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The truth function $f_{\neg}$ is defined by the following table: Since modal operators are unary connectives and since there exist different notions of alethic necessity (necessary truth) and alethic possibility (possible truth), a rather natural question then is whether negations can be analyzed in a revealing way as modal operators, see the entry on modal logic.
Unlike the examples from Pollock and Buridan, however, we cannot understand such possibility without possible truth in terms of expressing a possibly true proposition while not being possibly true itself.
Propositions do not express propositions, of course, and so we cannot understand their possibility without possible truth in this way (Plantinga 1981).
What possible "truth" could such fictions offer?
(ii) Although the MTC for necessary truth is correct, the MTC for possible truth is incorrect: it provides necessary but insufficient conditions for ensuring possible truth.
Furthermore, even though necessary truth can be determined in polynomial time, possible truth is NP-hard.
Similar(24)
A possibility-first approach holds that we first arrive at knowledge of possible truths, and then aim to determine what necessary truths hold.
While the pres Congress and the courts were busy developing evidence in the case, the principals, apparently, were covering their tracks, and as time went on, trying to suppress al the major organs of possible truth-telling.
And that ambiguity frees them up to suggest a range of possible truths.
This allows them to be embraced as possible truths so their morals gain more weight in the eyes of their audiences.
(For an extreme case, consider V = ∅.) One natural thing to require is that all combinatorially possible truth-value assignments to the propositional variables are provided, i.e., that ∀X ⊆ ℕ ∃v ∈ V ∀k ∈ ℕ [v pk) = T] iff k ∈ X.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com