Re: The Foundation of Linguistic truth is stipulated relations between finite strings

On 2024-09-14 14:01:31 +0000, olcott said:

On 9/14/2024 3:26 AM, Mikko wrote:

On 2024-09-13 14:38:02 +0000, olcott said:
 

On 9/13/2024 6:52 AM, Mikko wrote:

On 2024-09-04 03:41:58 +0000, olcott said:
 

The Foundation of Linguistic truth is stipulated relations
between finite strings.
 The only way that we know that "cats" <are> "animals"
(in English) is the this is stipulated to be true.
 *This is related to*
Truth-conditional semantics is an approach to semantics of
natural language that sees meaning (or at least the meaning
of assertions) as being the same as, or reducible to, their
truth conditions. This approach to semantics is principally
associated with Donald Davidson, and attempts to carry out
for the semantics of natural language what Tarski's semantic
theory of truth achieves for the semantics of logic.
https://en.wikipedia.org/wiki/Truth-conditional_semantics
 *Yet equally applies to formal languages*

 No, it does not. Formal languages are designed for many different
purposes. Whether they have any semantics and the nature of the
semantics of those that have is determined by the purpose of the
language.

 Formal languages are essentially nothing more than
relations between finite strings.

 Basically a formal language is just a set of strings, usually defined
so that it is easy to determine about each string whether it belongs
to that subset. Relations of strings to other strings or anything else
are defined when useful for the purpose of the language.
 

 Yes.
 

Thus, given T, an elementary theorem is an elementary
statement which is true.

 That requires more than just a language. Being an elementary theorem means
that a subset of the language is defined as a set of the elementary theorems

 a subset of the finite strings are stipulated to be elementary theorems.
 

or postulates, usually so that it easy to determine whether a string is a
member of that set, often simply as a list of all elementary theorems.
 

 Yes.
 

https://www.liarparadox.org/Haskell_Curry_45.pdf
 Some of these relations between finite strings are
elementary theorems thus are stipulated to be true.

 No, that conficts with the meanings of those words. Certain realtions
between strings are designated as inference rules, usually defined so
that it is easy to determine whether a given string can be inferred
from given (usually one or two) other strings. Elementary theorems
are strings, not relations between strings.
 

 One elementary theorem of English is the {Cats} <are> {Animals}.

There are no elementary theorems of English.

The only way that way know that the set named "cats" is a subset
of the set named "animals" is that it is stipulated to be true is
that it is stipulated.

The meanings of most English words (including "cat", "is", and "animal"
do not come from stipulations but tradition. The tradition is not
always uniform although there is not much variation with "cat" or
"animal" and what there is that does not affet the truth of "cats are
animals". The answers may vary if you ask about more extic beings like
sponges or slime molds.
The statement "cats are animals" is regarded as true because nobody has
seen or even heard about any being that satisfies the traditional meaning
of "cat" but not the raditional meaning of "animal".

The set of properties that belong to the named set of "cats" and the set
of "animals" is also stipulated to be true. "cats" <have> "lungs".

Sharks are usually consederd "animals" but don't have lungs. THerefore
"lungs" is not relevant above.

Thus True(L,x) merely means there is a sequence of truth
preserving operations from x in L to elementary theorems
of L.

 Usually that prperty of a string is not called True. Instead, a non- empty sequence of strings where each member is an elementary theorem or can be
inferred from strings nearer the beginning of the sequence by the inference
rules is called a proof. The set of theorems is the set that contains every
string that is he last members of a proof and no other string.

 The elementary theorems (ET) are stipulated to have the semantic property
of Boolean true.

Maybe, maybe not. More importantly, they are defined to have the property
of being theorems. A theorem may be true about someting and false about
something else.

Other expressions x are only true when x can be derived by applying a
sequence of truth preserving operations to (ET) (typically back-chained inference).

The meaning of "truth preserving" depends on the meaning of "true", which
is usually not used in formal systems. Instead, non-elemetary theorems
are regured to be inferred with the inference rules of the theory (usually
borrowed from some logic).

Postulates, theoresm, inference rules and theorems are not parts of a
language but together with language constritue a large system that is
called a theory.

 That is typically the way it is done yet becomes difficult to understand
when applied to natural language. We never think of English as dividable
into separate theories.

That is the way formal theories are best presented. Natural languages are
not formal and not theories.

We construe English as also containing all of the semantics of English.

It often is. However, much can be said abour English and other languages
without mentioning semantics, for example that the typcal word order is
that the subject is before the verb and the object, if there is one, is
after the verb.

We never have systems of English whether the same expression is the
truth in one system and a lie in another system.

Of course we have. The meaning of a sentence often depends on where
or when it is said. For exampe "France is a kingdom" used to be true
but is not anymore.

In order to discuss meanings and truth a still larger
system is needed where the strings of a theory are related to something
else (for example real world objects or strings of another language).

 Not really. When we have a separate model theory then crucial
details get overlooked.

Not necessarily, and crucial detains can be overlooked anyway.
A separate model theory forces at least some consideration of
semantics.

When we look at a language (including all of its semantics as)
relations between finite strings then we can see all of the
details with none overlooked.

That way you are likely to overlook the relations of the strings to
non-strings. Such realtions are often crucial to the purpose or an
application of the language.

From Tarski's perspective this would mean that a language
is its own metal-language.

Tarski could assume so because Gödel ahd shown how one can use
arithmetic as a meta-language. Hoever, a more natural approach
would be to use a theory of strings as the meta-language and
the meta-theory.
--
Mikko