On 7/3/24 10:14 AM, olcott wrote:
On 7/3/2024 6:45 AM, Richard Damon wrote:
On 7/2/24 11:39 PM, olcott wrote:
On 7/2/2024 10:18 PM, Richard Damon wrote:
On 7/2/24 11:00 PM, olcott wrote:
Every {analytic} proposition X having a truth-maker is true.
Every {analytic} proposition X having a truth-maker for ~X is false.
Those expressions of language left over are not not truth bearers.
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And the "truth-maker" in a formal system needs to be from the formal system itself, unless the proposition IS a truth-maker itself of the formal system.
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Yes.
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Also, most propositions actually need MULTIPLE truth-makers to make them true.
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Yes.
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True(L,x) and False(L,x) where L is the language and x is the
expression of that language rejects self-contradictory undecidable
propositions as not truth-bearers.
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So, what is the value of:
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True(L,x) where x, in language L is the statement "not True(L,x)"
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It is that as I have always been saying, that x is not a truth bearer.
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And so True(L, x) must be false,
Is "a fish" true or false or neither?
That "a fish" is not true does not make it false.
Neither, so True(L, "a fish") is false. (assume "a fish" is a syntactically expressible statement in L)
The True predicate saying false doesn't mean the statement is false, just that it isn't true.
The problem comes when the language is expressive enough to build statement that are self-referential (even indirectly self-referential).
If we can form the statement x in L to be "~True(L, x)", then that system can not have a Truth Predicate, which is what Tarski is showing.
and thus we are saying that x, which is defined to "not True(L, x)" must be true, so not only are you wrong about it not being a truth bearer, you are wrong about not being true.
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It has the same truth value as "a fish"
Then so does your True predicacte, and thus isn't a predicate.
Thus, making you a LIAR.
Or, does your logic say that "not false" as a logical expresion isn't true? and thus your logic fails to hold to the rule of the excluded middle?
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Self-contradictory expressions are not truth-bearers
thus have no truth value.
But the Truth Predicate, as Tarski defines it, can take as input non-truth-bearing statements, and indicate they are not true.
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Or is your True(L,x) not a predicate that always gives an True or False answer? (which is the requirement that Tarski has)
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As I have always been saying X is true, or false or not a truth bearer.
"a fish" is not a truth bearer.
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And "True(L, x)" needs to return True if x is True, and False if x is False, or not a truth bearer.
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*That is not the way True(L,x) works*
True(L,x)
returns true if x is true and false if x not true.
Right so if x is defined as ~True(L, x) is not a truth bearer, and thus True(L, x) returns false, the x is defined as the negation of a false expression which is true. So you now have a true express also being a non-truth bearer and you system is inconsistant.
False(L,x) is True(L,~x)
returns true if x is false and false if x not false.
True(L, "a fish") is false and False(L, "a fish") is false.
and if True(L, x) where x in L is ~True(L, x) says that x isn't true because it is not a truth bearer, you system breaks.
So, since x defined as "not True(L,x)" is True if True(L, x) says no, then True failed to live up to its requirements.
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And you show you are unable to understand what requirements are.
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Only expressions of language requiring an infinite number of steps
such as Goldbach's conjecture slip through the cracks. These can
be separately recognized.
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How?
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We ourselves can see that it can be proven in an infinite
sequence of steps thus an algorithm can see this too.
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So, you think the Goldbach's conjecture IS true? Show your proof and win the prize,
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An infinite sequence can prove Goldbach's conjecture is true or false.
No, because a "Proof" is BY DEFINTION a finite sequence.
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Why do they need a seperate rule?
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It is the only thing that does not fit perfectly in truth-maker theory.
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But there are MANY such statements, so you are just admitting that your theory is just full of holes.
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All of the important things can be done in finite proofs.
Only the unimportant things require infinite proofs.
The is no such thing as an infinite proof, not in classic logic.
There are statements that are TRUE due to an infinite sequence of truth persevering steps, but that sequence of steps is not a proof.
It seems you don't understand the difference between truth and knowledge.
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{Analytic} propositions are expressions of formal or natural language
that are linked by a sequence of truth preserving operations to the
verbal meanings that make them true or false. This includes expressions
of language that form the accurate verbal model of the actual world.
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But that isn't correct for formal systems. so you just wrote yourself out of the problems.
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It is correct in the correct notion of formal systems.
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No, it isn't the case that the VERBAL meanings have anything to do with it.
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To cover the entire body of all {analytic} truth we
have (a) formal systems of logic and math using formal languages.
To cover all the rest we have (b) a correct verbal model of
the actual world specified using formal language that can
be translated to and from natural language.
Which seems to be just double talk.
Note, one big problem with your definition is we don't have the entire body of {analytic} truth, only the "body" of known {analytic} truths. And it doesn't really form a single "body" because each "truth" is attached to the system it comes out of, and is dependent on it. In fact, there are many "truths" that are just inconsistant with each other if you ignore the system they come out of.
And NO {analytic} truth relates to the actual world, just models of it that have specific assumptions defined as there essential truths, because everything we know about the actual real word is based at least somewhat on an empirical observation.
It is the FORMAL meanings, defined in the system that define it.
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And Infinite Chains genrate semantic truth.
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They have no significant practical application.
I guess you don't think Mathematics has significant practical applicaition.
Also, just because something is true in a "verbal model" of the world doesn't make it true in a given formal system.
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The accurate verbal model of the actual world contains
all of this.
but isn't part of a formal system.
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Formal systems are NOT based on "Natural Language" but ONLY their own Formal Language, and need not have any direct bearing on the "actual world", but tend to create there own world, which may be used as a way to modle ideas about our actual world, or maybe not.
