Re: Readings in (some of the) foundations of mathematics --- tree of knowledge

On 7/4/2026 1:58 AM, Mikko wrote:
> On 03/07/2026 18:23, olcott wrote:
>> On 7/3/2026 3:41 AM, Mikko wrote:
>>> On 02/07/2026 17:45, olcott wrote:
>>>> On 7/2/2026 1:44 AM, Mikko wrote:
>>>>> That depends on the semantic system. Often the meaning of the word
>>>>> "cat" indeed involves that what is called a "cat" is also called
>>>>> an "animal" but there are other posiibilities. Conseqently, the
>>>>> sentence "cats are animals" can be a semantic tautology that tells
>>>>> nothing about the real world, 
>>>>
>>>> It tells us exactly one thing about the real world 1 != 0
>>>
>>> A tautology tells nothing about the real world. Sometimes one can
>>> have a false impression that something is said about the real world
>>> when a tautology is presented. But that impression is a consequence
>>> of insufficient or invalid consideration of logic and semantics.
>>>
>> Stipulative definition of relations between finite
>> strings is the only way that these finite strings
>> acquire semantic meaning.
> 
> For some kind of formal semantics where the meaning of a fintite
> string is another finite string (or perhaps, in some cases, the
> same). That way does not get any real world semantics, though
> it can extend real world semantics if you already have some.
> 

All of meaning expressed in language works this same way.

>> Try to find some other way that "cats" <are> "animals"
>> can acquire semantic meaning besides Davidson Semantics.
> 
> They come from experiences about uses of those words by other people.
> Likewise for most of commonly used words and phrases.
> 

If this was true then Chinese would not exist.
Stipulated relations between finite strings is
the only way that language acquires meaning.

-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).