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The Unprovable Liar

 
 
saw038
 
Reply Wed 21 Sep, 2016 10:53 pm
Kurt Gödel stated:

"What I am saying cannot be proven."

He did this within individual systems of mathematics, and concluded that if the statement was provable within that particular system, then the formula was untrue.

Math is our most precise measure of arriving at truth.

What do you think this states about the human mind and our ability to comprehend the world?
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Type: Question • Score: 2 • Views: 8,308 • Replies: 75
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Thomas33
 
  2  
Reply Thu 22 Sep, 2016 03:43 am
Truth is the problem of communication. I'm not sure whether mathematics is the means of humanity.
saw038
 
  1  
Reply Thu 22 Sep, 2016 10:32 am
@Thomas33,
It is certainly hard to argue with though. If someone proves something with math, it becomes quite hard to counter them, except with logic or more math.
0 Replies
 
Kolyo
 
  1  
Reply Thu 22 Sep, 2016 03:01 pm
Bookmark.
InfraBlue
  Selected Answer
 
  2  
Reply Thu 22 Sep, 2016 04:07 pm
@saw038,
saw038 wrote:

Kurt Gödel stated:

"What I am saying cannot be proven."

He did this within individual systems of mathematics, and concluded that if the statement was provable within that particular system, then the formula was untrue.

Math is our most precise measure of arriving at truth.

What do you think this states about the human mind and our ability to comprehend the world?


This paradox and others illustrate the limits of language and, consequently, our ability to comprehend the world since we use language in that endeavor.
saw038
 
  1  
Reply Thu 22 Sep, 2016 04:14 pm
@Kolyo,
What?
cicerone imposter
 
  2  
Reply Thu 22 Sep, 2016 04:26 pm
@InfraBlue,
Is it the limit of language or our perception of what we call reality?
Kolyo
 
  2  
Reply Thu 22 Sep, 2016 05:34 pm
@saw038,
I was bookmarking the thread in order to return later.
saw038
 
  1  
Reply Thu 22 Sep, 2016 05:39 pm
@Kolyo,
Ohh, I'm new to this website so I didn't think of that!
0 Replies
 
catbeasy
 
  0  
Reply Thu 22 Sep, 2016 06:46 pm
@InfraBlue,
Yes, I gotta agree with this. Language obeys a set of rules and is ordered by who-knows-what in the brain into what we call logic; which is essentially a way of saying this premise is consonant with this other premise - the degree of consonance or dissonance determining the truth or falsehood of whatever is being examined.

You might say this boils down to pattern recognition.

Math is a subset of our language. More discrete than general language. The limits of being able to logically prove something are indeed limited by our language and show that at some point we can be content a truth can be obtained that we define heuristically, at whatever level that might be at..

Perhaps though I might take issue with the OP saying that math is our most precise measure at arriving at truth. I think you have to qualify that. There are at least quicker ways to some truths..that don't have the burden of logical proof as such..
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InfraBlue
 
  2  
Reply Thu 22 Sep, 2016 11:45 pm
@cicerone imposter,
cicerone imposter wrote:

Is it the limit of language or our perception of what we call reality?

Well, Gödel was referring to language (mathematics), but our perception also limits our ability to comprehend the world and renders our comprehension subjective. Something as simple as color perception varies among different individuals, e.g. the dress:

http://i1020.photobucket.com/albums/af324/infrablu/the%20dress_zpshdws0knp.jpg

I see the dress as white and gold.
saw038
 
  1  
Reply Thu 22 Sep, 2016 11:55 pm
@InfraBlue,
I also see white and gold. However, this could go back to Kant's idea of a priori. We perceive things through our sense organs, but we will never know things in and of themselves, because everything is a function of our limited senses.

While these perceptual concepts may vary among individuals, Godel was pointing out that within any system, there is always one fundamental flaw which it cannot prove; one fundamental blind spot.

So, using this dress as an example, and maybe stretching his theory a little, the blind spot for humans in general could be our varying degrees acuity in our sense organs.

