Author Topic: You cannot define Truth  (Read 3271 times)

Offline Baruch

You cannot define Truth
« on: May 06, 2018, 03:48:57 PM »
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Even within mathematics, truth cannot be defined within a jargon, it takes a meta-jargon.  But given human language, it would take a meta-human language (something no human can ever do) to define truth within any native language.  And in so far as thought is just internalized natural language, you can't even think the truth.
« Last Edit: May 06, 2018, 07:13:50 PM by Baruch »
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Offline Baruch

Re: You cannot define Truth
« Reply #1 on: May 06, 2018, 07:12:16 PM »
This of interest to me, because I would like to know, if I have a coded message, if I can tell if the coded message is true, even if I can't decode the message.

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Any message can be converted into a long positive integer per Godel numbering.  Tarski is all about ... how can we apply the logical notion of truth (a limited definition) to Godel numbered logical statements.  Tarski's theorem is that we cannot define truth within an object language, you have to have a metalanguage to assess true statements.  Given that, logic cannot be used to prove the truth of logical statements (aka depends on the truth of the premises, unless you have a tautology or a contradiction).  This is a problem for logic, a logical paradox within logic itself, that is not tied to natural language paradox like "liar's paradox".  It only assumes the validity of the arithmetic of the positive integers ... not even zero or negative numbers need be used).  Addition, multiplication, powers, roots are defined.  Negation, subtraction and division are undefined.  Primes are defined however.

So given that I can Godel number a natural language statement, converting that statement into a long integer, can I use the Tarski Theorem to state that ... the truth of the natural language statement is undefined, unless I uses a meta-language?  Well that is a paradox, same as happens with mere pure logic statements.  I would have to have a supernatural language to assess the truth of a natural language ... but that is impossible, if everything is defined as natural.  Any meta-language devised by people, would still qualify as natural.
« Last Edit: May 06, 2018, 07:14:11 PM by Baruch »
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Offline Baruch

Re: You cannot define Truth
« Reply #2 on: May 06, 2018, 09:01:18 PM »
Per Marcus de Sautoy ... if a logical statement is put into a Godel numbering, and you have a set of axioms that are put into a Godel numbering, then that logical statement is a theorem (derivable from the axioms) if the Godel numbering of the logical statement can be factored by the Godel numbers of the axioms, with no irreducible remainder left over (that is, a number that isn't an axiom).  This I will play with this week.

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« Last Edit: May 06, 2018, 09:04:20 PM by Baruch »
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Offline Baruch

Re: You cannot define Truth
« Reply #3 on: May 06, 2018, 09:21:30 PM »
The problem of not being able to define an interior without an exterior (in a logical sense) impacts the potential for understanding consciousness, and the practicality of AI.

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Offline SGOS

Re: You cannot define Truth
« Reply #4 on: May 07, 2018, 04:52:15 AM »
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So given that I can Godel number a natural language statement, converting that statement into a long integer, can I use the Tarski Theorem to state that ... the truth of the natural language statement is undefined, unless I uses a meta-language?  Well that is a paradox, same as happens with mere pure logic statements.  I would have to have a supernatural language to assess the truth of a natural language ... but that is impossible, if everything is defined as natural.  Any meta-language devised by people, would still qualify as natural.
Logic has it's limitations.  It's value is that it is the best tool we have to gain knowledge.  It is better than a meta-language by virtue of the fact that meta-language is just a made up word for a thing which no one understands, because it doesn't exist.  Meta-language is the bait at the end of the maze.  Just keep making up bigger and bigger nonsense words or nonsense speculations, until you think you have invented the final solution.  Unfortunately, there isn't even a final solution.  That's why we need rules to guide us and keep us from cluttering up our minds with junk thoughts.

Offline Baruch

Re: You cannot define Truth
« Reply #5 on: May 07, 2018, 06:33:38 AM »
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Logic has it's limitations.  It's value is that it is the best tool we have to gain knowledge.  It is better than a meta-language by virtue of the fact that meta-language is just a made up word for a thing which no one understands, because it doesn't exist.  Meta-language is the bait at the end of the maze.  Just keep making up bigger and bigger nonsense words or nonsense speculations, until you think you have invented the final solution.  Unfortunately, there isn't even a final solution.  That's why we need rules to guide us and keep us from cluttering up our minds with junk thoughts.

