 'PC' in its primordial state. I guess you are ahead of both the theists and me by not even identifying what you think might have been the primordial constituent of reality. So without identifying it, you don't have to define it.

But, as I have also pointed out, the theists posit huge (even infinite) complexity to their God in the beginning, whereas I posit only simplicity as you do.

Russell's Paradox
Thank you for your excellent discussion of Russell's Paradox and the notions of self-reference, infinity, and time.

I think our disagreement here won't be resolved by either of us dishing up more servings of drinking water. I think the stumbling block is our different views on whether concepts can (or do) exist without first having been conceived in a mind. You say "yes" and I say "no'. This is equivalent to whether mathematics is discovered or invented respectively (and respectfully as well).

I say that no mathematical concept, thus no mathematics, exists unless and until some conscious mind conceives of the concept and integrates it into a developing body of mathematical concepts comprising a particular mathematical system or theory according to some arbitrarily but deliberately chosen rules.

I think you would say that concepts, such as the implications of logical rules, exist independently, and more importantly, prior to the existence, of any mind.

For example, we said,

The laws follow on as necessary consequences of the PC's consistency decision and the particular choices of primitives, axioms, definitions, and boundary conditions.

OK. This is true of all mathematical laws. Thus (to take an example) given a right-angled triangle in a 2-dimensional plane conforming to Euclid’s 5 postulates of geometry, the law that the square of the hypotenuse is equal to the sum of the squares of the other two sides is a necessary mathematical law. There is no way that the PC could have “created” a universe in which this law (given the postulates and definitions) would have been false. Thus in a very real sense, this law (given the postulates and definitions) “exists” independently of the PC.

It is this "very real sense" of existence which I can't swallow.

But, if I did swallow it, I would agree that a static Platonic world exists populated by all concepts that might ever be discovered by mathematicians, and that that Platonic world existed at least at the time of the BB, if not before. Certainly long before the first animal appeared on earth.

But I don't swallow it. I would agree that a Platonic world does exist, at least if you claim that it is populated by any concept currently in someone's mind, or even in someone's memory, or even in symbolic form in a book. In this way, you could have a Platonic world completely resident in the physical world (assuming people's minds and memories are all in the brain, which I doubt, if not deny). But even with this type of Platonic world, there remains the question of how one "does mathematics". I think this is at the root of our problem.

In school, we are taught to develop proofs a step at a time and write them down in sequence. The correct answer is a static set of propositions listed in order, such that if a sceptic were to attend to the propositions in sequence, each should progressively dispel any doubt as it is pondered and understood, until the last one which should prove the theorem. So I ask (in the spirit of Beethoven and Goethe) what exactly is the mathematics here? Is it that static list of propositions? Or is it the time-dependent development of concepts and understanding in the conscious mind of the person either reading the list or originating it in the first place? Of course I claim it is the latter, and I suspect you would say it is the former.

If you are right, I'm wondering where that list was at or around the time of the BB, and wherever it was, how did it get to be there? Talk about complexity.

If I am right, then there is definitely a time-dependency involved in "doing mathematics".

In the context of the Barber of Seville, what you call a problem with self-referentiality, I say is due to the time-dependence. For example, in the definition, Let A = {A,B}, you would say it is self-referential because 'A' appears in the definition of 'A'. True enough. I agree.

But instead of simply legislating against self-reference because we have noticed it leads to problems, I say the problem arises because we have violated a rule I think we should abide by. That rule is that in the sequential development of the concepts of a system, any definition can be made using only terms that have been previously defined along with the undefined primitives. The "previously" gives the time-dependency away. This rule prevents recursive definitions, because at the "time" we set about to define 'A', in this example, we do not have a defined 'A' to use in the definition.

I have to eat some words here. I previously said about this example, "Logically, it seems to me that there is no reason we can't define 'A' this way." It now seems to me that there is good reason to disallow this definition. It is only when you view the list of propositions and definitions as a static entity that this definition seems to make logical sense. So, it seems to me that in your view you would say that the definition is logical, but it should be legislated against because it is self-referential. In my view, I say the definition is not legal because "at the time" the definition is being made, the term 'A' has not "yet" been defined. (The time-dependencies are in scare quotes.)

Now with regard to infinity, it isn't that I think the notion of infinity is the problem or leads to problems. What I think is that, first of all, I don't think you can, or at least nobody has yet, define the notion of infinity in a consistent way. The ancients defined it, if at all, in nonsensical ways. Cantor, with the first rigorous definition immediately noticed consequent paradoxes.

What I object to is the assumption that concepts can come into existence without first being conceived by a mind. So I object to all genetic methods of "producing" sets of infinite cardinality, such as the infinite set of integers. You seem to have a similar objection to some of the methods mathematicians have used to define the integers. As I said before, I don't agree with Leopold Kronecker who claimed that the infinite set of integers were given to us by God. The only integers we have available to us to use are those conceived by us directly, or those explicitly generated by finite machines conceived and built by us. In all such cases, the integers are finite, and there have only ever been a finite number of them defined and used. Moreover, I predict that there never will be a time when an infinite set of integers will be available for our use.

Thus having rejected the idea that "Russell’s paradox is a contradiction entailed only by notions of infinite sets", we get back again to the question of why you think the notion of an infinite set involves contradiction.

My position is not that infinity leads to problems. Instead my position is that we can't reasonably define anything infinite, and when we try to pull tricks to define infinity, those tricks lead to problems. The tricks, like Hilbert's genetic definitions, are what I think should be disallowed, just like the trick of recursive definition.


Warm regards,

Paul

 

[moving finger]

I think you'd need to ask this question of a physicist. Heisenberg was quite a bright chap and a good physicist, and not in the habit of voicing his personal beliefs as if they were facts.

None of that makes him infallible.

A wave-particle seems a good example.

In what sense? Can you express this in a form of a proposition which has neither a “yes”, “no” nor “meaningless” answer?

Metaphysical questions are undecidable because both of their 'reasonable' answers give rise to contradictions. By 'reasonable' here I mean reasonable according to rules of ordinary logic. For example, the proposition that the universe arises ex nihilo is logically incoherent, the proposition that it arises from something pre-existent is logically incoherent, and therefore the question of how it arises is a metaphysical (undecidable) question.

Why is the notion that the universe has existed for all time incoherent?

A meaningless question does not have a yes/no answer, but this does not mean we have rejected the law of the excluded middle.

Do you think Heisenberg didn't know this?

Canute, with all due respect it gets a little tiring when you simply keep referring to other people when backed into a corner, instead of addressing the issue at hand. Other people, even brilliant scientists, are not infallible, and they don’t have the secret to the universe. Again with all due respect I think you need to start forming your own opinions, supported by your own arguments. To continually refer to “other experts” without further argument is self-defeating and does not constitute a rational or logical argument in support of your position.

Very true. Let us say then the the universe arises only in a particular sense.

In what sense? What exactly do you mean by “the universe arises”?

To a mystic asking whether the universe arises from something or nothing is like me asking you whether you've stopped beating your wife. In Zen the repsonse may be 'Mu', a word meaning, roughly, there is nothing to say because the question embodies a false assumption and any answer would therefore be misleading.

What false assumption does it embody, in your opinion?

I gather that you're a logical positivist.

How on Earth do you arrive at this conclusion?

If you disagree, perhaps you could provide an example of a proposition which you believe is neither true, false nor meaningless, but is instead “imaginary”?

Light is a wave.

Whether light is measured to be a wave or a particle depends on how you measure it. Specify how it will be measured and this determines whether you will measure it to be a wave or a particle.

Human being have freewill.

Define freewill, then we may be able to debate this further.

Light is a particle.

Whether light is measured to be a wave or a particle depends on how you measure it. Specify how it will be measured and this determines whether you will measure it to be a wave or a particle.

Human being do not have freewill

Define freewill, then we may be able to debate this further.

The universe arises ex nihilo. The universe arises from something.

Define “arise from” then we may be able to debate this further. Do you assume a backdrop of time against which the universe “arises”?

God exists. God does not exist.

Either of these may be true – the fact that we do not know which is true does not make the proposition “imaginary” – it simply points to limits in our knowledge.

Bear in mind that the term 'imaginary' is used in its mathematical sense.

Bear in mind that the term “imaginary” in mathematics means something quite different to “imaginary” in normal language. A proposition based on mathematical imaginary terms is still either true or false (or meaningless).

You see – no imaginary propositions at all (excluding the mathematical kind of course – if you wish to claim that all imaginary propositions are of the mathematical kind then I do not disagree)

Point number one is that I regrettably use the term 'PC' to refer to two separate and distinct entities: first is the truly primordial entity, about which we can say very little if anything, and which existed only as prior to and until the first change of anything occurred.

Can you elaborate on the properties/abilities of this entity? What was it capable of?

The important issue (it seems to me) is to establish which properties/abilities are truly primordial (ie a priori, or in the boundary conditions), and which properties/abilities are emergent. If you are now claiming that all the PC’s properties/abilities are emergent and not primordial then that is worth clarifying.

So, when you claim that my notion of PC is "inherently complex", I agree only as long as you mean PC in the second sense above. It was not complex at the outset.

You will need to explain then just what properties/abilities you believe your “PC at the outset” possesses, before we can move on.

You would be correct in suspecting that I feel that need as long as you interpret the term 'world' to mean our familiar 4D physical space-time continuum which began its existence with the BB. In this case, I do feel the need to assume such properties as being extant sometime prior to the BB in order to adequately explain the high improbability of the BB's initial boundary conditions and to adequately explain other phenomena such as the origin of life and the origin of consciousness in living organisms.

