Re: True on the basis of meaning --- Good job Richard !

On 5/13/24 11:04 AM, olcott wrote:

On 5/13/2024 6:18 AM, Richard Damon wrote:

On 5/12/24 11:41 PM, olcott wrote:

On 5/12/2024 7:35 PM, Richard Damon wrote:

On 5/12/24 8:07 PM, olcott wrote:

On 5/12/2024 6:55 PM, Richard Damon wrote:

On 5/12/24 7:22 PM, olcott wrote:

On 5/12/2024 6:02 PM, Richard Damon wrote:

On 5/12/24 6:56 PM, olcott wrote:

On 5/12/2024 5:40 PM, Richard Damon wrote:

On 5/12/24 5:54 PM, olcott wrote:

On 5/12/2024 3:33 PM, Richard Damon wrote:

On 5/12/24 2:36 PM, olcott wrote:

On 5/12/2024 1:22 PM, Richard Damon wrote:

On 5/12/24 2:06 PM, olcott wrote:

On 5/12/2024 12:52 PM, Richard Damon wrote:

On 5/12/24 1:19 PM, olcott wrote:

On 5/12/2024 10:33 AM, Mikko wrote:

On 2024-05-12 14:22:25 +0000, olcott said:
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On 5/12/2024 2:42 AM, Mikko wrote:

On 2024-05-11 04:27:03 +0000, olcott said:
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On 5/10/2024 10:49 PM, Richard Damon wrote:

On 5/10/24 11:35 PM, olcott wrote:

On 5/10/2024 10:16 PM, Richard Damon wrote:

On 5/10/24 10:36 PM, olcott wrote:

The entire body of expressions that are {true on the basis of their
meaning} involves nothing more or less than stipulated relations between
finite strings.
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You do know that what you are describing when applied to Formal Systems are the axioms of the system and the most primitively provable theorems.
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YES and there are axioms that comprise the verbal model of the
actual world, thus Quine was wrong.

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You don't understand what Quite was talking about,
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I don't need to know anything about what he was talking about
except that he disagreed with {true on the basis or meaning}.
I don't care or need to know how he got to an incorrect answer.
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You don't seem to understand what "Formal Logic" actually means.
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Ultimately it is anchored in stipulated relations between finite
strings (AKA axioms) and expressions derived from applying truth
preserving operations to these axioms.

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Which you don't seem to understand what that means.
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I understand this much more deeply than you do.

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In and about formal logic there is no valid deep understanding. Only
a shallow understanding can be valid.
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It turns out that ALL {true on the basis of meaning} that includes
ALL of logic and math has its entire foundation in relations between
finite strings. Some are stipulated to be true (axioms) and some
are derived by applying truth preserving operations to these axioms.

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Usually the word "true" is not used when talking about uninterpreted
formal systems. Axioms and what can be inferred from axioms are called
"theorems". Theorems can be true in some interpretations and false in
another. If the system is incosistent then there is no interpretation
where all axioms are true.
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I am not talking about how these things are usually spoken of. I am
talking about my unique contribution to the actual philosophical
foundation of {true on the basis of meaning}.

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Which means you need to be VERY clear about what you claim to be "usually spoken of" and what is your unique contribution.
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You then need to show how your contribution isn't in conflict with the classical parts, but follows within its definitions.
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If you want to say that something in the classical theory is not actually true, then you need to show how removing that piece doesn't affect the system. This seems to be a weak point of yours, you think you can change a system, and not show that the system can still exist as it was.
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This is entirely comprised of relations between finite strings:
some of which are stipulated to have the semantic value of Boolean
true, and others derived from applying truth preserving operations
to these finite string.
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This is approximately equivalent to proofs from axioms. It is not
exactly the same thing because an infinite sequence of inference
steps may sometimes be required. It is also not exactly the same
because some proofs are not restricted to truth preserving operations.
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So, what effect does that difference have?
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You seem here to accept that some truths are based on an infinite sequence of operations, while you admit that proofs are finite sequences, but it seems you still assert that all truths must be provable.
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I did not use the term "provable" or "proofs" these only apply to
finite sequences. {derived from applying truth preserving operations}
can involve infinite sequences.

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But if true can come out of an infinite sequences, and some need such an infinite sequence, but proof requires a finite sequence, that shows that there will exists some statements are true, but not provable.
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...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
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When we look at the way that {true on the basis of meaning}
actually works, then all epistemological antinomies are simply untrue.

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And Godel would agree to that. You just don't understand what that line 14 means.
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It can be proven in a finite sequence of steps that
epistemological antinomies are simply untrue.
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So?
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So that directly contradicts what Gödel said in the quote thus proving
that Gödel and Tarski were both fundamentally incorrect in the basic
foundation of their work.
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Where does he say wha tyo claim?
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He says that it can be *USED* for a similar proof.
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*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS*
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS*
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS*
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS*
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But he showed how it was used, so you are just proven wrong.
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This proves that he did not understand undecidability, thus making
the rest of his paper moot.

