From Newsgroup: comp.ai.philosophy

On 7/15/2020 9:57 AM, olcott wrote:

On 7/14/2020 11:13 PM, olcott wrote:

On 7/14/2020 10:30 PM, David Kleinecke wrote:

On Tuesday, July 14, 2020 at 7:55:25 PM UTC-7, olcott wrote:

These terms were used perfectly according to their standard meaning:
-a >>>mathematical mapping in T from -a to a Boolean value<<<

Lt occurs to me that we all would be happier if that was:
-a-a-a mapping in T from -a onto the two-member set {true, false}

You improved my words yet again, good job.

https://en.wikipedia.org/wiki/Bijection,_injection_and_surjection

The function is surjective, or onto, if each element of the codomain
is mapped to by at least one element of the domain.

A map is a way of associating unique objects to every element in a given set. So a map f : A raa B from A to B is a function f such that for every
a ree A, there is a unique object f(a) ree B. The terms function and mapping are synonymous for map. https://mathworld.wolfram.com/Map.html

reC-a (TruthBearer(T,-a) rao f(T,-a) ree {true, false})

For all -a of theory T -a is a truth bearer in T if and only if there is a function in T from -a to exactly one element of the set of {true, false}.

--
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.
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