Ahhh, now this is interesting. Which particular BB boundary conditions are you referring to? Are you suggesting that the PC is responsible for deliberately manipulating the BB conditions such that our universe would be conducive to the emergence of biological lifeforms, in some kind of PC-managed “experiment”?

On the other hand, if you interpret 'world' to mean all of reality, then I think you and I are pretty much in agreement. We both think things (the world of reality) started out extremely simple, and that all complexity emerged as a result of recombinant changes over long periods of time. We disagree on some details, like the lengths of time involved (my estimate being vastly longer than yours), or the sequence of appearance of various specific phenomena (e.g. consciousness vs. organisms, concepts vs. mind).

I wonder why you think it requires more than 13 billion years for such things to emerge?

Probably the most contentious of these details is whether there is some fundamental constituent of consciousness (whatever that is) which was primordial. I say "yes" and I think you say "no".

That is correct. I believe consciousness is emergent, not primordial. Even if yoru PC has no other properties, this is one thing that makes your premise inherently more complex (in the sense of packing more into the assumptions).

But in my view, whatever that fundamental constituent is (was), it is not at all the complex entity or idea we refer to as consciousness (whatever it is). I have speculated that the fundamental constituent is something like a rudimentary ability to know, or ability to realize, or as Lars suggested, an ability to experience, or as Gregg Rosenberg has suggested, a receptive principle.

It seems to be a matter of opinion as to whether that is a complex assumption or not. It doesn’t seem any less complex (to me) than “In the beginning was the Word, and the Word was God…….”

Now to figure out whether such a primordial ability or principle can give rise to consciousness as we know and experience it, it seems to me, would take the same sort of investigation Goethe and Beethoven went through trying to identify the same thing for music (as the two of us imagined it).

It seems that once one posits a primordial consciousness, then surely any type of emergent consciousness is possible – the sky is the limit. Nothing is really left in the explanation, since all the important properties are packed into the assumptions.

But to draw a comparison, you can have vibrations without a mind, but you can't have music without both vibrations and a mind.

That depends on one’s definition of music. If one defines music in the same sense as you seem to define concept, then it is an inherently mental thing (in which case it entails a mind, by definition). But I do not see that it is necessary to define music in this sense.

I'd say that a similar thing is true for concepts: you can have entities or things without a mind, but you can't have concepts without a mind. And, further, I'd say that you can't have consciousness without a mind. These, of course are only my opinions, and even though I have poured them into your water glass, I don't expect that you will easily swallow them. That's fine. I just wanted to offer them to you and get your response.

It seems to me that it all comes down to definitions. You seem to define music as “something experienced by a mind”, and the same with concept, and the same with consciousness. If you define these concepts in such a way then of course it follows that they require a mind. But I do not see that this is the only way such concepts can be defined.

Perhaps we should start with consciousness. How would you define consciousness? What are the necessary and sufficient conditions for consciousness?

Yes, you have that right except that in this case, I claim that the boundary conditions we are talking about are the truly primordial conditions, which greatly precedes the BB. And, the "somehow 'built-in'" is the "fundamental constituent of consciousness" I talked about above. I believe there was such a constituent and you evidently don't.

Correct.

I should point out that I do believe in emergent phenomena. Moire patterns, and the Mandelbrot Set are examples of emergent phenomena. So is the wetness of water. But it is my opinion that conscious experience is different in kind from all emergent phenomena and that it requires something more to get it to happen or exist. I think that "something more" is ontologically fundamental. And, it seems that you can't swallow that.

I see no need to “swallow it”, because I believe I can see how consciousness emerges from non-consciousness. This being the case, why posit consciousness as being primordial?

I don't think it is that drastic. I think we are talking the same language, but that we have been using different connotations of the words 'PC' and 'world'. Hopefully, we can get over that misunderstanding. As I said before, I think our respective views of what actually happened at the ultimate "beginning" are not all that different.

Of course you would like to believe this, because the one of the arguments I am using against your PC is that it is inherently complex. At the end of the day, the fundamental difference between is that you believe consciousness is an a priori assumption (built-in to the boundary conditions) whereas I do not.

I was going to categorically deny this by saying that the theists have never defined their notion of 'God'.

It’s clearly defined in the bible. In the beginning was the Word, and the Word was God. That’s a very simple assumption, surely?

But I realized that I have never really defined my notion of 'PC' in its primordial state. I guess you are ahead of both the theists and me by not even identifying what you think might have been the primordial constituent of reality. So without identifying it, you don't have to define it.

I am not so arrogant or misguided to claim that we can possibly know what existed (if anything) prior to the Big Bang, but I do claim that the Big Bang itself was purely a physical process, and all complexity in our world, including consciousness, arose from purely emergent physical processes, and none of it is primordial. I believe we can explain emergent consciousness from first principles “within” the world defined by the Big Bang – whereas you seem to think that consciousness cannot be explained as an emergent process and therefore needs to be built-in to the premises.

But, as I have also pointed out, the theists posit huge (even infinite) complexity to their God in the beginning, whereas I posit only simplicity as you do.

Infinite complexity? What’s in a Word?

I know you would like us all to believe that your premise is simplistic. But as I have said, in the end your premise packs in consciousness as an a priori assumption – that makes it inherently more complex than any premise which posits complexity as an emergent property.

I think you would say that concepts, such as the implications of logical rules, exist independently, and more importantly, prior to the existence, of any mind.

Yes, I would.

In school, we are taught to develop proofs a step at a time and write them down in sequence. The correct answer is a static set of propositions listed in order, such that if a sceptic were to attend to the propositions in sequence, each should progressively dispel any doubt as it is pondered and understood, until the last one which should prove the theorem. So I ask (in the spirit of Beethoven and Goethe) what exactly is the mathematics here? Is it that static list of propositions? Or is it the time-dependent development of concepts and understanding in the conscious mind of the person either reading the list or originating it in the first place? Of course I claim it is the latter, and I suspect you would say it is the former.

I suggest you are confusing ontic with epistemic reality. The time-dependent development of concepts reflects our knowledge of mathematics (epistemic reality). The theorems that we prove true always have been true (ontic reality), even before we discovered those theorems. We do not suddenly “make something true” by proving it true – all we are doing is discovering a truth that was always there, waiting to be uncovered.

If you are right, I'm wondering where that list was at or around the time of the BB, and wherever it was, how did it get to be there? Talk about complexity.

That complexity was always there – even in your notion of the world. Take my example again of a right-angled triangle in a 2-dimensional plane conforming to Euclid’s 5 postulates of geometry. The law that the square of the hypotenuse is equal to the sum of the squares of the other two sides is a necessary mathematical law. Do you believe there is any way that the PC could have “created” a universe in which this law (given the postulates and definitions) would have been false?

Now with regard to infinity, it isn't that I think the notion of infinity is the problem or leads to problems. What I think is that, first of all, I don't think you can, or at least nobody has yet, define the notion of infinity in a consistent way. The ancients defined it, if at all, in nonsensical ways. Cantor, with the first rigorous definition immediately noticed consequent paradoxes.

OK, we are making progress. The diversion on Russell came about because you claimed that the notion of a “set of all logical possibilities” leads to contradiction, and I asked you to give an example. We have eliminated the Russell example that you gave. Do you have any other example?

(I have already mentioned my belief is that Cantor’s entire edifice is built on the incoherent notion that one can have an infinite set of finite integers – which is imho nonsensical but vehemently defended by the mathematical establishment)

What I object to is the assumption that concepts can come into existence without first being conceived by a mind. So I object to all genetic methods of "producing" sets of infinite cardinality, such as the infinite set of integers. You seem to have a similar objection to some of the methods mathematicians have used to define the integers. As I said before, I don't agree with Leopold Kronecker who claimed that the infinite set of integers were given to us by God. The only integers we have available to us to use are those conceived by us directly, or those explicitly generated by finite machines conceived and built by us. In all such cases, the integers are finite, and there have only ever been a finite number of them defined and used. Moreover, I predict that there never will be a time when an infinite set of integers will be available for our use.

It depends what you mean by “available for our use”. We “make use” of real numbers like e and Pi and 1/3 and root 2, all of which are irrational hence “infinite” in length when expressed as numbers.

My position is not that infinity leads to problems.

That’s progress. Earlier you were claiming that infinity leads to contradictions (which implies problems).

Instead my position is that we can't reasonably define anything infinite, and when we try to pull tricks to define infinity, those tricks lead to problems. The tricks, like Hilbert's genetic definitions, are what I think should be disallowed, just like the trick of recursive definition.

We cannot reasonably define anything infinite?
How many digits are there in the full decimal expansion of Pi, or of root 2, or of e?
Perhaps you cannot conceive of the full decimal expansion, therefore you conclude that it does not exist. This gets back to our fundamental difference in belief in the Platonic world. I believe that the full decimal expansion of Pi exists in the Platonic world, but I guess you do not.

Best Regards

 

[Canute]

None of that makes him infallible.

Of course not. But he's more infallible on QM than you or me.

In what sense? Can you express this in a form of a proposition which has neither a “yes”, “no” nor “meaningless” answer?

I gave you half a dozen when you asked the first time.

Why is the notion that the universe has existed for all time incoherent?

If by 'universe' you mean this one then this would be obvious. If you mean 'all that there is' then it would mean that time existed 'before the BB'.

In what sense? What exactly do you mean by “the universe arises”?

Well, clearly this universe appears to exist, and clearly once it didn't.

What false assumption does it embody, in your opinion?

The assumption that the universe arises from something or nothing.

