Question

Suppose we had a multiset of truth values [T, T], and that was it. Letting those be indexed as T1 and T2, suppose a twofold fragmenting of a related set of propositions (maybe not a set of all-propositions-whatsoever) and say that propositions from fragment A are true only when they map to T1 and B's elements go with T2. Then, however, sometimes elements of B map to T1, say: and that is how falsity arises, here (mismatches of T-maps).

Is that enough to have a theory of falsehood in a truth-value multiset, or would attempts to translate/encode [T, T] as {T, F} not work out like that at all?

Answer 1

A multiset of truth values [T, T] is insufficient to represent a theory of falsehood, as it cannot capture the mismatches in truth-value mappings. Therefore, attempts to translate or encode [T, T] as {T, F} would not accurately represent falsehood.

Step-by-step explanation:

The question is asking whether a multiset of truth values, such as [T, T], can be used to represent a theory of falsehood. In this case, the multiset consists of two true values, T1 and T2. The question proposes a twofold fragmenting of the propositions, where A's elements are true when they map to T1 and B's elements are true when they map to T2.

If elements of B sometimes map to T1, it would result in mismatches of truth-value mappings, which can be considered as the source of falsity. This indicates that the multiset [T, T] is not sufficient to represent a theory of falsehood, as it cannot capture the mismatches in truth-value mappings.

Therefore, attempts to translate or encode [T, T] as {T, F} would not accurately capture the concept of falsehood within the truth-value multiset.