## Is this an improved definition of a truth bearer?

What is the basis for reason? And mathematics?

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Skepdick
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### Re: Is this an improved definition of a truth bearer?

PeteOlcott wrote: Wed Feb 26, 2020 5:05 pm We are way past understanding that Wittgenstein was correct about Gödel being wrong?
There is nothing TO understand!

Gödel pointed out that reasonably powerful axiomatic system that can do arithmetic can't be consistent AND complete.

That means you have a choice. You can choose to optimise for consistency (which is what Mathematicians do), or you can choose to optimise for completeness (which is what Logicians do).

You are only focusing on Gödel's incompleteness theorem. You are ignoring Gödel's completeness theorem.

Truth IS provability, but ONLY in first order logic. It does not apply to higher order logics.

https://en.wikipedia.org/wiki/G%C3%B6de ... ss_theorem
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.

You are agreeing with Gödel and you don't even know it.
PeteOlcott
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### Re: Is this an improved definition of a truth bearer?

Skepdick wrote: Wed Feb 26, 2020 5:08 pm
Truth IS provability, but ONLY in first order logic. It does not apply to higher order logics.
You seem to persistently fail to understand. That is probably because you only glance over my words
without bothered to really understand what I am saying.

Within the entire body of analytical knowledge truth is exactly one of two things:
(1) Expressions of language (finite strings) that have been defined to have the semantic property of Boolean True.
Corresponding to Axioms of a formal system. (Curry 1977:45)

(2) Truth preserving operations (finite string transformations) applied to these expressions of language (finite strings).
Corresponding to Theorems of a formal system.

This proves that True(X) and Provable(X) cannot ever possibly diverge.

Curry, Haskell 1977. Foundations of Mathematical Logic. New York: Dover Publications, 45
We begin by postulating a certain non void, definite class {E} of statements, which we call elementary statements...

The statements of {E} are called elementary statements to distinguish them from other statements which we may form from them or about them in the U language...

Then the elementary statements which belong to {T} we shall call the elementary theorems of {T}; we also say that these elementary statements are true for {T}. Thus, given {T}, an elementary theorem is an elementary statement which is true. A theory is thus a way of picking out from the statements of {E} a certain subclass of true statements…

The terminology which has just been used implies that the elementary statements are not such that their truth and falsity are known to us without reference to {T}.
nothing
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### Re: Is this an improved definition of a truth bearer?

PeteOlcott wrote: Mon Feb 24, 2020 11:34 pm A Truth Bearer is an analytical expression of formal or natural language that specifies a relation that can be tested and resolved to a single Boolean value.
Do you have the means/apparatus to test such expressions, if provided?
PeteOlcott
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### Re: Is this an improved definition of a truth bearer?

nothing wrote: Wed Feb 26, 2020 5:58 pm
PeteOlcott wrote: Mon Feb 24, 2020 11:34 pm A Truth Bearer is an analytical expression of formal or natural language that specifies a relation that can be tested and resolved to a single Boolean value.
Do you have the means/apparatus to test such expressions, if provided?
https://www.researchgate.net/publicatio ... y_YACC_BNF
Skepdick
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### Re: Is this an improved definition of a truth bearer?

PeteOlcott wrote: Wed Feb 26, 2020 5:29 pm
Skepdick wrote: Wed Feb 26, 2020 5:08 pm
Truth IS provability, but ONLY in first order logic. It does not apply to higher order logics.
You seem to persistently fail to understand. That is probably because you only glance over my words
without bothered to really understand what I am saying.

Within the entire body of analytical knowledge truth is exactly one of two things:
(1) Expressions of language (finite strings) that have been defined to have the semantic property of Boolean True.
Corresponding to Axioms of a formal system. (Curry 1977:45)

(2) Truth preserving operations (finite string transformations) applied to these expressions of language (finite strings).
Corresponding to Theorems of a formal system.

This proves that True(X) and Provable(X) cannot ever possibly diverge.

Curry, Haskell 1977. Foundations of Mathematical Logic. New York: Dover Publications, 45
We begin by postulating a certain non void, definite class {E} of statements, which we call elementary statements...