How on Earth do you arrive at this conclusion?

Because you argue that metaphysical questions are analytically or self-referentially undecidable and not statements about the world.

Whether light is measured to be a wave or a particle depends on how you measure it. Specify how it will be measured and this determines whether you will measure it to be a wave or a particle.

Exactly.

Define freewill, then we may be able to debate this further.

Maybe we've got enough disagreements on the go already.

Define “arise from” then we may be able to debate this further. Do you assume a backdrop of time against which the universe “arises”?

According to physicists spacetime came into existence with the universe.

Either of these may be true – the fact that we do not know which is true does not make the proposition “imaginary” – it simply points to limits in our knowledge.

I'm suggesting that neither of them are true.

Bear in mind that the term “imaginary” in mathematics means something quite different to “imaginary” in normal language. A proposition based on mathematical imaginary terms is still either true or false (or meaningless).

You miss the point. Brown suggests that we use complex values in our thinking. He is not suggesting that some propositions are imaginary, he's suggesting that some questions have complex answers.

You see – no imaginary propositions at all (excluding the mathematical kind of course – if you wish to claim that all imaginary propositions are of the mathematical kind then I do not disagree)

What do you mean by an 'imaginary proposition'?

regards
Canute

 

[moving finger]

None of that makes him infallible.

Of course not. But he's more infallible on QM than you or me.

When he joins the forum I’ll bear that in mind.

In what sense? Can you express this in a form of a proposition which has neither a “yes”, “no” nor “meaningless” answer?

I gave you half a dozen when you asked the first time.

And none of the ones you gave entail “imaginary” status. They can each be treated as either true, false or meaningless.

Why is the notion that the universe has existed for all time incoherent?

If by 'universe' you mean this one then this would be obvious. If you mean 'all that there is' then it would mean that time existed 'before the BB'.

It’s not at all obvious. If time was created along with the BB then our universe (ie the one resulting from the BB) has existed for all time, by definition.

In what sense? What exactly do you mean by “the universe arises”?

Well, clearly this universe appears to exist, and clearly once it didn't.

“once” means “on one occasion only, at one time, at a particular time” - the statement “once it didn’t” therefore implicitly assumes a time when the universe did not exist. But if time was created along with the BB then there was no time when the universe did not exist (these kinds of concepts should appeal to a mystic)

What false assumption does it embody, in your opinion?

The assumption that the universe arises from something or nothing.

Which is exactly what you have done yourself – in saying (as you did earlier) that “the universe arises” you have already assumed some backdrop of time against which it arose. That may be a false assumption.

How on Earth do you arrive at this conclusion?

Because you argue that metaphysical questions are analytically or self-referentially undecidable and not statements about the world.

Could you give an example where I have done this?

Whether light is measured to be a wave or a particle depends on how you measure it. Specify how it will be measured and this determines whether you will measure it to be a wave or a particle.

Exactly.

Which goes to show that the question is meaningless unless it is formulated correctly – ie to include the way it will be measured. Nothing to do with imaginary.

Define freewill, then we may be able to debate this further.

Maybe we've got enough disagreements on the go already.

Then I cannot agree that this is an example of an imaginary proposition.

Define “arise from” then we may be able to debate this further. Do you assume a backdrop of time against which the universe “arises”?

According to physicists spacetime came into existence with the universe.

That’s interesting, don’t you think? Then how can it make sense to ask what was (temporally) before the universe? Again a meaningless question.

Either of these may be true – the fact that we do not know which is true does not make the proposition “imaginary” – it simply points to limits in our knowledge.

I'm suggesting that neither of them are true.

And I’m suggesting that, if the question has any meaning, one of them is true and one of them is false. We just don’t know which.

Bear in mind that the term “imaginary” in mathematics means something quite different to “imaginary” in normal language. A proposition based on mathematical imaginary terms is still either true or false (or meaningless).

You miss the point. Brown suggests that we use complex values in our thinking. He is not suggesting that some propositions are imaginary, he's suggesting that some questions have complex answers.

I thought we were talking about whether a proposition could be evaluated in terms of “true” “false” “meaningless” or “imaginary”? Can you explain how we now get onto the issue of complex answers?

You see – no imaginary propositions at all (excluding the mathematical kind of course – if you wish to claim that all imaginary propositions are of the mathematical kind then I do not disagree)

What do you mean by an 'imaginary proposition'?

I thought we were talking about whether a proposition could be evaluated in terms of “true” “false” “meaningless” or “imaginary”. If a proposition is evaluated “true” then it would be a true proposition. Similarly, if a proposition were evaluated “imaginary” (if such a thing has any meaning) then it seems to me that it would be reasonable to call it an imaginary proposition. Would you prefer a different expression?

Best Regards

 

[Tournesol]

By 'reasonable' here I mean reasonable according to rules of ordinary logic. For example, the proposition that the universe arises ex nihilo is logically incoherent,

Not really. "Everything must have a cause" is itself metaphsyics,
not logic.

However, if we modify the tertium non datur rule this opens up a third possibility.

In Zen the repsonse may be 'Mu', a word meaning, roughly, there is nothing to say because the question embodies a false assumption and any answer would therefore be misleading.

A false assumption like "everything must have a cause" ?
But that is again a modification to
metaphysics, not logic.

 

[Eric England]

Not really. "Everything must have a cause" is itself metaphsyics, not logic.

I would think it depends on the definition of logic. I think Homer and Bart said it best, when Bart said "duh"and Homer said "doh"!

 

[selfAdjoint]

Kant remarked that to say the universe came into existence at some moment, and to say that there is an infinite regress of prior causes, are both incoherent. You pays your money and you takes your choice.

 

[Tournesol]

The definition of logical truth is "that which cannot be denied withut
contradiction". "Every event has a cause" can be denied without
contradiction.

 

[moving finger]

In Zen the repsonse may be 'Mu', a word meaning, roughly, there is nothing to say because the question embodies a false assumption and any answer would therefore be misleading.

In science, Mu would be translated as “meaningless”.

Example Question : In the absence of any kind of measurement, is the quantum object a wave?

Answer : The question is meaningless, because it embodies a false assumption (that a quantum object has either a wave or a particle property in absence of measurement), and any answer would therefore be misleading. Presumably a Zen Buddhist would in such a case answer Mu.

Similarly, to ask "Is the King of France bald?" is meaningless (Mu), because it makes a false assumption that there is an existing entity which is "the King of France".

As I’ve pointed out earlier, “True”, “False” and “Meaningless’ are all we need.

Best Regards

 

[moving finger]

Kant remarked that to say the universe came into existence at some moment, and to say that there is an infinite regress of prior causes, are both incoherent. You pays your money and you takes your choice.

If time is created along with the universe, then neither of Kant's alternatives are applicable. In such a case, the universe would not come into existence at any "moment", because the very idea of associating a moment with the creation assumes a backdrop of time against which the universe is created. Neither would there need to be an infinite regress of prior causes (since this also assumes a time prior to the creation).

Did Kant address this possibility? That it perhaps makes no sense to talk of time existing prior to the universe "coming into existence", because time is created along with the universe?

Best Regards

 

[Tournesol]

No, several of K's anomalies are undermined
by modern develoments.

 

[Canute]

As Self-Adjoint mentions, Kant was clear about the incoherence of both these ways of conceiving of the origin of the universe. But all philosophers reach the same view as far as I know. This is why the questions of its origin is an undecidable metaphysical question. As S-E says, we pays our money and we take our choice. Unless, that is, we modify the tertium non datur rule.

When he joins the forum I’ll bear that in mind.

Ok. I prefer to assume he knew more than you and I do about physics and formal logic even though he isn't a member.

And none of the ones you gave entail “imaginary” status. They can each be treated as either true, false or meaningless.

Or they can be treated as having complex values for answers, as I am suggesting.

It’s not at all obvious. If time was created along with the BB then our universe (ie the one resulting from the BB) has existed for all time, by definition.

Yes. Here we meet a language problem. My view is that time is not fundamental, that it has no inherent existence. However, as Huxley points out in his book on mysticism, the words we use are designed for use in time and this causes all sorts of problems. You have to allow a bit of slack on this topic, otherwise it becomes impossible to discuss it. The universe exists in some sense so it arises in some sense. But by saying this I do not mean to imply that time is fundamental, or that the universe exists inherently.

Which is exactly what you have done yourself – in saying (as you did earlier) that “the universe arises” you have already assumed some backdrop of time against which it arose. That may be a false assumption.

I completely agree. In the Buddhist view the phenomena of this world are 'evanescent thing-events' rather as they are in physics and exist, inasmuch as they do, now and only now. There's probably a better term than 'arise' I could have used, but I suspect all the alternatives would also imply time.

Could you give an example where I have done this?

No need. I must have misjudged you position from what you've been saying about solipsism. I though you must apply the same logic to all metaphysical questions. Obviously not.

Which goes to show that the question is meaningless unless it is formulated correctly – ie to include the way it will be measured. Nothing to do with imaginary.

I think you'll see this is not the case if you rephrase the question as 'What is it that, when we observe it, appears to be either a particle or a wave?

This is not a meaningless question unless we assume that particles and waves are two things rather than two aspects. If they are two things then yes, the question would be meaningless. But if they are the dual-aspects of something ontologically prior then the question is meaningful and has a complex value, in Brown's sense of the term, for an answer. The answer, whatever it is, requires that as well as particles and waves there is something that is not a particle or a wave. Thus, as well as these two logical possibilities there is a paradoxical third option. We have no term for this third thing so just call it a 'wave-particle' or 'wavicle'. It's the best we can do in natural language. The concept of a 'wavicle' is pardoxical precisely because it contravenes the 'no third option' rule.