This last paragraph is more of my opinion. What do you think?
fresco
 
  1  
Reply Fri 23 Sep, 2016 12:14 am
@saw038,
As you already know, the word 'proof', like any other word, is context bound. I suggest you look at 'Pragmatism' whose most recent exponent was probably Richard Rorty (Pilosophy and the Mirror of Nature. Most of the questions you are posing have been 'dispensed with' by the Pragmatists with adages such as 'truth is what works'.
A second source of reference which deals with your questions might be texts on the 'Realism Anti-realism' in science. These can be found in any good philosophy of science compendium.
saw038
 
  1  
Reply Fri 23 Sep, 2016 12:21 am
@fresco,
I will definitely look into it! Thank you for your input.

But I posed the question because Godel has proposed a very profound proposition for different systems within mathematics, as well as proposing some of the limitations of mathematics, which have been further been investigated to be true; there are certain limits that mathematics cannot answer like Gregor Cantor's idea of different levels of infinity.
0 Replies
 
XxSiCxX
 
  1  
Reply Fri 23 Sep, 2016 12:29 am
@InfraBlue,
I just have to say I completely love the dress bit.
I am one of those people on the other end of it and see the dress as blue and black.
0 Replies
 
catbeasy
 
  1  
Reply Fri 23 Sep, 2016 10:30 am
@fresco,
Quote:
'truth is what works'.

I could be wrong, but I believe this is formally called heuristics..
fresco
 
  1  
Reply Fri 23 Sep, 2016 11:38 pm
@catbeasy,
Not quite. Heuristics is descriptive of a methodology which works rather than what is agreed as an 'episteme' or 'fact'. Rorty actually qualifies the Pragmatist's definition with 'truth is what it is good to believe'. This qualification gives 'good' a much more neutral implication than what is implied by 'an ethical judgement', in order to encompass 'aspects of currently accepted scientific paradigm', but both implications involve either universal or local social agreement. This locality factor is why a religious group, say, with a common belief system can validly use the word 'truth' for 'what works' parochially between themselves, irrespective of their futile hope to establish its universality.
catbeasy
 
  1  
Reply Fri 23 Sep, 2016 11:54 pm
@fresco,
Interesting. Reading your comment, I think my use of the term was because I thought the point was something different. Apparently I misunderstood, or at the least did not give due to the nuance I think you are implying..In what sense are you defining pragmatism say as opposed to heuristics? And how does it apply to the discussion? Thanks for any clarification..
fresco
 
  0  
Reply Sat 24 Sep, 2016 01:21 am
@catbeasy,
Pragmatism was/is a philosophical position in line with Kant's point that we can never know 'the world' directly. Nietsche's point that there is no way of deciding between 'appearance' and ' ultimate reality' also figures in the pragmatic dismissal of 'ultimate reality' as a meaningful concept. Godel's incompleteness theorem for formal mathematical systems underscores the point from a the point of view of classical logic, by showing that any formal system has at least one axiom whose 'truth' has to be assumed. Indeed the questioning of such axioms (such as Euclid's geometric ones, or Newton's physics) has led to more useful/pragmatic systems of what we call 'knowledge'.

In general, without recourse to the philosophical literature, debates such as this about words such as 'liar' and 'proof' tend to little more than 'opinion games' if it is assumed those words have fixed rather than contextual meanings. But I realize that the motivation for engaging in such debates in multifaceted.
fresco
 
  1  
Reply Sat 24 Sep, 2016 02:44 am
@saw038,
With reference to my last post, perhaps you should have pointed out that there is a distinction between 'truth' (which is assigned by humans) and 'validity' which refers to the structure of logical arguments.
With reference to Godel, it was of course his support for Cohen's proof that there both 'is' and 'is not' an infinity lying between Cantor's two infinities. It was that point that led to to the more general view about the limitations of 'mathematics'. And if you want to pursue another angle, the word 'is' has been considered so problematic in philosophy that some have tried to bsn the verb 'to be' in philosophical debate! (ref 'Eprime').
 

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