Non-Contradiction

I think both JLN and I have conceded that...but this says nothing in particular about "reality" except where "truth values" have been agreed.

(3 +3 = 6 is valid for all bases above 7, but its applicability/truth fails when we ask "If it takes 3 minutes to boil an egg, how long for 2 eggs ?)

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truth
Joe, I think that the "rule" of non-contradiction is axiomativc, reflecting the disposition of human thinking. We cannot imagine its falsehood. Its application in a logical process is "valid" when the process conforms with the axiom/rule. But we must keep in mind that the rule tells us only about our epistemologidal dispositions, not necessarily about the rest of the world. It is quite possible--and it may already be the case--that the rule, and others of its sort, might be grossly inadequate for the explication of phenomena at, say, the sub-atomic level of observation.

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I tried to be (a) general,
but I turned out nothing.

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truth
To be no-thing is to be every-thing. That's pretty general.

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No-thing and every-thing, I believe, are the two defining extremes.
The first, no-thing, has no structure by definition. The second, by way of russels paradox, seems to be unable of having any structure too. Because any structure in everything would lead to categorisation, and where does 'everything' have it's place in such a scheme? And a set of 'everythings' ?
So maybe there is some-thing that no-thing and every-thing have in common, and that is a lack of any-thing.
Smile

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fresco wrote:

I think both JLN and I have conceded that...but this says nothing in particular about "reality" except where "truth values" have been agreed.

"Truth values" are not open to dispute, at least as I understand them. But then perhaps you're talking about "truth values" in some sense other than formal logic?

fresco wrote:

(3 +3 = 6 is valid for all bases above 7, but its applicability/truth fails when we ask "If it takes 3 minutes to boil an egg, how long for 2 eggs ?)

It fails because boiling two eggs is not additive in nature. But certainly three eggs plus three eggs equals six eggs.

JLNobody wrote:

Joe, I think that the "rule" of non-contradiction is axiomativc, reflecting the disposition of human thinking. We cannot imagine its falsehood. Its application in a logical process is "valid" when the process conforms with the axiom/rule. But we must keep in mind that the rule tells us only about our epistemologidal dispositions, not necessarily about the rest of the world. It is quite possible--and it may already be the case--that the rule, and others of its sort, might be grossly inadequate for the explication of phenomena at, say, the sub-atomic level of observation.

The law of non-contradiction is, to be sure, a rule for interpreting reality, as are all logical rules. That is why, when we come across something that appears to violate the rule, we are left either doubting the thing or doubting the rule. That the law of non-contradiction has been so robust is, I think, something of a testament to its close coherence to reality.

More importantly, the law permits us to make definite conclusions about things. If, for instance, the law did not apply, we could never say anything certain about anything, for we could never be sure if something were "A" or "not-A." At most, we could say that a thing had some indeterminate tendencies of "A" and "not-A." Indeed, not only would we be unable to say anything more definite about the thing, but we would be equally unable to say anything definite about "A-ness" in general. And that, I contend, is not simply logically invalid, it is empirically unsupportable.

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Joe

Formal logic is just that - "formal" Smile

TRIVIALLY
All Presidents have red hair
Queen Elizabeth is a president
Therefore Queen Elizabeth has red hair.

"Truth values" are extrinsic to logic itself.

Irrespective of traditional problems with the word "all", your knowledge or assignment of truth values of the nature of "eggs" "boil" "addition" "Queen Elizabeth" red hair" etc etc are all language/culture/experience specific.

In an interactionist reality "knowledge" is about "appropriate action".

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Joe,

You talk of "empirical testing" as though this were clear cut.

What do you make of the celebrated "wave particle" debate in physics where the two categories were assumed to be mutually exclusive?
It is precisely from these "empirical problems" that the applicability of binary logic in particular has been questioned.

Your central thesis seems to be that if we can't apply binary logic then "nothing (meaningful) can be said". This is clearly fallacious for example with respect to concepts such as " balance of probabilites" . You are merely stating a particular view of "semantics" based on static objective set membership. I suspect an elementary Google search on "semantics" would tell a very different story.

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fresco wrote:

Joe

Formal logic is just that - "formal"

TRIVIALLY
All Presidents have red hair
Queen Elizabeth is a president
Therefore Queen Elizabeth has red hair.

"Truth values" are extrinsic to logic itself.

Well, then we clearly have different notions of "truth value."

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fresco wrote:

Joe,

You talk of "empirical testing" as though this were clear cut.