Then I cannot agree that this is an example of an imaginary proposition.

I'm not suggesting there's any such thing as an 'imaginary proposition'. But see below.

That’s interesting, don’t you think? Then how can it make sense to ask what was (temporally) before the universe? Again a meaningless question.

It is not meaningless to ask what was prior to the Big Bang as long as we are careful not to make assumptions about what we mean by 'prior'. If we mean previous in time then I'd say that it's not a meaningless question but an irrational one. But it is possible to ask what is prior to spacetime without descending into meaninglessness as long as we accept that to do so we have little choice but to use rather inapropriate terms.

And I’m suggesting that, if the question has any meaning, one of them is true and one of them is false. We just don’t know which.

Yes, I know this is what you're suggesting. What I'm suggesting is that we should introduce complex values into our reasoning in order to overcome the paradoxes the result from your assumption, which is the assumption that gives rise to all the undecidable questions that plague metaphysics.

I thought we were talking about whether a proposition could be evaluated in terms of “true” “false” “meaningless” or “imaginary”? Can you explain how we now get onto the issue of complex answers?

Sure. Brown gives examples of contradictions that arise is ordinary equation theory that we currently solve by the use of complex values (such as sqrt-1). He goes on to suggest, consistent with the idea that mathematics can model reality, that we adopt the same approach to solve the contradictions that arise in metaphysics. He claims that the need to take this approach follows from the nature of reality. (In other words, this is not just a question of adopting a convenient methodology).

For example. In Brown's view solipsism is neither true nor false. We've had enough battles over this one so pick any metaphysical of your choice. Take the question - Is the universe caused? Metaphysicians are stumped completely by this one. Neither answer makes sense. Brown's suggestion is that this is because we refuse to suspend the tertium non datur rule in metaphysics, even though we modify it all the time in quantum mechanics and mathematics. The 'complex value' here, which would be the answer to this 'first cause' question, is 'yes and no'. Here we find ourselves back with the 'causeless cause' of Taoist cosmology and of the perennial philosophy in general.

You may not agree with Brown but it is worth noting that some understanding of his ideas will make the mystical cosmology much more comprehensible. In this view metaphysical questions are undecidable because neither of their answers is correct.

I thought we were talking about whether a proposition could be evaluated in terms of “true” “false” “meaningless” or “imaginary”. If a proposition is evaluated “true” then it would be a true proposition. Similarly, if a proposition were evaluated “imaginary” (if such a thing has any meaning) then it seems to me that it would be reasonable to call it an imaginary proposition. Would you prefer a different expression?

I see what you mean but yes, personally I find this a slightly confusing expression. (Even though your's may be a mathematically correct expression). I prefer to think of this in terms of questions and answers. This amounts to the same thing but avoids the phrase 'imaginary proposition' which sounds a bit peculiar in everyday language.

The question 'Does God exist?' would be meaningful - the general view these days is that the logical positivists failed in the end to show that such questions are not meaningful - but would not have a yes or no answer. This is the view of the mystics and of many modern theologians. It is not that the answer cannot be known, so it is said. The question does not have a yes or no answer precisely because its answer can be known and it is not yes or no. Those who claim to know the answer say that the truth is too subtle to express in a on/off, yes/no, wave/particle kind of way.

In science, Mu would be translated as “meaningless”.

Yeah, that's close enough unless you want to be picky.

Example Question : In the absence of any kind of measurement, is the quantum object a wave?

Answer : The question is meaningless, because it embodies a false assumption (that a quantum object has either a wave or a particle property in absence of measurement), and any answer would therefore be misleading. Presumably a Zen Buddhist would in such a case answer Mu...

Similarly, to ask "Is the King of France bald?" is meaningless (Mu), because it makes a false assumption that there is an existing entity which is "the King of France".

This isn't a correct understanding of the use of the word, but it's something like this.

As I’ve pointed out earlier, “True”, “False” and “Meaningless’ are all we need.

Yes. However, what you've said does not determine what is the case.

Cheers
Canute

 

[Eric England]

How about "mass, space, and time can neither be created nor destroyed – but are infinitely existent within something greater in principle"?

(maybe the "big bang" is just a metaphor for "geeks wanting a date"?)

 

[Tournesol]

As Self-Adjoint mentions, Kant was clear about the incoherence of both these ways of conceiving of the origin of the universe.

And clearly wrong in some cases.

But all philosophers reach the same view as far as I know.

Nowadays, philosophers are clear that you can't reach two opposite conclusions using the same assumptions. Kant's antinomies
are not genuine dichotomies.

This is why the questions of its origin is an undecidable metaphysical question. As S-E says, we pays our money and we take our choice. Unless, that is, we modify the tertium non datur rule.

We don't need to modify T.N.D if we are not dealing with genuine
dichotomies. Moreover, where his we can find a way through
his antinomies (for instance with the finte-but-unbounded
universe) we are appealing to specific ideas, not a
vague yes-and-no.

 

[Mickey]

Simply put, the 4D conception of the universe and our place in it is our working model and provisional. It makes no difference what anyone believes. If it's true, we'll get to it through the course of our investigation.

Unless, of course, you believe that belief alone can create or somehow secure truth (a not uncommon view), in which case you'll find yourself in an epistemological quandary, and a cold and isolated one in my opinion.

 

[Canute]

Nowadays, philosophers are clear that you can't reach two opposite conclusions using the same assumptions. Kant's antinomies
are not genuine dichotomies.

I sort of agree with the first statement, but I'd rather say that we can reach two opposite conclusions from the same assumption and that when we do this shows the assumption is absurd, which to me was Kant's point.

But if this second statement is true how would we explain why metaphysics still exists as an academic discipline?

 

[Paul Martin]

Can you elaborate on the properties/abilities of this entity? What was it capable of?

The truly primordial PC has only one property/ability. My guess is that that property/ability can be approximately characterized as the ability to know, or to realize, or to experience, or as a receptive principle.

The evolved PC developed additional emergent properties/abilities which I think you characterized pretty well with your list: "it thinks, it knows, it understands, it perceives, it makes decisions, it is conscious, it has intentions and desires". In addition, I think it can be confused, surprised, pleased, disappointed, and capable of making errors.

The important issue (it seems to me) is to establish which properties/abilities are truly primordial (ie a priori, or in the boundary conditions), and which properties/abilities are emergent. If you are now claiming that all the PC’s properties/abilities are emergent and not primordial then that is worth clarifying.

I hope the above response has made the distinction clear.

I believe I can see how consciousness emerges from non-consciousness. This being the case, why posit consciousness as being primordial?

Again, I don't think we are that far apart. If you review the list above, you will see that 'consciousness' appears as a property of the evolved PC, not the primordial PC. What I posit as being primordial is that elusive property I have identified with the ability to know, etc. Whatever that property is, I would say that it is non-conscious by definition. So I agree with you that consciousness evolved and emerged from non-consciousness. But...and I think this is the difference between you and me, I think that there was a primordial constituent which provided a necessary condition for consciousness: something like an ability to know or a receptive principle.

It seems to be a matter of opinion as to whether that is a complex assumption or not. It doesn’t seem any less complex (to me) than “In the beginning was the Word, and the Word was God…….”

I agree. Opinions vary widely on this question.

Ahhh, now this is interesting. Which particular BB boundary conditions [for the Big Bang] are you referring to?

At least these:
1. The choice of logic system and axiomatic system used to derive the algorithms (laws of physics) which determine the geometry of the "universe" and the behavior of particles, waves, and other constituents of the "universe".

2. The choice of physical constants such as the "Just Six Numbers" described by Martin Rees.

Are you suggesting that the PC is responsible for deliberately manipulating the BB conditions such that our universe would be conducive to the emergence of biological lifeforms, in some kind of PC-managed “experiment”?

Yes. I suspect that many alternatives might have been tried "before" those of our universe were stumbled upon or otherwise figured out.

I wonder why you think it requires more than 13 billion years for such things to emerge?

Just a hunch.

It seems to me that it all comes down to definitions.

Yes. I think our differences are primarily, if not exclusively, semantic.

You seem to define music as “something experienced by a mind”, and the same with concept, and the same with consciousness. If you define these concepts in such a way then of course it follows that they require a mind. But I do not see that this is the only way such concepts can be defined.

I would be very interested to hear one of those other ways.

Perhaps we should start with consciousness. How would you define consciousness?

I made an attempt at this some time ago, and you had trouble accepting it. I defined consciousness to be an experience that I have. I suggested that you define consciousness as an experience you have and that we try to reconcile our respective definitions by engaging one or more third parties and compare reports of the experience. Thus we could make the subjective objective by noticing that when another person reports his/her subjective experience, which to us would be objective, it could be compared to other objective reports. To the extent that a consistent set of reports emerges, it could be taken to be an objective definition of 'consciousness'. Of course, if people have different experiences, for example if some are truly "conscious" and others are not, it might be difficult to infer that fact.

What are the necessary and sufficient conditions for consciousness?

Good question. I have suggested that the ability to know, or to experience, or to realize is a necessary condition. As for being sufficient, I suspect that some sort of logical calculus, as employed by Spencer-Brown, might be able to demonstrate that all the features/properties of consciousness could be inferred from that one necessary condition. That's just another hunch, but it might be worth pursuing.

I believe we can explain emergent consciousness from first principles “within” the world defined by the Big Bang – whereas you seem to think that consciousness cannot be explained as an emergent process and therefore needs to be built-in to the premises.

