What does paradox reveal about the nature of truth?

The subjectivity-objectivity dichotomy is perhaps a red herring, because it implies the lay-concept of the possibility of an "objective truth" which is "absolute".

That possibility is never considered by "science" which proceeds paradigmatically (Kuhn: The Structure of Scientific Revolutions). A paradigm is a socio-linguistic network which directs and categorizes observation according to agreed theoretical constructs. Indeed, it defines was is currently to be accepted as "science". Logic (which is based on abstract set theory) can only operate after set allocation into categories. If sufficient counter-examples accumulate to the functionality of the theory in making predictions, the paradigm can shift, and "sufficiency" is negotiable. Kuhn points out that contrary to Popper's logical "falsifiability principle", one counter example is rarely sufficient.

So "scientific truth" can shift according to the functionality of the paradigm. Despite being superseded by the relativistic paradigm in terms of range of application, Newton's Laws are still "true" in the sense that they still work in limited contexts. So in the sense that observers mutually define the context, they define "truth". On this point it is neither "correct" nor "incorrect" to say, for example, that "the sun moves across the sky", despite the layman's inability to understand the universality of the "point of view" issue.

And as for the OP about what "logical paradoxes tell us about the nature of truth" I would say nothing other than the limits of the applicability of logic relative to socio-linguistics. Wittgenstein dismissed Russell's paradox as an aberrant "word game".

I have never implied the possibility of an "objective truth." Just a certain level of truth that we humans can rely on to a certain degree of confidence.

If we didn't have any confidence in what we believe, all lives will be in chaos, and nobody will have the ability to achieve what he/she chooses to do.

Most people go from place to place believing that the street they drive on will be there when they drive to work or to another destination. That's sort of the objective truth that is reliable to a high degree of confidence. They are able to plan without having to worry about what they believe still exists in their daily lives.

I am actually more interested in Godel's theorem than I am in Russell's paradox.

Wittgenstein dismissing the Russell's paradox as an aberrant "word game" is hardly surprising, considering how willing he was to sacrifice language's ability to abstract for the dissolving of any philosophical problem.
As he said, "...the clarity we are aiming at is indeed complete clarity. But this simply means that the philosophical problems should completely disappear."

I contend that while it probably is possible to change language so that philosophical problems are un-discussable, this does not really resolve such problems, rather it shuts our eyes to them.

Additionally:
I do not think that Wittgenstein's strategy that I generously call "eliminating loose hierarchies" or derogatorily call "dumbing down of languages", even is successful in eliminating paradoxes.
That strategy actually was employed in an attempt to "rescue" set theory. The attempt was unsuccessful, as even after those changes were made, the theory still fell under the domain of axiomatic systems that Godel's incompleteness theorem shows to have undecidable propositions.

I disagree. Logical paradoxes pre-suppose static set theory which is ultimately dependent on dynamic cognitive linguistic operations.
For example I perfectly understand a sentence like....
" The only certainty in the universe is that there is no certainty".
...and I suggest you understand it too .
In real life communication, dynamic semantics trumps static logic because transitional cognitive states are operating which resolve potential paradoxes by shifting levels of meaning.

I am fond of quoting this Crocodile Dundee exchange to show how a linguistic marker (in this case the word "knife") changes its functional identity (set membership credentials) according to dynamic shifts in context.

Mick and Sue are confronted by a would-be mugger
SUE: Watch out Mick, he's got a knife !
MICK: That's not a knife... (pulls out his large bush-knife)...That's a knife !
(mugger flees).

What exactly would a non-static set theory be?
I don't understand the issue with dynamic operations being performed on the static substrate of axioms and propositions. [The computational model of cognition as I understand it.]
Why do you imply that this paradigm should be abandoned?


I don't see that a computational model of cognition is incapable of those same shifts in context. I can write a code for a program which reassigns a computational marker dependent upon arising conditions.

I like the Crocodile Dundee example.

I think that fundamentally I am not convinced that a "dynamic semantics" cannot be encoded within a computational system. Consequently, I am not convinced that even "dynamic semantics" can resolve all paradoxes (even while shifting meaning).

Well maybe the spectacular failure of AI attempts at such encoding may convince you!
As a result of such failure, second generation cognitive scientists, such as Eleanor Rosch have had some success in promoting Wittgenstein inspired "category theory" to explain semantic drift within the dynamics of communication.
Attempts to solve the "encoding problem" suffer from two major problems.
1. Even traditional logicians like Quine have now accepted that "words" are not representational of (isomomorphic to) an observer independent reality.
2. The nature of "categories" appears to be a function of bodily and social experience with what we call "the world" and computation/machine algorithms cannot reflect that experience.

Well I must admit I am not that familiar with how "spectacular" those failures have been (I need to look further into this).
My first reaction to this however is that AI research, in my opinion, is still quite a new field of research; thus I have my doubts that the non-discovery of a solution implies that no solution exists.

In what sense are you using the term "words" in this context? Do you mean words in human language?


Somewhat related:
Are you familiar with the work of Stephen Wolfram on cellular automata?
His work has shown that cellular automata (very simple computational rules) can produce some very complex and structured but essentially "unpredictable" results. He even presented a model of something very similar to our reality using cellular automata.

Wolfram's model was able to model an arbitrarily high number of "spacial" dimensions and what from the perspective of one within the system would view as "time", using simply simple automata progressing through one operation at a time on one bit at a time (a linear program). Within the model there is even an absolute maximum "speed" at which one structure can propagate effects to another structure.

