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

Op 15.sep.2024 om 10:32 schreef Mikko:

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

On 2024-09-04 03:41:58 +0000, olcott said:
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The Foundation of Linguistic truth is stipulated relations
between finite strings.
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The only way that we know that "cats" <are> "animals"
(in English) is the this is stipulated to be true.
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*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
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*Yet equally applies to formal languages*

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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.

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

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

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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

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

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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.
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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.

That is not how it normally works. Animals have properties. If we find something with the properties of an animal, we conclude (not stipulate) that it is an animal.
If we find an unknown object, we are not free to stipulate that its an animal. We look at the properties, reason and conclude whether or not it is an animal.
When we look at a cat, we see it has the properties of an animal, then we conclude (not stipulate) that it an animal.
Some people are stipulating facts, but fact are things to conclude from observations and reasoning.
Stipulating that a car is an animal may fit the logic system, but that does not make it true.

 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.