Close. I think that consciousness cannot be explained as an emergent process "within" the world defined by the Big Bang and that it needs some initial built-in primordial condition.

I suggest you are confusing ontic with epistemic reality. The time-dependent development of concepts reflects our knowledge of mathematics (epistemic reality). The theorems that we prove true always have been true (ontic reality), even before we discovered those theorems. We do not suddenly “make something true” by proving it true – all we are doing is discovering a truth that was always there, waiting to be uncovered.

Thank you for the suggestion. But I would say that almost all ontic reality is epistemic reality. "Almost" because whatever that initial necessary condition was (the ability to know, etc.) it is the only ontic reality. From then on, the epistemic reality as developed by PC as it evolved came to comprise what we normally think of as physical reality. In a sense PC discovered the implications of consistency, which did not in itself make them true, but they did not exist either ontologically nor epistemically until the initial premises were chosen. Now, whether the implications came into existence then or waited until they were discovered, is, I suppose, an open question. But I maintain that they did not exist prior to the choice of the premises. The limitations on the movements of the bishop did not exist prior to the definition of the game of Chess.

If you are right, I'm wondering where that list was at or around the time of the BB, and wherever it was, how did it get to be there? Talk about complexity.

That complexity was always there – even in your notion of the world. Take my example again of a right-angled triangle in a 2-dimensional plane conforming to Euclid’s 5 postulates of geometry. The law that the square of the hypotenuse is equal to the sum of the squares of the other two sides is a necessary mathematical law. Do you believe there is any way that the PC could have “created” a universe in which this law (given the postulates and definitions) would have been false?

Yes, I believe there is a way in which the PC could have "created" a universe in which the Pythagorean theorem does not hold. That way is to choose an initial geometry which is non-Euclidean. PC is not restricted to choosing Euclid's 5 postulates. If other postulates are chosen, different consistent geometries result in which the Pythagorean theorem does not necessarily hold. I maintain that the Pythagorean theorem did not exist, ontically or epistemically until after the postulates of Euclid were defined and considered. So in my view, that complexity was not always there, which makes your scheme more complex than mine.

It depends what you mean by “available for our use”. We “make use” of real numbers like e and Pi and 1/3 and root 2, all of which are irrational hence “infinite” in length when expressed as numbers.

You might say we make use of the notion, but I claim that we do not ever make use of the numbers, like e, Pi, and root 2. We make use only of rational approximations to those "numbers". The number 1/3 is different. It is a rational number and we can use its exact value in calculations.

We cannot reasonably define anything infinite?

That's what I am saying.

How many digits are there in the full decimal expansion of Pi, or of root 2, or of e?

"Full"? What do you mean by 'full'? Do you mean 'all'? I have already explained why the notion of "all" leads to trouble. The same trouble arises when you try to define the "full decimal expansion of Pi.

This gets back to our fundamental difference in belief in the Platonic world. I believe that the full decimal expansion of Pi exists in the Platonic world, but I guess you do not.

True, I do not. And it gets back to my question of where that expansion, or the Platonic world was at or around the time of the Big Bang. You said "That complexity was always there" which seems to be much more complexity than I posit. It seems as complex as "turtles all the way down" to me.

Good talking with you, MF

Warm regards,

Paul

 

[Paul Martin]

As I’ve pointed out earlier, “True”, “False” and “Meaningless’ are all we need.

I agree with Canute here. There is a fourth category of propositions, which, after thinking about it probably is bigger than the first two categories combined and might even be larger than the "Meaningless" category.

The fourth category is "It depends". It depends on the resolution of ambiguity.

So, I say that Canute's example of "God exists." falls in the fourth category. It depends on what you mean by 'God'. If, by 'God' you mean 'the Sun', then not many people would deny the existence of the Sun, so by definition, "God exists" would be true. Other clarifications of the meaning of 'God' would make the proposition false. And, I would suggest, a great many others would make the proposition meaningless.

Brown suggests that we use complex values in our thinking. He is not suggesting that some propositions are imaginary, he's suggesting that some questions have complex answers.

I can't speak for Brown, but I would suggest being careful in our use of words like 'imaginary' and 'complex'. Both these words have fairly well understood connotations in ordinary usage, and they both have precisely defined meanings in mathematics. It is a stretch to find cases in which both the vernacular and the mathematical definitions make sense for the same usage and where the meaning is the same either way.

Nonetheless, I think that the terms were well-chosen by mathematicians to illustrate how certain mathematical concepts were received when first introduced, and that they can still be helpful to us in pondering some new and complex ideas, as long as we are careful.

I thought we were talking about whether a proposition could be evaluated in terms of “true” “false” “meaningless” or “imaginary”. If a proposition is evaluated “true” then it would be a true proposition. Similarly, if a proposition were evaluated “imaginary” (if such a thing has any meaning) then it seems to me that it would be reasonable to call it an imaginary proposition. Would you prefer a different expression?

I think the expression 'imaginary' fits very well to my fourth category. These statements depend for their truth or falsity on someone's world-view, i.e. on their imagination. Statements in this category are true or false or meaningless only in the context of some particular imagined world-view.

It is not meaningless to ask what was prior to the Big Bang as long as we are careful not to make assumptions about what we mean by 'prior'. If we mean previous in time then I'd say that it's not a meaningless question but an irrational one. But it is possible to ask what is prior to spacetime without descending into meaninglessness as long as we accept that to do so we have little choice but to use rather inapropriate terms.

I think this is an excellent example of what I am talking about. It depends on what you mean by 'time'. I'm not sure, but I suspect that when Hawking talks about "imaginary time", he is trying to describe a notion which has a mathematical analog in the notion of imaginary numbers. I don't think he is using the term as we use it in vernacular English.

If the number line is seen as a dimension of space, then the addition of the complex numbers adds a second dimension to the number space making it a number plane. Similarly, I think that if time is seen as a dimension, then we may posit that there is another dimension of time producing a temporal plane rather than simply a line. So if we ask "What is prior to spacetime as originated by the BB?" we must be clear about which dimension of time we mean. I think that for the dimension of time marked by our clocks and calendars, the question is meaningless. But I think that if we mean a second and distinct dimension of time, then the question might very well have a meaningful answer.

If time is created along with the universe, then neither of Kant's alternatives are applicable. In such a case, the universe would not come into existence at any "moment", because the very idea of associating a moment with the creation assumes a backdrop of time against which the universe is created. Neither would there need to be an infinite regress of prior causes (since this also assumes a time prior to the creation).

I don't think Kant considered the possibility of multiple temporal dimensions. If time is created along with the universe, then it seems reasonable that this might be a new dimension of time, which does not rule out the possibility that there was at least one previously existing dimension of time, which would still exist as one axis of a temporal plane.

It is not meaningless to ask what was prior to the Big Bang as long as we are careful not to make assumptions about what we mean by 'prior'. If we mean previous in time then I'd say that it's not a meaningless question but an irrational one. But it is possible to ask what is prior to spacetime without descending into meaninglessness as long as we accept that to do so we have little choice but to use rather inapropriate terms.

I'd say it is not meaningless to ask what was prior to the Big Bang as long as we are careful to make assumptions, and to be clear about them, about what we mean by 'prior'. In particular, we need to be clear about which time dimension we are talking about.

Warm regards,

Paul

 

[moving finger]

Hi Paul

I have tried to focus on responding to the parts of your post where I believe there are issues worthy of further discussion.

The truly primordial PC has only one property/ability. My guess is that that property/ability can be approximately characterized as the ability to know, or to realize, or to experience, or as a receptive principle.

Quite a few concepts packed into here.

What is “ability to know” in this context? In the context of human knowledge we may define knowledge as justified true belief, which entails that the agent forms a justified belief about something which is also a true belief. But it seems to me that you mean something quite different when you use knowledge in the context of the PC. But what exactly?

Does the ability of the PC to “know”, “realise” and “experience” entail that the PC is conscious? I guess yes, but I would need you to confirm this.

The evolved PC developed additional emergent properties/abilities which I think you characterized pretty well with your list: "it thinks, it knows, it understands, it perceives, it makes decisions, it is conscious, it has intentions and desires". In addition, I think it can be confused, surprised, pleased, disappointed, and capable of making errors.

Most of these properties would seem to be inherent in the primordial PC. How can it know or realize, for example, without thinking? How can it realize without understanding? How can it experience without perceiving? How can it do any of these things without being conscious?

I hope the above response has made the distinction clear.

Yes, it has helped. Unfortunately it also confirms that your primordial PC possesses a lot of inherently complex properties. I know you will deny these are complex, but so too can the theist deny that God is complex.

Again, I don't think we are that far apart. If you review the list above, you will see that 'consciousness' appears as a property of the evolved PC, not the primordial PC. What I posit as being primordial is that elusive property I have identified with the ability to know, etc. Whatever that property is, I would say that it is non-conscious by definition.

That seems a difficulty to me. Any normal definition of knowledge would entail that the agent possessing that knowledge is conscious. Could you define clearly what you mean by knowledge in this context?

So I agree with you that consciousness evolved and emerged from non-consciousness. But...and I think this is the difference between you and me, I think that there was a primordial constituent which provided a necessary condition for consciousness: something like an ability to know or a receptive principle.

I cannot comment until I understand better just what you mean by “know” in this context. Clearly you do NOT mean justified true belief (the standard definition of knowledge), because belief entails consciousness.

I would be very interested to hear one of those other ways.

Music could be defined as particular vibrations which conform to certain rules.