Thanks for that Wolfram reference. I'll look it up.

As for the "words" issue, I take the view that words are abstract tokens like currency, but like the value of currency their semantic import/worth is subject to contextual negotiation.(ref: Mick's "knife"). This is of course counter to the naive realists view that words represent observer independent "things". (A point is made in the philosophical literature about the difference between representation and re-presentation i.e. re-evoking an observer state. In German the distinction is explicitly captured by the two words Dastellung and Vorstellung, See Heidegger for example)

You're welcome. I read it in his A New Kind of Science, I think in the last 1/4 of the book (sorry I don't know where my copy is right now).

So your view is kind of that a word can only be properly interpreted in a "hermeneutic" sense?

Or in essence, to "accurately" describe the meaning of any 'word' requires the knowledge of everything about the reality in which it was spoken at the time it was spoken.

Yes...that is Quine's conclusion. In fact post modernists like Derrida would go further in stressing there is never an "accurate" state of semantic relationships even for a single speaker whose own internal state is constantly shifting. (To some extent these "identity issues" have been taken up on the Buddhist Self thread).

Respectfully as possible, Matt...you folk are doing with language what some people do with clothing.

Clothing is about keeping warm. The facts that it is used to hide various body parts...or is used by some to indicate social status or social superiority or superior aesthetic taste...are incidentals that are carried to extremes by people who are extreme.

Words...language...is about communicating. The facts that some make it pretty or have rules or to indicate social status or intellectual superiority...are incidentals that are carried to an extreme by people who are extreme.

To suppose for one second that language is meant to convey anything significant about the REALITY is absurd...so it can easily be argued that finding fault with its inadequacy to do that really makes marginal sense.

But I guess it is an interesting diversion...and I indulge in interesting diversions all the time.

This is what a paradox reveals about the nature of truth...That no living thing fully conceptually understands, or can identify the nature of truth as a conceptual concept...And the only thing that could, would be a divine being that would not be paradoxical...Hence, why I am a theist...

It is possible that no divine being exists, but I reject this notion, because if it is actually true, I really can not fathom a reason for the concept of existence itself on any level...And it is backed up by what I have said above that a paradox points to no one being able to conceptually understand the true nature of truth itself...

And from the way I subjectively see things, If there is no substantial reason for existence to even occur, then why would it actually happen?

If it happened on its own, It seems (in theory) it would have been able to not allow it to happen on its own...And since it has happened it seems that something had a determinative reason to grant existence to actually be, over non-existence...Since it seems something had a determinative reason for existence to exist...It seems it is harder for me to rationalize that existence is by chance, than it is that there is a divine creator, with an incomprehensible understanding...about existence, and everything that is incorporated into the notions of non-existence, and existence, and every other concept.

And I think a God would be capable of understanding the nature of truth, because it is not a conceptual concept to God, but it is a being so above everything else, that this incomprehensible beings actions are predicated by "truth" And all other incomprehensible concepts so that it does not view anything conceptually, or in perceptive/subjective ways, but as ultimate as anything could ever be...regarding every single object that is non-existent or existent....

If it happened on its own, It seems (in theory) it would have been able to not allow it to happen on its own...

And existence itself would be limited in some sort of way...Which would make existence by chance incompatible with why existence even exists...

Or existence itself must have a mind of its own, or a superior creationist that gives existence itself the qualifications of what the qualities of existence, and non-existence are...as well as everything else...

If existence had the ability to not allow existence to exist as its determinative of nothing but itself...As it had the ability to allow existence to exist by a determinative of nothing but itself, It still implies a creationist...not evolution, or chance...

How could non-existence itself with no determinative of anything but itself, have the ability to create existence by itself if it is determinative of nothing but itself? Unless there is a creationist involved?

In terms of chance and probability, The odds are still greater than 50% for creationism than evolution...

I agree that it seems that way, especially because that is what our reality looks like from the perspective of Newtonian Mechanics. In the world looked at from this perspective, things seem to proceed in a causal nature from one step to the next. Like a line of dominos, each domino falls because of (and only because of) the previous domino falling.
It might not seem that way, if we had formulated our world view from the perspective of quantum mechanics, however. From this perspective there is never any guarantee that once a "domino" falls it will trigger the next to fall. There is no guarantee that a "domino" will not just fall, for no reason. "Dominos" might even pop in and out of existence. The most (at least for now) that can be said at this level is that there exists a certain probability that a domino will fall as a result of the previous domino.


You are saying that you want a "substantial reason" for existence. I can certainly understand wanting that. My wanting something or your wanting something does not obligate it to exist, however.
I would invite you maybe to consider what would qualify for you as a "substantial" reason for your existence.
Do you feel your existence is more meaningful as a domino in the chain set up by (presumably) God,
or do you feel your existence is more meaningful as a domino in the chain that might just happen to be.
I don't mean that last question to be rhetorical, or to imply that those are the only views available. I think they are the two views that you are comparing at the moment.

With all respect Frank,
I am concerned about things that are "significant about REALITY" and in order for Fresco and I (or anyone else) to communicate regarding this subject the only tool at our disposal is language (by your definition).
So from what I am gathering from your comment is basically.
Don't even bother.
I welcome your contribution.
I'm not yet ready to quit bothering, however.
Love-Matt

Ha!
Is this your way of telling me that I'm a broken record?