The statements of {E} are called elementary statements to distinguish them from other statements which we may form from them or about them in the U language...

Then the elementary statements which belong to {T} we shall call the elementary theorems of {T}; we also say that these elementary statements are true for {T}. Thus, given {T}, an elementary theorem is an elementary statement which is true. A theory is thus a way of picking out from the statements of {E} a certain subclass of true statements…

The terminology which has just been used implies that the elementary statements are not such that their truth and falsity are known to us without reference to {T}.
Pete, you are impervious to error correction and I am done trying to explain this to you in English.

I'll explain it to you in a language that has no wiggle-room for (mis)interpretation - empiricism.

Produce a "working solution" and I'll produce an input string that blows up your algorithm - then you can go and figure out where you fucked up on your own time.
PeteOlcott
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### Re: Is this an improved definition of a truth bearer?

Skepdick wrote: Wed Feb 26, 2020 10:34 pm Pete, you are impervious to error correction and I am done trying to explain this to you in English.

I'll explain it to you in a language that has no wiggle-room for (mis)interpretation - empiricism.

Produce a "working solution" and I'll produce an input string that blows up your algorithm - then you can go and figure out where you fucked up on your own time.
Some expressions of language are stipulated to be true and some relations between expressions of language are stipulated to be truth preserving. That really is all there is to the entire body of conceptual truth.

When you search everywhere and find that no counter-example can possibly exist, thenn (then and only then) you will know that I am right.

Skepdick
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### Re: Is this an improved definition of a truth bearer?

PeteOlcott wrote: Thu Feb 27, 2020 5:27 am Some expressions of language are stipulated to be true and some relations between expressions of language are stipulated to be truth preserving. That really is ALL there is to the entire body of conceptual truth.
Some of the truth is not ALL of the truth. This is precisely the implication of Gödel's incompleteness theorem.

It's precisely the job of the algorithm (which you claim to have created) to determine whether an arbitrary expression is true or false; and whether an arbitrary operator/predicate/relation is truth-preserving - but this is always being done (and this is the key part you keep missing). This is ALWAYS being done with respect to some particular set of grammar rules e.g a specified formal language!

You are failing to decouple the process of expression from the process of evaluation.

When you decouple expression from evaluation, then it will become obvious that the expression E may evaluate to Boolean:True in Grammar-A, AND it may evaluate to Boolean:False in Grammar-B.

And when you figure out that different grammatical rules produce different truth-values for the same expression, then you can go read about Wittgenstein's Rule-following paradox.
PeteOlcott wrote: Thu Feb 27, 2020 5:27 am When you search everywhere and find that no counter-example can possibly exist,
"An all-exhaustive search" is just another way of saying "complete", Pete. It's also known as Brute-force search.

Well done for figuring out what logical completeness is and how it works.
PeteOlcott wrote: Thu Feb 27, 2020 5:27 am thenn (then and only then) you will know that I am right.
Begging the question: Can you search everywhere to find that counter-example?
If the algorithm doesn't halt then it's still busy searching, and eventually it might find a counter-example.

When you realise that the search may never complete, then (and only then) you will know that you are wrong.
PeteOlcott
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### Re: Is this an improved definition of a truth bearer?

Skepdick wrote: Thu Feb 27, 2020 7:07 am
PeteOlcott wrote: Thu Feb 27, 2020 5:27 am Some expressions of language are stipulated to be true and some relations between expressions of language are stipulated to be truth preserving. That really is ALL there is to the entire body of conceptual truth.
Some of the truth is not ALL of the truth. This is precisely the implication of Gödel's incompleteness theorem.
There are some sentences that because of their semantic structure cannot possibly be resolved to True or False even though they are syntactically well formed. These sentences are not truth bearers. The example sentence used in the Tarski Undefinability Theorem is such as sentence.

The 1931 Incompleteness Theorem makes the same mistake yet no one ever boiled it down to its simplest possible essence the way that Wittgenstein did so they never see this: http://www.liarparadox.org/Wittgenstein.pdf

Some expressions of language are stipulated to be true and some relations between expressions of language are stipulated to be truth preserving.
This is all there is to the whole body of truth that can be expressed using language.

When you try and find a counter-example and find this is impossible, my point is proven.