I made an attempt at this some time ago, and you had trouble accepting it. I defined consciousness to be an experience that I have. I suggested that you define consciousness as an experience you have and that we try to reconcile our respective definitions by engaging one or more third parties and compare reports of the experience. Thus we could make the subjective objective by noticing that when another person reports his/her subjective experience, which to us would be objective, it could be compared to other objective reports. To the extent that a consistent set of reports emerges, it could be taken to be an objective definition of 'consciousness'. Of course, if people have different experiences, for example if some are truly "conscious" and others are not, it might be difficult to infer that fact.

Imho the problem with this is that it is not a definition of “what is meant by the word consciousness”, it is rather a description of “one of the possible properties of consciousness’ (viz – it is an experience one has). It seems to me to be much like defining a car as “an object combining metal, glass and rubber”.

What are the necessary and sufficient conditions for consciousness?

Good question. I have suggested that the ability to know, or to experience, or to realize is a necessary condition. As for being sufficient, I suspect that some sort of logical calculus, as employed by Spencer-Brown, might be able to demonstrate that all the features/properties of consciousness could be inferred from that one necessary condition. That's just another hunch, but it might be worth pursuing.

OK. To make progress we’ll need to know how you define knowledge in this context. I’m assuming that the JTB definition is not what you have in mind.

Yes, I believe there is a way in which the PC could have "created" a universe in which the Pythagorean theorem does not hold. That way is to choose an initial geometry which is non-Euclidean.

Paul, you are not reading my question correctly. We both know that the Pythagorean theorem assumes Euclid’s postulates (as I keep saying, one cannot make any conclusions without assumptions). My question was given the postulates and definitions (which includes Euclid’s postulates) do you believe there is any way that the PC could have “created” a universe in which this theorem did not hold?

The point I am trying to get at is GIVEN the axioms (including Euclid’s postulates), Pythagoras’ theorem inevitably follows. The PC has no choice in the matter.

PC is not restricted to choosing Euclid's 5 postulates.

I never said it was.

If other postulates are chosen, different consistent geometries result in which the Pythagorean theorem does not necessarily hold.

I agree. This is not the point.

I maintain that the Pythagorean theorem did not exist, ontically or epistemically until after the postulates of Euclid were defined and considered. So in my view, that complexity was not always there, which makes your scheme more complex than mine.

The deterministic relation between “axioms” and “theorem” was there before the PC came along. The PC perhaps chose particular axioms, from which the theorem followed inevitably. Having chosen the axioms, the PC had no subsequent power to choose the theorem, because the axioms (and not the PC) determine the theorem.

You might say we make use of the notion, but I claim that we do not ever make use of the numbers, like e, Pi, and root 2. We make use only of rational approximations to those "numbers". The number 1/3 is different. It is a rational number and we can use its exact value in calculations.

When I say that the relationship between the diameter and circumference of a circle is Pi, or the relationship between the side of a square and its diagonal is root 2, I am making use of a real number. I may not be able to enumerate that number in its entirety, but that does not prevent me from making use of it.

"Full"? What do you mean by 'full'? Do you mean 'all'? I have already explained why the notion of "all" leads to trouble.

Certainly one could interpret “full” as “all” in this context. You have provided an explanation based on Russell’s paradox which I have shown is based on self-referentiality, and is irrelevant to the question of “all”. I have not seen any other explanation from you which shows why the notion of “all” leads to problems. Perhaps you could clarify this.

True, I do not. And it gets back to my question of where that expansion, or the Platonic world was at or around the time of the Big Bang. You said "That complexity was always there" which seems to be much more complexity than I posit. It seems as complex as "turtles all the way down" to me.

We’ll have to agree to disagree here. The complexity was there in your PC world as well, but you simply deny it.

So, I say that Canute's example of "God exists." falls in the fourth category. It depends on what you mean by 'God'. If, by 'God' you mean 'the Sun', then not many people would deny the existence of the Sun, so by definition, "God exists" would be true. Other clarifications of the meaning of 'God' would make the proposition false. And, I would suggest, a great many others would make the proposition meaningless.

As I keep saying – the first thing we must do is make assumptions. Unless we assume the meanings of terms, we cannot evaluate propositions.

I can accept this is an example of “meaningless”, if the terms being used are ambiguous then the proposition is meaningless (another way of saying this is that the terms are not adequately specified, it is open to interpretation), in much the same way that “the quantum object is a wave” is meaningless (because the measurement conditions are not adequately specified, or open to interpretation). This is not a “fourth category” – it is the category “meaningless”.

In other words – the proposition “God exists” is either true or false (if one assumes a certain meaning for the terms used), or is meaningless (if one does not assume any particular meaning for the terms used, or if the meaning of the terms themselves is meaningless).

I think the expression 'imaginary' fits very well to my fourth category. These statements depend for their truth or falsity on someone's world-view, i.e. on their imagination. Statements in this category are true or false or meaningless only in the context of some particular imagined world-view.

Again, everything rests on assumptions. Make the assumptions, and one can evaluate in terms of true, false or meaningless. If there are no assumptions, then we are left only with meaningless. Imaginary does not enter into it.

I don't think Kant considered the possibility of multiple temporal dimensions. If time is created along with the universe, then it seems reasonable that this might be a new dimension of time, which does not rule out the possibility that there was at least one previously existing dimension of time, which would still exist as one axis of a temporal plane.

It also does not entail that there was ANY dimension of time prior to the Big Bang. In such a case, asking what was prior to the Big Bang would be as meaningful as asking “what is south of the south pole”?

Best Regards

 

[Tournesol]

Nowadays, philosophers are clear that you can't reach two opposite conclusions using the same assumptions. Kant's antinomies
are not genuine dichotomies.

I sort of agree with the first statement,

The statement:

"you can't reach two opposite conclusions using the same assumptions."?

but I'd rather say that we can reach two opposite conclusions from the same assumption

i.e the exact opposite ?

and that when we do this shows the assumption is absurd, which to me was Kant's point.

It would be his point if he was in fact working from
the same asumption in each case, although he wasn't.

But if this second statement is true

how would we explain why metaphysics still exists as an academic discipline?

It's not using absurd premises ?

 

[Lars Laborious]

Music could be defined as particular vibrations which conform to certain rules.

Nope, that's not music. Music are the stimuli that the vibrations create, and stimuli are something experienced by a mind. This is simply not a semantic interpretation of music, but the nature of all music. And this clearly is where you and Paul (and I) differ.
The vibrations have to be experienced to stop being just vibrations.

 

[moving finger]

Nope, that's not music. Music are the stimuli that the vibrations create, and stimuli are something experienced by a mind. This is simply not a semantic interpretation of music, but the nature of all music. And this clearly is where you and Paul (and I) differ.
The vibrations have to be experienced to stop being just vibrations.

That depends on how one defines music, doesn't it. The whole point I have been trying to make.

Best Regards

 

[Canute]

The statement: "you can't reach two opposite conclusions using the same assumptions." etc...

We are at cross purposes I suspect. We should not be able to reach two opposite conclusion from the same assumption. But quite often we do, and when we do this shows that our assumption is absurd. In other words, we can reach two opposite conclusions from the same assumption, but if we do this constitutes a reductio argument against the assumption because we know we should not be able to do this.

It would be his point if he was in fact working from
the same asumption in each case, although he wasn't... It's not using absurd premises ?

I believe he was. When he assumed ex nihilo creation the result was a contradiction. When he assumed an eternal substance the result was a contradiction. In each case he reached contradictory conclusions from his initial assumption, so he concluded that both assumptions are absurd.

So it would be because both assumptions give rise to contradictions that Metaphysics exists, the study of questions that seem to philosophers to have no reasonable answers whatever they assume. In other words, we could say that Metaphysics exists because our usual metaphysical assumptions give rise to contradictory conclusions.

In short, I don't agree that we cannot reach contradictory conclusions from the same assumption, but I agree that we should not. This is why I half agreed and half disagreed.

Canute

 

[Eric England]

Canute knows how to sit on a fence, while fully realizing that he is sitting on a fence. A rare talent, indeed. :-)

 

[Tournesol]

We are at cross purposes I suspect. We should not be able to reach two opposite conclusion from the same assumption. But quite often we do,

I disagree

I believe he was. When he assumed ex nihilo creation the result was a contradiction. When he assumed an eternal substance the result was a contradiction. In each case he reached contradictory conclusions from his initial assumption, so he concluded that both assumptions are absurd.

yes but his argumetns are undermined by things like fintie-but-unbounded strucutre of spacetime, as I previouisly noted.

So it would be because both assumptions give rise to contradictions that Metaphysics exists, the study of questions that seem to philosophers to have no reasonable answers whatever they assume. In other words, we could say that Metaphysics exists because our usual metaphysical assumptions give rise to contradictory conclusions.

A priori metaphysics is one thing, analytical metaphsyics another.

 

[Eric England]

"Aristotle, author of the earliest surviving text on logic, formulated a principle that later achieved the historical distinction of being called 'the first principle' as a proper name. It occurs in those of his writings that have come to be called the Metaphysics.

For the same (characteristic) simultaneously to belong and not belong to the same (object) in the same (way) is impossible.

This principle is the first expression of consistency in western thought. Any defining and reasoning in any language on any topic assumes it a priori. It cannot be doubted, as all doubting is based on inconsistency, which assumes consistency a priori." – Wikispeedia

Does this shed any light on anything?

 

[Canute]

Yes, it does seem to. This is the underlying issue.

 

[Paul Martin]

To make progress we’ll need to know how you define knowledge in this context. I’m assuming that the JTB definition is not what you have in mind.