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I already included that. By tacking on that it can
be in natural or formal language and include an accurate
model of the actual world Quine's objections that there
is no separately identifiable body of {analytic truth}
are overcome.
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But formal systems do not need to be "accurate models of the actual world", and what Quine was pointing out was that natural language is inherently a bad model as words can have too many different meanings.
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The formal system that is an accurate model of the actual world
has subsystems.
But we can't know what models actualy ARE accurate models of the actual world, just ones that seem accurate enough for what we are trying to do.
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Modern day philosophers at best only have a vague understanding
of what a truth-maker or truth-bearer is.
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Which is one reason to try to stay out of that realm, and stay in the formal systems without that problem.
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That most everyone else is ignorant is no excuse for
me to not make these things clear.
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Then go in and get out of Formal systems. The rules are different, and what works in one place doesn't necessarily work in the other.
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That you do not understand Montague semantics does not make
Montague Semantics incorrect.
No, you don't seem to understand it. Montague semantics is basical one attempt to make a formal system out of Natural language. It isn't a way to apply Natuaral language to an arbitrary Formal system.
Like many things, you have it backwards.
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Truthmakers
This much is agreed: “x makes it true that p” is a construction that signifies, if it signifies anything at all, a relation borne to a truth-bearer by something else, a truth-maker. But it isn’t generally agreed what that something else might be, or what truth-bearers are, or what the character might be of the relationship that holds, if it does, between them, or even whether such a relationship ever does hold. https://plato.stanford.edu/entries/truthmakers/
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So, it seems that part of your problem is that you don't understand that Tarski is talking PURELY in Formal Systems, with the rules there-in, and not your vague philospoplical systems.
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I take his scope and broaden it.
Within his narrow scope and my foundation of analytical truth
When X not provable or refutable from axioms merely means X is
not a truth-bearer in L.
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Nope, that is a LIE, and shows your ignorance, and that your foundation of anaklytc truth just can't handle the logic.
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The accurate model of the actual world has subsystems of
mathematical logic.
But we don't know what model is an accurate model of the actual world. That is what science has been working on, and it just has theories about what would be an accurate model.
You are just making your normal error of presuming we can know something we do not.
You just admitted that there were statements you "truth-maker" logic can't handle, because they need infinite steps.
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When my system handles much more than any other system could
possibly handle we don't reject it as useless because there
are things that it cannot currently handle.
When you can actually formalize you system, then we can talk. But until you can, you can't try to insert into other system.
So, now it seems you are saying that there are statements with actual truth value of true or false that are not "truth-bearers", in other words, you are admitting you definition is a self-contradiction.
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No at all. I sad nothing like this.
In rare occasions the truth-maker must have an infinite sequence.
So, G has truth-makers, but isn't prvovable.
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Haskell Curry presents an equivalent idea.
https://www.liarparadox.org/Haskell_Curry_45.pdf
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I have always known this for the whole two decades that I have
been working on this yet only now have all of the words to say it.
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You mean you have MISUNDERSTOOD It for two decades.
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I have just proved that my understanding is complete.
The inability for an infinite number of steps to be
processed in finite time is not any mistake that I made.
Nope, you have proved yourself hopelessly confused
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In Formal systems, there is no question about "Truth Makers" as Truth in a formal system is (generally) DEFINED as having a finite or infinite chain of semantic connections (Your truth preserving operations, which are defined in the system) from the pre-defined list of fundamental truths of the system (Your Truthmakers).
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Not quite. Some of the operations are not truth preserving.
https://en.wikipedia.org/wiki/Principle_of_explosion
In software engineering that would be called a kludge.
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You have shown that you don't understand logic well enough to understand that.
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Not at all. You have proven that your indoctrination
with falsehoods is too strong to be overcome. Most
people follow their herd.
WHAT Falsehood.
I that like your diagonalization proof you said would disproof Godel, and they you said that diagnonalization is nonsense?
So, you just admitted that you were a liar that pedels in nonsense.
What step in the demonstration of the principle of explosion is NOT a "truth-preserving" operation.
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The whole idea that any inference can be made without
semantic relevance is fundamentally incorrect.
But you don't understand the MEANING of semantic relevance in Formal logic,
Remember, the whole premise of the demonstartion is that it has already been established in the system that there exist a given contrdiction, that both X and ~X are both true.
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That assumption is proven to be incorrect by the law
of non-contradiction. When we have assumptions that contradict
axioms we throw out the assumption and keep the axiom.
But the principle of explosion is based on a system that has already broken the law of non-contradiction.
You just are too stupid to understand what you are saying.
*Three laws of logic apply to all propositions*
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
Nope, only is classic two-valued logic, and only for "correct" system/
And remember, The Principle of explosion is describing the effect of a system breaking the law of non-contradiction in one place, being able to break it in every place.
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The fundamental truths of the system have nothing making them true, except the system itself defining them as such.
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Kittens are baby cats and not fifteen story office building ONLY
by translating the accurate model of the actual world into the
arbitrary conventions of English.
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Which has nothing to do with "Formal Systems", you are just demonstrating you total lack of understanding of them.
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{kittens} ⊂ {cats}
{cats} ∩ {fifteen story office buildings} = ∅
Nope, only apply to a formal system that defined those terms.
You have admitted that much by claiming something must be true based on a given type of proof, which you than admit you don't know of the proof, but that that type of proof is just nonsense.
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That is the behavior of a two year old. If he first wants it, and kicks and screams for it, and then realizes he will not get it, decides it must by yucky and he never wanted it in the first place.
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Your "logic" makes about as much sense as that, namely it IS nonsense.
The Tarski Undefinability Theorem failed to understand truthmaker theory
Re: The Tarski Undefinability Theorem failed to understand truthmaker theory, because Olcott doesn't undestand