What do you make of the celebrated "wave particle" debate in physics where the two categories were assumed to be mutually exclusive?
It is precisely from these "empirical problems" that the applicability of binary logic in particular has been questioned.

I believe that the "wave-particle debate" is a debate precisely because the notion that light is both wave and not-wave (and particle and not-particle) goes against the law of non-contradiction. As I mentioned before, when we find something that appears to contravene the rule, we either doubt the empirical finding or we doubt the rule. I believe that, at present, physicists are still grappling with that question.

fresco wrote:

Your central thesis seems to be that if we can't apply binary logic then "nothing (meaningful) can be said". This is clearly fallacious for example with respect to concepts such as " balance of probabilites" . You are merely stating a particular view of "semantics" based on static objective set membership.

I would expect that set theory is fundamentally based on the law of non-contradiction. After all, if a set can also be a non-set, then what's left of the theory? To the extent that set theory says anything about the law of non-contradiction, then, I would imagine that the theory would support the law.

fresco wrote:

I suspect an elementary Google search on "semantics" would tell a very different story.

Now fresco, we've gone over this before: if there's something on the web that supports your position, it is your job to find it.

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Joe

Heres just one reference to the use of nonbinary logic in providing a semantic structure for contemporary problems of observation.

http://www.cs.berkeley.edu/Seminars/Archive/1999/10.Oct/991027.zadeh.html

I particularly draw your attention to the last two paragraphs.

Alternatively you might follow up any Wittgenstein references on "meaning is use" which come from his later period when he rejected most of his early work on "logic" (tractatus-logico-philosophicus)

e.g.
<<Wittgenstein has shown us that language and intention are inseparable. We cannot represent the world without language, and we cannot mean anything without language. In his early work, Wittgenstein wanted to show that language mirrored reality. Each level of the world corresponded to a level in the structure of language. In his later work, however, Wittgenstein refuted this view. There is no reality over and above our conceptualisation of the world. It is impossible for us to step out of our language system and take an objective look at the world. The meaning of our thoughts and expressions do not exist independently of language. To question the meaning of a name, or expression, we must look at the role that the name, or expression plays in the language game. >> (Silby University of Canterbury 1998)

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Nonbinary logic is OK, but it is implemented and instrumented using a classical math logic. It is not to replace, but to augment.
Remember that any number system can be basically modeled using a binary sistem. Any B-tree structure can be modeled using a binary tree. Any N-logic we know can be moddeled using binary logic.

In the end, most are implemented as cumputer progams, which run on ... boole algebra.

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Relative

If you are saying that all "numbers" are reducible to binary expressions, I must of course agree. However a reading of Kosco's "Fuzzy Thinking" yields a specific rejection of the law of the excluded middle (which I believe is related to non-contradiction). Thus what may be mathematical extension or continuity may be a philosophical departure or discontinuity. After all, "probability functions" are non controversial as mathematical entitities but highly problematic in terms of "meaning". (ditto Heisenberg's principle etc)

Also, although I've not been into this, I am not sure whether computational "neural networks" work on "straight" Boolean logic, and this seems to be the domain of fuzzy set applications. Nor indeed may this be the case for Prigogene structural dynamics which has also been used for formal modelling of perceptual processes. (Capra).

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Neural networks work perfectly well under boolean algebra. I will have to look up Prigogene structural dynamics.
There is no rejection of the law of the excluded middle in 'Fuzzy thinking' in _binary logic_, there is a creation of _another_ formal system using 'fuzzy thinking' which defines it's own 'logic', but that new 'logic' doesn't _replace_ the reasoning logic, it defines a new tool for solving problems. It uses reasoning logic to be formally defined itself. It is in this new logic that there is no excluded middle, but it's like comparing apples and bananas.
You can write 'there is no law of excluded middle' in this thread, you can argue for it, but meanwhile the messages and the forum are _implemented_ using binary logic, and you cannot change that.

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truth
Is it ever appropriate (i.e., useful) to see light as composed of "wavicles"?

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Relative,

Kosco does not seem to agree with your reducibility argument. On page 24 he produces the following table to introduce the priciples of "Fuzzy Thinking".

BIVALENCE................ MULTIVALENCE

Aristotle......................Buddha
A or not-A...................A and not-A
exact..........................partial
all or none...................some degree
0 or 1..........................continuum between 0 and 1
digital computer...........neural network (brain)
Fortran........................English (natural language)
bits.............................fits

If you are saying the "meaning" of the second column "rests" on the meaning of the first column
you have missed the essential non dualist element implied by "Buddha".....

