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

On 7/4/2026 9:07 AM, Alan Mackenzie wrote:
> [ Followup-To: set ]
> 
> In sci.math olcott <[email protected]> wrote:
> 
> [ .... ]
> 
>> A complete finite list of "atomic facts" of general
>> knowledge tells us everything that can be expressed
>> in language. This finite list also has all of the
>> kinds of relations between these facts.
> 
> Seems doubtful.  Falsehoods can also be expressed in language, together
> with that vast trove of expressions which are neither true nor false.  In
> fact, when it comes to "everything that can be expressed in language", a
> list of "atomic facts" would appear to be unhelpful, just as much as a
> list of "atomic falsehoods" would be, whatever that might mean.
> 

A complete finite list of "atomic facts" of general knowledge
only includes true truth bearers and only facts that cannot
be derived from anything else. This excludes falsehoods and
expressions that are neither true nor false. It is the axiomatic
basis of knowledge of the world.

>> -- 
>> Copyright 2026 Olcott
> 


-- 
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).