Re: True on the basis of meaning --- Tarski

On 2024-05-17 17:28:19 +0000, olcott said:

On 5/17/2024 10:56 AM, Mikko wrote:

On 2024-05-16 16:00:59 +0000, olcott said:
 

On 5/15/2024 3:43 AM, Mikko wrote:

On 2024-05-14 15:18:22 +0000, olcott said:
 

On 5/14/2024 4:16 AM, Mikko wrote:

On 2024-05-13 14:34:12 +0000, olcott said:
 

On 5/13/2024 3:52 AM, Mikko wrote:

On 2024-05-12 17:19:48 +0000, olcott said:
 

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

On 2024-05-12 14:22:25 +0000, olcott said:
 

On 5/12/2024 2:42 AM, Mikko wrote:

On 2024-05-11 04:27:03 +0000, olcott said:
 

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.
 

 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.
 

 YES and there are axioms that comprise the verbal model of the
actual world, thus Quine was wrong.

 You don't understand what Quite was talking about,
 

 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.
 

 

 You don't seem to understand what "Formal Logic" actually means.
 

 Ultimately it is anchored in stipulated relations between finite
strings (AKA axioms) and expressions derived from applying truth
preserving operations to these axioms.

 Which you don't seem to understand what that means.
 

 I understand this much more deeply than you do.

 In and about formal logic there is no valid deep understanding. Only
a shallow understanding can be valid.
 

 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.

 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.
 

 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}.

 What matters is that you are not talking about those things as they
are usually spoken of. The consequence is that nobody is going to
understand you, and the consequence of that probably is that you
cannot contribute.
 

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.

 Most of that doesn't require any stipulations about semantics but
can be done with finite strings and their relations. Semantics is
only needed to choose interesting problems and, if a problem can
be solved, to interprete the solution.
 

 The only way that a system of formalized natural language can
possibly know that {dogs} <are> {animals} is that it must be told.
See also Davidson's truth conditional semantics.
https://en.wikipedia.org/wiki/Truth-conditional_semantics
 The only way that "dogs are animals" acquires semantic
meaning is the stipulated relation: {dogs} <are> {animals}.
 

This is approximately equivalent to proofs from axioms.

 It shouod be exactly equivalent.
 

It is not exactly the same thing because an infinite sequence of
inference steps may sometimes be required.

 Infinite sequences create more problem than they solve. For example,
you can prove that 1 = 2 with the infinite sequence
 

 For real world things that are never required. The various
conjectures seem to require an infinite sequence of inference steps.

 That is not known. There are real world problems that are not yet
solved without an infinite seqeunce of inference steps and there
remains the possibility that some of them, or one that is not yet
thought to be a problem but will be, that cannot be solved without
an infinite sequence of inference steps.
 Anyway, whether real world problems are solvable without an infinite
sequence of inference steps is irrelevanto to the topic "True on the
basis of meaning".
 

 My whole purpose with this whole thread is to show exactly how
epistemological antinomies can be recognized and rejected thus
not form the basis for any undecidability proofs or Tarski's
undefinability theorem.

 There are provable sentences of the form A -> B where A is some
hypthesis and B is an epistemological antimńomy. How are these
true statments handled when B is rejected?

 Epistemological antinomies have no truth value and implication
requires a pair of truth bearers that have a Boolean value thus
your expression is rejected as a type mismatch error.

 So if X is true and Y something complicated we cannot trust that
X or Y is true without analyzing that Y?
 

 The lack of any sequence of truth preserving operations from
expressions of language that have been stipulated to be true
--set of finite string semantic meanings that form an accurate
--model of the general knowledge of the actual world.
to x or ~x indicates that x is not a truth bearer and must
be rejected as a type mismatch error in any formal system of
bivalent logic.
 *This seems to screen out any any all undecidable inputs*

In my example X is one of those statements that are true according
to what is said above. Y is a syntactically correct formulat but
so compicated that to determine its truth value would require a
considerable effort.
I asked whether one must analyze Y in order to determine whether
X or Y is true. You didn't answer.
--
Mikko