Logic prevents one kind of screw up ... inconsistency.  Without empirical evidence to go with it, it is toothless.  Math isn't derivable from logic.  Mathematicians do meta-languages (not ordinary language at all).  In math, there is an uncountable hierarchy of meta languages, just as one would suspect ... meta goes to meta-meta etc.  And yes, we still don't know what Platonic Forms are, though they are inspired by math.  Ideal triangles etc.

Math isn't junk thought ... unless you want to stick to Euclid and Pythagoras level of math.
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Re: You cannot define Truth
« Reply #6 on: May 07, 2018, 01:48:05 PM »
"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
Bertrand Russell
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"Being dead is like being stupid, it's only painful for others."
Ricky Gervais

Offline Baruch

Re: You cannot define Truth
« Reply #7 on: May 07, 2018, 05:51:31 PM »
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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
Bertrand Russell

True, if you say that it is abstract rather than concrete.  Bertrand Russell made Plato spin in his grave ;-)
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Offline SGOS

Re: You cannot define Truth
« Reply #8 on: May 07, 2018, 07:31:06 PM »
Quote
You cannot define Truth
Sure you can.  Greatest I Am will do it for you for free.

Offline Baruch

Re: You cannot define Truth
« Reply #9 on: May 07, 2018, 08:44:29 PM »
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Sure you can.  Greatest I Am will do it for you for free.

Everyone here is the Truth ... because all atheists are ... dum dum dum ... Jesus!

2+2=4 is consistent.  But consistently isn't truth, unless one is playing semantic games, which nobody here would ever ever do ...
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Offline Cavebear

Re: You cannot define Truth
« Reply #10 on: May 09, 2018, 06:40:02 AM »
Truth is facts put together in a coherent system. 
Atheist born, atheist bred.  And when I die, atheist dead!

Offline Baruch

Re: You cannot define Truth
« Reply #11 on: May 09, 2018, 07:08:01 AM »
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Truth is facts put together in a coherent system.

Not relevant.  The article is pure rationalism and its limitations, limitations of coherence.  Empiricism is very important ... those facts on the ground.  Getting those facts on the ground into relative coherence is useful too.
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Offline Baruch

Re: You cannot define Truth
« Reply #12 on: May 13, 2018, 11:56:51 AM »
More references on this topic:

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"No sufficiently powerful language is strongly-semantically-self-representational."  even for arithmetic, you can't consistently define what is true about it without using something outside of arithmetic.  Now extend this to natural language ... you cannot define what is true in natural language, without using words outside of natural language ... in practical terms, if you have a finite vocabulary, to define the truth of that vocabulary, you have to use words outside of it (this is a clear corollary with Godel's results).  So we add a new word.  But we are in infinite regress, we can define the truth of the extended language without adding another word, and so on.

Critics of this say ... you get into circularity.  And I reply ... yes, that is exactly the problem with any natural language.  A dictionary is a big circular (web like) self definition.  What makes it valuable it going outside of it, to the real physical world aka empiricism.

This is why we never get anywhere ... we don't share the same theory of semantics ...

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And of course, even within a particular theory, we don't agree on the details.  Monkeys all the way down.
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Offline Baruch

Re: You cannot define Truth
« Reply #13 on: May 13, 2018, 12:02:54 PM »
The reason why the culture of a language is important ...

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Words/concepts group differently in different languages.  Technically, the dictionary definition of a word isn't universal, but depends on cultural context.  How different languages group words, how they reflect different cultural styles of thinking, is why I like language studies.
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Offline Draconic Aiur

Re: You cannot define Truth
« Reply #14 on: May 14, 2018, 11:32:14 PM »
Googled Truth

Quote
truth
tro͞oTH/Submit
noun
noun: truth
the quality or state of being true.
"he had to accept the truth of her accusation"
synonyms:   veracity, truthfulness, verity, sincerity, candor, honesty; More
antonyms:   dishonesty, falseness
that which is true or in accordance with fact or reality.
noun: the truth
"tell me the truth"
synonyms:   what actually happened, the case, so; More
antonyms:   lies, fiction
a fact or belief that is accepted as true.
plural noun: truths
"the emergence of scientific truths"
synonyms:   fact, verity, certainty, certitude; More
antonyms:   lie, falsehood

Bam! Defined Truth!

 

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