The modalities of truth
I think that the "empirical" truths (which state "A"), are a subset of the "possible" ones (that state "A" or "not-A"), and these are a subset of the "contingent" truths (which are the non-necessary ones, i.e, the truths whose denial does not led to a contradiction).
Then, regarding "A", we can to define the "empirical" truth as "A", the "possible" one as "A or not-A" and the "necessary" one as "If not-A then B and not-B".
Where do you think the analysis fails?
Then, regarding "A", we can to define the "empirical" truth as "A", the "possible" one as "A or not-A" and the "necessary" one as "If not-A then B and not-B".
Where do you think the analysis fails?
Comments (5)
It is false to say 'possible A' claims 'A or not A'.
It is false to say 'A or not A' is contingent.
'A or not A' is tautologous, necessarily true.
"A" is necessarily true iff "not-A -> (B and not-B)"
"A" is possible true iff "A or not-A" is true
"A" is empirically true iff "A" is true
What fails in these definitions?
1."A" is necessarily true iff "not-A -> (B and not-B)", is invalid.
It fails when "A" is necessarily true if "not-A -> (B and not-B)".
(not-A -> (B and not-B)) iff A, is a theorem.
(not-A -> (B and not-B)) iff necessary A, is not a theorem.
2. "A" is possible true iff "A or not-A" is true
A or -A, is true for all values of A. Possible A is false when a is A contradiction.
3. "A" is empirically true iff "A" is true.
False, 'B or not-B' is true and 'B or not-B' is not empirical.
I want to say that a "unnecessary" conclusion can be "invalid" in two ways ("possibly" and "impossibly" true). MP inference is a valid scheme (necessary), AC is invalid but "possible" and MT asymmetric (to infer "A") is "impossible" to be true.
If something is not necessary, then it is contingent; if contingent, it can be possible and impossible. If it possible, also it can be "real" or "empirically" true.