Skepdick
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### Re: Is this an improved definition of a truth bearer?

PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm There are some sentences that because of their semantic structure cannot possibly be resolved to True or False even though they are syntactically well formed.
You are still failing to decouple expression from evaluation. There are very many syntactically well formed sentences that can be expressed.
That is exactly what makes a language useful and powerful - the ability to express ideas.

That those well-formed expressions can't be evaluated as either True or False is an evaluation problem! The fact that those expressions can't be reduced to true/false doesn't diminish their expensive power/utility.

You have figured out that language refuses to fit into two neat boxes. So what?

You have fallen into the trap of colorless reductionism The world is not black and white - it's colourful!
PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm These sentences are not truth bearers. The example sentence used in the Tarski Undefinability Theorem is such as sentence.
Then they aren't truth bearers. But they are information bearers.

In 2020 we care about information more than we care about truth.
PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm The 1931 Incompleteness Theorem makes the same mistake yet no one ever boiled it down to its simplest possible essence the way that Wittgenstein did so they never see this: http://www.liarparadox.org/Wittgenstein.pdf
You've done it (apparently). Congratulations. Nobody cares.

If it's possible in theory, but impossible in practice - your theory is wrong.
PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm Some expressions of language are stipulated to be true and some relations between expressions of language are stipulated to be truth preserving.
And it is your algorithm's job to figure out which is which.
PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm This is all there is to the whole body of truth that can be expressed using language.
That's an incomplete conception of truth.
PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm When you try and find a counter-example and find this is impossible, my point is proven.
We are still looking for a counter-example. When we are done looking (which is never), your point will be proven.

Like every dumb theoretician you ignore time and how it applies to the halting problem in practical terms.
PeteOlcott
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### Re: Is this an improved definition of a truth bearer?

Skepdick wrote: Fri Feb 28, 2020 7:48 am
PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm Some expressions of language are stipulated to be true and some relations between expressions of language are stipulated to be truth preserving.
And it is your algorithm's job to figure out which is which.
PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm This is all there is to the whole body of truth that can be expressed using language.
That's an incomplete conception of truth.
PeteOlcott wrote: Thu Feb 27, 2020 5:56 pm When you try and find a counter-example and find this is impossible, my point is proven.
We are still looking for a counter-example. When we are done looking (which is never), your point will be proven.
The above delimits the body of conceptual truth apart from the body of empirical truth in that the former can be completely expressed using language whereas the latter requires sensory stimulus from the sense organs.

The entire body of knowledge that can be expressed using language is entirely comprised of: expressions of language stipulated to be true and relations between expressions of language that are stipulated to be truth preserving.

When a counter-example is sought by a categorical search, one runs out of elements of the finite set of categories.

When one tests the expression of language: "This sentence is false." One finds that it is not a truth bearer, thus a type mismatch error for Boolean evaluation.

Skepdick
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### Re: Is this an improved definition of a truth bearer?

PeteOlcott wrote: Fri Feb 28, 2020 4:14 pm The above delimits....
Then stop delimiting things.
PeteOlcott wrote: Fri Feb 28, 2020 4:14 pm The entire body of knowledge that can be expressed using language is entirely comprised of: expressions of language stipulated to be true and relations between expressions of language that are stipulated to be truth preserving.
I reject your definition because my coffee is cold and yesterday was Thursday.
PeteOlcott wrote: Fri Feb 28, 2020 4:14 pm When a counter-example is sought by a categorical search, one runs out of elements of the finite set of categories.
You are going on in circles. That is what completeness means.
PeteOlcott wrote: Fri Feb 28, 2020 4:14 pm When one tests the expression of language: "This sentence is false." One finds that it is not a truth bearer, thus a type mismatch error for Boolean evaluation.
The stop testing the trivial case, and stop thinking in Booleans.

I believe that I have no beliefs. Assign a truth-value to that one.

It's a perfectly valid and informative English expression. It's perfectly valid grammatically in naive set theory also, if one accepts the unrestricted axiom of comprehension. It just so happens that it leads to a contradiction, but I don't mind that - you do.

And if you don't like it - you can fuck off
PeteOlcott
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### Re: Is this an improved definition of a truth bearer?