JLN will like Kosko's introduction to this chapter...

<<Shuzan (926-992 AD) once held up a bamboo stick to an assembly of his disciples and declared: "Call this a stick and you assert, Call it not a stick and you negate. Now, what would you call it? Speak ! Speak! " . One of the disciples came out of the ranks, took the stick and broke it in two, exclaiming "What is this ?">>

In mathematical parlance the nominal level of measurement (set assignment) is axiomatic to traditional logic, and all subsequent measurement. But philosophically that very level involves interaction of observer and observed and depends on local functionality which is in dynamic flux.

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joefromchicago wrote:

Quote:

Twyvel, if all you want to do is talk about cats, then go ahead. If you want to talk about the validity of non-contradiction, however, your empirical objections are inconsequential.

You are the one who brought poinsettias and cats into this discussion, not I.

You bring empirically based statements into the discussion and then object when others attempt to counter those statements with empirical observations. Go figure, Confused

Unless we are restricting this talk to mathematics, which we are not, then objections are going to be empirically based just like your opening post is empirically based.

You wrote:

I believe that the "wave-particle debate" is a debate precisely because the notion that light is both wave and not-wave (and particle and not-particle) goes against the law of non-contradiction. As I mentioned before, when we find something that appears to contravene the rule, we either doubt the empirical finding or we doubt the rule. I believe that, at present, physicists are still grappling with that question.

You are putting forward here an empirical objection to the law of non-contradiction. You are your own contradiction joefromchicago.

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Quote:
If the definitions of "good" and "bad" in this statement are deficient, then all that is necessary is to refine the definitions. You seem to think, on the other hand, that if the definitions are deficient, the logic is flawed. That, I contend, is itself a logically flawed argument.

It's not a question of the logic being flawed. The issue is simply that your Opening post;

A thing cannot simultaneously be both "A" and "not-A."

or the Law of non-contradiction, is not an absolute.

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Quote:
This is merely a restatement of the "arrow paradox." If duration is an illusion, then everything is an illusion, including you and your empirical observations regarding cats, twyvel. Consequently, you cannot disprove the law of non-contradiction since you cannot disprove anything.

That duration is an illusion is not the main point here. The main point is, if the duration needed for X to effect Y is an unknown then we cannot say what takes place in that unknown duration, i.e. X could effect Y in more then one way.

Quote:

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Having renounced the reality of all evidence, you are, once again, left with nothing but your beliefs.

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No, you say and act both "as if" and "as it is." Face it, twyvel, you want to have it both ways: you want to hold on to facts while simultaneously dismissing them all as illusions. Undoubtedly, you cling to empirical truths because, without them, you have nothing but faith -- a thoroughly understandable and perfectly acceptable position that, for some strange reason, you find impossible to take.

do not know

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And as regards contradictions, for someone to claim that they can observe the awareness that they are is a contradiction.

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Why?

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Quote:
How do you know that?

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twyvel,

Joe's argument against what is "obvious" to some of us, is that if so, "nothing meaningful" can be said about "anything". But he refuses to acknowledge different versions of "meaning" presumably because he has vested interests in those based on "naive realism". For example, he is "factually incorrect" when he says physicists are "still grappling with wave-particle duality". They have in fact "moved on" from a paradigm rooted in naive realism to one involving the inclusion of "the expectations of the observer". But the point is that Joe can isolate such shifts as "local anachronisms yet to be resolved" in order to maintain to his view of "meaning". This reminds me a little of religious fundamentalists who "explain" scientific evidence for the age of the Earth etc, on the basis of ad hoc reformulations on the "length" of a biblical "day".

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fresco,

I believe there is very strong evidence that not only the form, also the essence of the right side can be expressed using language from the left side.

BIVALENCE................ MULTIVALENCE
*2^1............................2^n

Aristotle......................Buddha
A or not-A...................A and not-A
*precision.....................depth

exact..........................partial
all or none...................some degree
*singlevariate............multivariate

0 or 1..........................continuum between 0 and 1
*{0,1}........................... 0.x1x2x3x4x5...xn... every xk is in {0,1}

digital computer...........neural network (brain)
*hardware....................software (it is not evident that neural network=brain)

Fortran........................English (natural language)
*simple grammar.............. complex grammar

bits.............................fits
*me..............................you

If I simplify my point : 2 just happens to be the first sensible base and is most basic. Any multivariate multidimensional system (that we can currently formally comprehend) can be expressed in terms of 1 and 0, and this is called digital.