You are correct. I do not accept JTB.

In the context of human knowledge we may define knowledge as justified true belief, which entails that the agent forms a justified belief about something which is also a true belief.

Here you have articulated most of the difficulties I have in accepting JTB. I'll take them in the order you presented them.

First of all, IMHO, "the context of human knowledge" is too confining. Just this morning I was reading Cicero's "Scipio's Dream" in which he described how insignificant human affairs appear from the perspective of the planets of the outer solar system. He even mentioned how much less significant from the perspective of "what the Greeks call the Milky Way". But now that we can ponder the place of the Milky Way in the space-time of our physical universe since the BB, and beyond that, to the hyperdimensional possibilities for "reality" opened up by mathematics, and by the ability to review the vast amount of accumulated "human knowledge", and by the attempts by people who claim to have gained information from mystical sources to articulate what they learned from it, the realm of human affairs seems less significant by many orders of magnitude.

I think it is OK in many, if not most circumstances, to talk within the context of human knowledge. But if we take on the challenge of trying to understand all of reality, I am convinced that we need to broaden the context considerably.

Second, you say that the true belief must be "justified". The problem I have here is "Who is the judge?". Who gets the job of justifying that the belief is true? The believer? Then each believer has her/his own knowledge, and there may be vast inconsistencies among the various knowledge systems (which is the case in human affairs in spades). If the judge is not the believer, then who? The Academy of Arts and Sciences? The Surgeon General, or the National Science Advisor? I can think of no acceptable candidate.

Third, you say that knowledge consists of "true" beliefs. There are many beliefs, but which of them is true? You and I debated once whether one could know anything infallibly. We agreed that the adverb 'infallibly' was redundant because any reasonable definition of 'to know' would entail certain knowledge. I.e. you might be able to know that something is false, but you can't "know" something that is false. In that debate you convinced me to change my mind and I now accept the notion that if there is any certain knowledge at all that can be known, there isn't very much. I suspect that the only certainly true proposition is that "thought happens". And, if that proposition is not certain, then I suspect no proposition is certain. So if we limit knowledge to "true" beliefs, then I am afraid that the set of knowledge is nearly empty.

Fourth, you say that knowledge is beliefs. Yes, it is only the justified true beliefs, but it is beliefs all the same. But what, for heaven's sake, is a belief? IMHO this is such a vague and slippery concept that it hardly qualifies as the basis on which to define the concept we are trying to understand, that of knowledge. Is a belief a hunch? A feeling? By whom? Is it a brain state? A particular pattern of concentrations of various chemicals in the blood? Is it an articulated set of language statements? Is it revealed by the history of the believer's actions? What? It just seems too murky for me.

But it seems to me that you mean something quite different when you use knowledge in the context of the PC. But what exactly?

Yes, very different indeed. But what exactly is harder to answer.

In my view, the mystery we are trying to solve is that of the existence of conscious experience. I know (er...I mean that I believe) that you think there is no mystery about it and that you have a satisfactory explanation of how consciousness arose in biological organisms here on Earth some time in the past few billion years.

As with any explanation we accept, we can take one of at least four positions: We can be happy with our explanation and talk to no one about it; We can be happy with our explanation and talk to others about it with the intention of getting them to agree with it; We can try to find out about competing explanations in order to challenge them with our own; We can try to find out about competing explanations in order to challenge our own.

In my case, I have come up with an explanation for consciousness that involves a rudimentary primordial constituent of consciousness (the primordial PC) which evolved to become the "modern" PC which is the one and only consciousness in all of reality and which "drives" all organisms, including you and me, as one would "drive" a remote controlled vehicle. I am eager to hear alternative explanations which will solve the mystery of consciousness better than mine, and I am eager to hear criticisms of my explanation which show any nonsense in it. That is why I participate in this forum. I am happy to derive important side benefits, such as the sheer pleasure of conversing with intelligent people, but that is not the primary reason.

I am delighted that you asked me, albeit indirectly, what I mean by 'knowledge' in the context of PC. I hope I can make some sense in my explanation:

As you have pointed out, consciousness is, or at least seems to be, vastly complex. We can introspect on some of its aspects, such as memory, sensation, perception, logical inference, imagination, feelings, and on and on. But when I consider those things, it seems that they can all be reduced to some type of knowing. So let me take a crack at defining the verb 'to know'.

To know is to have access to information (i.e. the "known" information) at what seems to be the present moment in the stream of conscious thought. 'Information', I define (slightly modifying Shannon's) as a difference that makes a difference to the knower. The 'knower' is defined as the conscious agent experiencing the stream of conscious thought.

Thus, working from the first principle, of "thought happens", we have the inference that since thought happens, it must happen "to" some agent we call the thinker. Thoughts change, so from the perspective of the thinker, there is a "stream of conscious thoughts" which consists of thoughts which have happened and the thought currently happening. This defines a dimension of time separating past thoughts from present thoughts and it provides a category in which to place "future thoughts", should there be any. Some, if not all, thoughts may consist of patterns of differences. These are defined as information, and if we consider a difference to be the value of one bit, then information can all be expressed as sets of numbers. When a particular set of information is present in the currently happening stream of consciousness, then we say it is "known" and we define knowledge to be any set of information that can be present in the currently happening stream of consciousness.

Now, this definition is consistent with the difficulties we wrestled with concerning "certain knowledge". Let me explain how. Consider the question, "Does the thinker know that it knows?" Well, in order to know that it knows, e.g. A, it must have information available in the present which represents the proposition that it knows A. If that proposition is true, then by definition, A must also be represented by information available in the present.

For example, if I asked you whether you know the name of your fourth grade teacher, you might respond with something like, "Hmmm, let me think...I think it was...no...Oh yes, I remember. It was Miss Jones." At that moment, you could, by my definition, say that you know the name of the teacher and that you know that you know the name of the teacher. Now, if you thought about what I just wrote, you could then say that you know that you know that you know the name of the teacher. But this does not continue indefinitely. In fact it doesn't usually continue much beyond this level. Only when you expressly consider the fact that you know that you know something, can you pack your present consciousness with a long string of I know that I know that I know that I know...s.

So, what then, in this context is certain knowledge? Could we say that we know A? Or can we say that we know A if and only if we can also say that we know that we know A? Or does the chain have to extend even longer than that?

Regardless of the answer to the above questions, there is the added complexity of the case during the interval when you are trying to remember that teacher's name and you haven't yet quite got it. Could you say that you know the name but have just forgotten?

It seems that we are almost compelled to call that forgotten information 'knowledge'. Otherwise the set of knowledge would be vanishingly small. It would consist only of what the thinker was actively thinking about at the moment.

So far, I have only attempted to define 'knowledge'. Now let me try to relate it to the context of PC, as you asked. In my view, as well as in your view, the complex capabilities of consciousness emerged during a process of evolution of some parts of reality. And, we both seem to agree that at the very outset of this evolutionary process, things (or thing) were extremely simple. So in my view, I am interested in identifying the extremely simple necessary precursor to consciousness. I have guessed that it is some sort of ability to know.

Using my definition of 'to know', that means that there was some rudimentary ability to apprehend or recognize or realize the existence of some difference. That's it.

You have objected that such an ability must bring with it all the other complex aspects of consciousness. I disagree. In my view, and with my definition, a thermostat knows when a particular temperature threshold has been crossed. In fact, it reports this knowledge in certain cases to the furnace. Now is that system conscious? Hardly. I think neither of us would claim that it is. But I say that the system does contain knowledge.

I'm running short of time, and I'm probably writing too much already, but I'll summarize some thoughts I have had on this issue. I think there are two types of information: I call them 'upward information' and 'downward information'. Upward Information is coded in numbers and it informs an agent "higher" in a hierarchy of agents. E.g. the thermostat sends Upward Information to the furnace. Downward Information is not encoded in numbers, but is what we call analog information. An example of Downward Information is the position and momentum of a billiard ball. This information is communicated downward (in a sense) to the configuration of other balls on the table and it informs the future state of that configuration.

I apologize for having to run, but this will give you something to think about until I get back.

Warm regards,

Paul

 

[Tournesol]

First of all, IMHO, "the context of human knowledge" is too confining. Just this morning I was reading Cicero's "Scipio's Dream" in which he described how insignificant human affairs appear from the perspective of the planets of the outer solar system. He even mentioned how much less significant from the perspective of "what the Greeks call the Milky Way". But now that we can ponder the place of the Milky Way in the space-time of our physical universe since the BB, and beyond that, to the hyperdimensional possibilities for "reality" opened up by mathematics, and by the ability to review the vast amount of accumulated "human knowledge", and by the attempts by people who claim to have gained information from mystical sources to articulate what they learned from it, the realm of human affairs seems less significant by many orders of magnitude.

If you want to communicate with people who don't have mystical sources of knowledge,. you need to justify yourself in terms
of their understanding of knowlege.

Second, you say that the true belief must be "justified". The problem I have here is "Who is the judge?". Who gets the job of justifying that the belief is true? The believer? Then each believer has her/his own knowledge,

There are standards of justification articulated by philosophers
and logicians. and if everyone follows the standards, the
need not disagree.

Third, you say that knowledge consists of "true" beliefs. There are many beliefs, but which of them is true?

The ones that correspond to reality.

I suspect that the only certainly true proposition is that "thought happens". And, if that proposition is not certain, then I suspect no proposition is certain. So if we limit knowledge to "true" beliefs, then I am afraid that the set of knowledge is nearly empty.

True beliefs and certainly true beliefs are two very different
animals. A belief can be true for mistaken
or chance reasons -- a lucky guess, for instance.