Skepdick wrote: Fri Feb 28, 2020 4:16 pm
PeteOlcott wrote: Fri Feb 28, 2020 4:14 pm The above delimits....
Then stop delimiting things.
PeteOlcott wrote: Fri Feb 28, 2020 4:14 pm The entire body of knowledge that can be expressed using language is entirely comprised of: expressions of language stipulated to be true and relations between expressions of language that are stipulated to be truth preserving.
I reject your definition because my coffee is cold and yesterday was Thursday.
PeteOlcott wrote: Fri Feb 28, 2020 4:14 pm When one tests the expression of language: "This sentence is false." One finds that it is not a truth bearer, thus a type mismatch error for Boolean evaluation.
The stop testing the trivial case, and stop thinking in Booleans.

I believe that I have no beliefs. Assign a truth-value to that one.
For my actual self I comprehend that beliefs are nothing more than the bias of emotional attachment to opinion so I reject them on this basis.

This is off the top of my head, thus possibly incorrect:
∃x ∃y (Has_Property(x,y) & Has_Property(x, ~Has_Property(x,y))) is self-contradictory thus false.
Skepdick
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### Re: Is this an improved definition of a truth bearer?

PeteOlcott wrote: Fri Feb 28, 2020 4:29 pm For my actual self I comprehend that beliefs are nothing more than the bias of emotional attachment to opinion so I reject them on this basis.
It's a perfectly valid and informative English expression. It's also grammatically valid in naive set theory if you accept the unrestricted axiom of comprehension. It just so happens that it leads to a contradiction, but I don't mind that - you do.

And if you don't like it - you can fuck off
PeteOlcott wrote: Fri Feb 28, 2020 4:29 pm This is off the top of my head, thus possibly incorrect:
∃x ∃y (Has_Property(x,y) & Has_Property(x, ~Has_Property(x,y))) is self-contradictory thus false.
Contradictions are not true or false. Contradictions are contradictions - they exist by definition. Unhandled exceptions. You know how to deal with those, right?

What truth-value you assign to them is a matter of choice.

Contradictions exist. I am evidence to that fact.

I exist and I don't exist. Contradiction!!! One of them is false.

Which one?
PeteOlcott
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### Re: Is this an improved definition of a truth bearer?

Skepdick wrote: Fri Feb 28, 2020 4:31 pm
PeteOlcott wrote: Fri Feb 28, 2020 4:29 pm For my actual self I comprehend that beliefs are nothing more than the bias of emotional attachment to opinion so I reject them on this basis.
It's a perfectly valid and informative English expression. It's also grammatically valid naive set theory, if you accept the unrestricted axiom of comprehension. It just so happens that it leads to a contradiction, but I don't mind that - you do.

And if you don't like it - you can fuck off
PeteOlcott wrote: Fri Feb 28, 2020 4:29 pm This is off the top of my head, thus possibly incorrect:
∃x ∃y (Has_Property(x,y) & Has_Property(x, ~Has_Property(x,y))) is self-contradictory thus false.

What truth-value you assign to them is a matter of choice.

Contradictions exist. I am evidence to that fact.
You are conflating the existence of a contradiction with the Boolean evaluation of a contradiction.
Contradiction is asserting that the union of a pair of disjoint sets is not the empty set.
∃n ∈ ℕ (n > 5 & n < 3)
Skepdick
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### Re: Is this an improved definition of a truth bearer?

PeteOlcott wrote: Fri Feb 28, 2020 4:39 pm You are conflating the existence of a contradiction with the Boolean evaluation of a contradiction.
Contradiction is asserting that the union of a pair of disjoint sets is not the empty set.
∃n ∈ ℕ (n > 5 & n < 3)
Pete, you are STILL trying to build a system that is consistent AND complete.

YOU.CAN. NOT. DO. THAT.

Gödel gave you the greatest gift in the world: a choice. So choose, damn it! Quit playing stupid games with yourself.

Here is a truth-bearer for you: consistency XOR completeness = 1

Pay close attention to the fact that XOR is NOT a truth-preserving relation. 1 XOR 1 = 0

Liar liar, pants on fire?