And it is certain that most of the world can be modelled this way.

===========
I actually believe that consciousness does not arise from a neural network or any algorithmical process, and this is in no conflict with good old logic, and is actually a consequence of it.
===========

You can of course play with different models, but it is _very_ hard to substitute logic with anything remotely so powerful.

Just broadening the spectrum of choices (saying 'partial' instead of yes/no) does not conjure new logic; it only adds some new tools in the toolbox.
It's like you have 1, and then use this 1 to define natural numbers (Peano axioms). Using natural numbers you obtain integers, then rational numbers. From there it is just another hop to continuum and real numbers.
Even if you consider that rational numbers are something drastically more powerful than integers, even though real numbers are even more powerful(you have continuum between 0 and 1), and there are infinitely more real numbers than integers, they are all just numbers. They follow from integers, and they follow from 1. Tensor calculus does not invalidate simple 1+1=2 any more so than multivalence invalidates bivalence.

You can throw in any complexity on top of that, any number of dimensions, hell even _infinitely many dimensions_ as is done in quantum mechanics, you basically still rely on logic, and that relies on 'exclusion of the third'.

We don't have to sack our very best ideas to make progress; we build on them.

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twyvel wrote:

You are the one who brought poinsettias and cats into this discussion, not I.

You bring empirically based statements into the discussion and then object when others attempt to counter those statements with empirical observations. Go figure,

Given that the evidence which demonstrates the obvious falsity of your statement is so readily available, I'll assume that your error is the result of a simple mis-reading rather than an attempt at a deliberate misrepresentation. I brought up the "poinsettia" example as a way to demonstrate the law of non-contradiction, not to prove it. In contrast, you brought up empirical objections in a futile attempt to disprove the law. That's the difference.

twyvel wrote:

You wrote:

I believe that the "wave-particle debate" is a debate precisely because the notion that light is both wave and not-wave (and particle and not-particle) goes against the law of non-contradiction. As I mentioned before, when we find something that appears to contravene the rule, we either doubt the empirical finding or we doubt the rule. I believe that, at present, physicists are still grappling with that question.

You are putting forward here an empirical objection to the law of non-contradiction. You are your own contradiction joefromchicago.

It's not my objection, and so, at least, I cannot be accused of contradicting myself.

twyvel wrote:

Quote:
If we reduce it to: X cannot be simultaneously good and bad for Y.

Are you saying that "good" and "bad" are empirical concepts?

twyvel wrote:

It's not a question of the logic being flawed. The issue is simply that your Opening post;

A thing cannot simultaneously be both "A" and "not-A."

or the Law of non-contradiction, is not an absolute.

Really? How do you know?

twyvel wrote:

How do you know that?

twyvel wrote:

That duration is an illusion is not the main point here.

Then why did you bring it up?

twyvel wrote:

The main point is, if the duration needed for X to effect Y is an unknown then we cannot say what takes place in that unknown duration, i.e. X could effect Y in more then one way.

So what?

twyvel wrote:

How do you know that?

twyvel wrote:

So what? If everything is an illusion, how can we know that? Indeed, if everything is an illusion, then our idea of "illusion" is also an illusion.

twyvel wrote:

do not know.

How do you know that you don't know?

twyvel wrote:

Unless one knows the truth they are pretending to some extend.

How can you tell the difference?

twyvel wrote:

Well, the whole thing may be a dream, in which case I may be wrong. But then if one contends that the whole thing is a dream, there is no possibility of being right.

twyvel wrote:

How do you know that?

twyvel wrote:

It's blatantly obvious to some of us that awareness cannot be observed, cannot be objectified, cannot be made an object to itself. When one goes looking for the observer they end up in an infinite regress,.... or a never ending..........

At last, twyvel! You've finally answered the question that I have been posing all along. Apparently, the long-awaited answer to "how do you know that?" is "it's blatantly obvious to some of us."

Really, twyvel, I'm rather disappointed. To think that I've been waiting so long for this. The mountain labored mightily and produced a mouse.

twyvel wrote:

No, I "don't get it" because I have never seen any cause to give credence to your argument. Since you deny concepts such as "subjectivity" and "awareness," there's simply no compelling reason to accept any statement that you might make regarding "subjectivity" or "awareness."

twyvel wrote:

And you know that because it's "blatantly obvious," right?

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