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It shows no such thing.
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Since, As I have pointed out, the actual statement, which you don't seem to even be able to understand, is NOT an epistemological antinomy, just shows that you don't understand anything about the topic you are talking about.
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You don't seem to understand even basic English, so you have no place trying to talk about theories based on the "meaning of words", as you have proved yourself incompetent.
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Tarski anchors his entire proof in the above Gödel quote so
we can't just say one one little quote does not ruin the whole thing.
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Yep, and he is right.
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The Liar Paradox is easily rejected by the correct foundation of
{true on the basis of meaning} on the basis that it cannot be
derived by applying truth preserving operations to finite strings
that are stipulated to have the semantic value of Boolean true.

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Yes, the liar paradox is a statement that can be neither true or false.
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Tarski thought that he proved that True(L, x) cannot be defined on
the basis that he could not prove that an expression that is not true
is true.

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Nope. You seem to have a mental block on this.
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The point is that if "True(L, x)" is a predicate, then it ALWAYS has a truth value, and that value is true if the statement is true, and false if the statement is false, or not a truth bearer.
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True(English, "a fish") is a type mismatch error, they must be
excluded and not merely construed as untrue.
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No, since "a fish" is not a truth bearer, True(English, "a fish") must return false.
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 Then it must also return false for ~X where X = "a fish"

Yes.

 

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True(English, "this sentence is untrue")
is ALSO a type mismatch error, that must be
excluded and not merely construed as untrue.
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Nope, since "this sentence is untrue" is not a true statement, True(English, "this sentence is untrue") must return false.
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 Different yet equivalent protocol.

Nope.
True(L, f) must ALWAYS be a truth bearer, and thus ~True(L, f) must also be one.

 

Remember, the truth predicate "True" doesn't return the truth value of the expression, so doesn't have an answer for a non-truth-bearer, but is a PREDICATE, that always returns a value, which is TRUE if the expression is a true expression, and false for everything else.
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 Boolean True(L,x) can return false when x is not a truth bearer
yet must also return false for ~x.

But the problem wasn't given ~x.
Remember, p defined as ~True(L, p) is BY DEFINITION a truth bearer, as True must return a Truth Value for all inputs, and ~ a truth valus is always the other truth value.

 

Tarski shows, that in a logic system capable of building references, that the statement:
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p defined as ~True(L, p)
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has no legal values for True(L, p)
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If True(L, p) is true, the p is ~true or false, but then True(L, false) can not be true.
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If True(L, p) is false (because perhaps we think p isn't a truth bearer) we find that p = ~false, or p is true, and thus we find that we just made True(L, true) to be false.
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*There is no truth without a truthmaker*
Meaning that expression X must be linked by a sequence of
truth preserving operations to expressions of language that are stipulated as having the semantic value of Boolean true or
expression X is simply untrue. The same applies to ~X/unfalse.

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And the True predicate detects if such a sequence exists for its input expression in the domain specified.
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 Great! You seem to be understanding this quite well.
 

So, you don't see the contradiction it produces?

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So, we can not build a predicate that always tells us if a statement it true.
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For all expressions that are {true on the basis of their meaning} expressed as relations between finite strings, every expression X
or its negation ~X either has a sequence of truth preserving operations
from expressions stipulated to be true or it is not a truth bearer.

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So, non-truth-bearers are just not true for the Truth Predicate, so it is supposed to return false.
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 Non-truth bearers such as "a fish" are also untrue in actual reality.
 

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It is sort of like Sipser machine, that accepts all inputs that D accepts, and reject all inputs that D either rejects or doesn't answer about.
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 Yes that seems to be correct.
That would seem to indicate that Halts(L, x) and ~Halts(L, x)
should both return false for pathological inputs.

Not possible.
~ applies to the VALUE it was provided with, so if Halts(L, x) returns false, ~Halts(L, x) must return true.
Otherwise, your negation operator is broken.
To do what you want, you need to go to three (or more) valued logic, which is outside the domain of what Tarski was talking about.

 

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Somehow, this straight forward proof is just above your head, likely because you don't understand the implactions of something being a predicate.
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What screwed him up the most it that this sentence IS TRUE:
This sentence is not true: "This sentence is not true"
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The above is the simplest possible example of a sentence in
Tarski's theory (quoted sentence) and his metatheory (outer sentence)

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Nope, you miss the diference between a statement saying an expression is true, and a PREDICATE.
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The predicate implements the algorithm that I have already specified
twice in this same message.
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A Statement might not be a truth bearer, but a predicate ALWAYS is.
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X = "a Fish"
True(English, X)  false meaning X is untrue
True(English, ~X) false meaning X is unfalse

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Right. (Except that "English" isn't a formal system, which is the domain of the supposed Truth Predicate True).
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 Montague showed how to sufficiently formalize English declarative
sentences. The Cyc project has done this very extensively with their
CycL language. The parser for such a system could simply reject
"a fish" or "this sentence is not true".
 

But what value should:
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x = ~True(L, x) return
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 The formal system that I propose could return false for
x and false for ~x indicating that x is not a truth bearer.

So you don't understand what ~True(L, x) means.
Seems about right.
It isn't asking about True(L, ~x)

 On this one topic you are doing better than anyone else
on any other forum.

And you are just showing how little you understand.

 

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https://liarparadox.org/Tarski_275_276.pdf
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