From Newsgroup: sci.math

On 2/9/2026 10:43 AM, Tristan Wibberley wrote:

On 09/02/2026 14:57, Mikko wrote:

Logic is not paralyzed. Separating semantics from inference rules
ensures that semantic problems don't affect the study of proofs
and provability.

Would you agree that inference rules are a formalisation of some semantics.

a) in a sense
b) yes, properly

?

And then a syntactical system is one in which there remains no
unformalised semantics (or, indeed, pragmatics), not even identification
of thought objects.

By the theory of simple types I mean the doctrine which says that the
objects of thought (or, in another interpretation, the symbolic
expressions) are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such
relations, etc. (with a similar hierarchy for extensions), and that
sentences of the form: " a has the property -a ", " b bears the relation
R to c ", etc. are meaningless, if a, b, c, R, -a are not of types
fitting together. Mixed types (such as classes containing individuals
and classes as elements) and therefore also transfinite types (such as
the class of all classes of finite types) are excluded. That the theory
of simple types suffices for avoiding also the epistemological paradoxes
is shown by a closer analysis of these. (Cf. Ramsey 1926 and Tarski
1935, p. 399)."

Semantics can be expressed entirely syntactically.
The most formal way to say this is that when all
expressions of language derive all of their semantic
meaning from other expressions of language, then all
knowledge that can be expressed in language is merely
relations between finite strings.

https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable for the entire body of knowledge.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21b-Linux NewsLink 1.2