You cannot get to "there are no true beliefs" from "there are no
certainly true beliefs".

Fourth, you say that knowledge is beliefs. Yes, it is only the justified true beliefs, but it is beliefs all the same. But what, for heaven's sake, is a belief? IMHO this is such a vague and slippery concept that it hardly qualifies as the basis on which to define the concept we are trying to understand, that of knowledge. Is a belief a hunch? A feeling? By whom? Is it a brain state? A particular pattern of concentrations of various chemicals in the blood? Is it an articulated set of language statements? Is it revealed by the history of the believer's actions? What? It just seems too murky for me.

And PC isn't slippery ?!

 

[Tournesol]

To know is to have access to information (i.e. the "known" information) at what seems to be the present moment in the stream of conscious thought. 'Information', I define (slightly modifying Shannon's) as a difference that makes a difference to the knower.

Does the information have to be accurate ? is it possible
to be misinformed ?

 

[Eric England]

What is there, that is absolutely true or absolutely false?

 

[Tournesol]

Who said anything about "absolute" ?

 

[Eric England]

I didn't make a statement, just asked a question.

 

[Paul Martin]

Paul, you are not reading my question correctly. We both know that the Pythagorean theorem assumes Euclid’s postulates (as I keep saying, one cannot make any conclusions without assumptions). My question was given the postulates and definitions (which includes Euclid’s postulates) do you believe there is any way that the PC could have “created” a universe in which this theorem did not hold?

The point I am trying to get at is GIVEN the axioms (including Euclid’s postulates), Pythagoras’ theorem inevitably follows. The PC has no choice in the matter.

I am reading your question correctly but we each want to emphasize something different. We each have been downplaying what the other wants to emphasize.

The issue is when certain concepts might have appeared for the first time. You say that certain concepts always existed, and I say that at the very beginning there were no concepts. Here's the progression I see:

First there were no concepts at all. Then there were choices to adopt certain concepts including rules of logic, axioms and the concept of consistency. Then there was the discovery that certain theorems inevitably follow and the PC has no choice but to accept those theorems, or to go back and change the set of adopted axioms and rules.

I think that in your picture, at the very beginning there were a huge number of concepts already in existence including all the implications of all the possible choices of axioms and rules. Sets of rules and axioms may be freely chosen later, but they bring along with them the constraints imposed by their implications.

The difference, again, is that I claim concepts do not exist unless and until they are conceived in a mind, and you seem to think concepts can and do exist without ever being conceived.

So, back to your specific example, I believe that "given the postulates and definitions (which includes Euclid’s postulates)", there is no way "that the PC could have “created” a universe in which this theorem did not hold." But, I don't agree with your premise. PC was not obliged to adopt Euclid's postulates. It was not a given. And the constraint you ask about does not arise unless and until PC adopts those postulates. If other postulates are chosen, which they very will could be, then the Pythagorean theorem wouldn't necessarily hold in the resulting universe.

I agree. This is not the point. ...

The deterministic relation between “axioms” and “theorem” was there before the PC came along. The PC perhaps chose particular axioms, from which the theorem followed inevitably. Having chosen the axioms, the PC had no subsequent power to choose the theorem, because the axioms (and not the PC) determine the theorem.

The point, it seems, is whether or not the deterministic relations existed before PC came along. I say no, since those relations are concepts and they can't exist without a conceiver, and you evidently say that concepts can, and do, exist without ever having been conceived. If that is your position, then I think we have found a fundamental point of disagreement between us.

We’ll have to agree to disagree here. The complexity was there in your PC world as well, but you simply deny it.

I agree that we will have to disagree. I deny that any concepts were "there" in the beginning of the PC world, thus I avoid the HUGE complexity of the existence of an unimaginably large set of all possible concepts at the very beginning. I also deny the existence of most of the complex aspects of consciousness in the PC. I think there is some simple primordial precursor of consciousness that did exist at the outset. Now, whether my denial is simple or not, I suppose each reader can judge for him/herself.

When I say that the relationship between the diameter and circumference of a circle is Pi, or the relationship between the side of a square and its diagonal is root 2, I am making use of a real number. I may not be able to enumerate that number in its entirety, but that does not prevent me from making use of it.

With respect, you are making use of the relationship, not the number. You frequently make use of numbers which approximate the relationship, but never the actual number itself.

You have provided an explanation based on Russell’s paradox which I have shown is based on self-referentiality, and is irrelevant to the question of “all”. I have not seen any other explanation from you which shows why the notion of “all” leads to problems. Perhaps you could clarify this.

Sorry for not being more explicit. When I answered you on this question earlier, I said that we probably wouldn't be able to go much further because we were not willing to "swallow" the other's position on whether concepts could exist without being conceived. This, I believe, is at the root of the problem of defining "all" of something. If, as you believe, all possible concepts can exist without ever being conceived, then there would be no problem of referring to "all" of something, except for self reference. But, if, as I believe, concepts cannot exist unless and until they are conceived, then the meaning of 'all' becomes time dependent. It will depend on the timing of the interpretation of 'all' with respect to the existence of concepts which might qualify to be in the set designated by "all".

For example, if the only numbers that exist are those that have been explicitly defined, as I say should be the case, then the set of "all numbers" will be different from the set of "all numbers" after some more of them have been explicitly defined in addition to the original ones.

Again, everything rests on assumptions. Make the assumptions, and one can evaluate in terms of true, false or meaningless. If there are no assumptions, then we are left only with meaningless. Imaginary does not enter into it.

Of course you can categorize propositions into those three categories if you like. But your third category, IMHO contains propositions which seem to me to be different enough that they deserve to be further split into two categories. Your "meaningless" category would include those that are pure gibberish which have no meaning whatsoever to anyone, and it would include those that have different meanings to different people. The various meanings would all be understandable, or at least parseable, to all, but just not agreed to by all.

Sorry for being so late with this response.

Warm regards,

Paul

 

[Paul Martin]

If you want to communicate with people who don't have mystical sources of knowledge,. you need to justify yourself in terms of their understanding of knowlege...There are standards of justification articulated by philosophers
and logicians. and if everyone follows the standards, the
need not disagree.

I agree that there are many different reasons for wanting to communicate with other people and that in general we needn't disagree. Most of the reasons are simply to get along with the business of living. The knowledge required for this is practical, but not very precise or even "true". If you want to communicate with scientists or with mathematicians, you need to understand their respective bodies of knowledge. Some of that scientific knowledge may not be true, and none of the mathematical knowledge is claimed to be true by the mathematicians themselves. But in philosophy, if we are trying to make sense of more comprehensive and mysterious issues, I think a different standard of "justifying" the truth or falsity of propositions is necessary. I don't think there is a satisfactory "standard" justification method.

There are many beliefs, but which of them is true?

The ones that correspond to reality.

That's easy to say, but difficult if not impossible to demonstrate.

Can you give me a proposition which you are certain corresponds to reality, other than "thought happens"?

True beliefs and certainly true beliefs are two very different
animals. A belief can be true for mistaken
or chance reasons -- a lucky guess, for instance.

You cannot get to "there are no true beliefs" from "there are no
certainly true beliefs".

I don't get the distinction. If a belief were true for mistaken or chance reasons, why wouldn't it be certainly true as well? It certainly is true, isn't it? The premise is that it is true so isn't it certainly true?

Hmmm. Maybe by 'certainly' you are referring to the believer and not to the proposition. The proposition is true. The belief in the proposition may range from weak to certain in the mind of the believer. Then to say that the proposition is "certainly true" we mean that the proposition is true and that the believer knows for sure that it is true. Is that what you mean? If so, then the question is how the believer can, in any circumstance, know for sure. What can anyone know for sure except for tautologies and that "thought happens"?

And PC isn't slippery ?!

PC is very slippery.

To know is to have access to information (i.e. the "known" information) at what seems to be the present moment in the stream of conscious thought. 'Information', I define (slightly modifying Shannon's) as a difference that makes a difference to the knower.

Does the information have to be accurate ? is it possible
to be misinformed ?

Those are both excellent questions. They get down to the heart of the matter IMHO. I'll take the second question first.

I would say that by definition, it is not possible to be misinformed unless the "access" mechanism altered the information on the way to the knower. So, if knowledge is defined as information available to the knower, then what happened to the information on the way doesn't matter. But that just puts the real question off.

Your first question is the real question. That is, must the information correspond to reality? And, if the answer is "yes", what is meant by 'correspondence'? Lots to think about.

Warm regards,

Paul

 

[Tournesol]

I agree that there are many different reasons for wanting to communicate with other people and that in general we needn't disagree. Most of the reasons are simply to get along with the business of living. The knowledge required for this is practical, but not very precise or even "true". If you want to communicate with scientists or with mathematicians, you need to understand their respective bodies of knowledge. Some of that scientific knowledge may not be true, and none of the mathematical knowledge is claimed to be true by the mathematicians themselves.

Huh ?

Can you give me a proposition which you are certain corresponds to reality, other than "thought happens"?

I don't need to. I was making a point about truth, not certainty.

I don't get the distinction. If a belief were true for mistaken or chance reasons, why wouldn't it be certainly true as well?

Because of what "certainly" means. It means "not possibly wrong".

It certainly is true, isn't it? The premise is that it is true so isn't it certainly true?

No. "X is not wrong" does not imply "X could not have possible been wrong"

I would say that by definition, it is not possible to be misinformed unless the "access" mechanism altered the information on the way to the knower.

So it is possible to be misinformed. And what if someone just lies to you ?