A perhaps naive characterization of verisimilitude is "closeness to truth," the proximity coming from the similarity. At least, the SEP article uses, "The number of planets is 9," as an illustrative example of a verisimilar claim modulo, "The number of planets is 8," as the correct option. So anyway, this is where I'm lost:
- Suppose that the question, "How many truth values are there?" is a legitimate/open/w/e question, with an answer scheme, "There are n truth values."
- Now, at first I thought that setting n = 0 would be foolish, but then I thought maybe that this could be construed as the case where the whole theory of truth-as-a-referent is as such denied.
- The case n = 1 would be a case of a negation-free logic, I think. Equivalently, a logic with only one (positive) truth value would be exhaustively trivial, or expressive of the concept of triviality, or whatever, e.g. as with the explosion function in classical logic vis-a-vis noncontradiction. A theory with an empty or negative truth value would arguably dissolve into the case of n = 0, or maybe it represents an important alternative in the theory of negation; who knows, for now it's not relevant(!).
- So the minimal nontrivial-and-possible value for n would be 2, but there are worked-out cases for n = 4 or even 16, say.
- There's a Łukasiewicz logic with countably-many truth values, and then fuzzy logic has Continuum-many.
- Suppose, then, that the correct value for n is 4. This answer to the initial question is then closer to the trivial/antipossible answers, "n = 0," and, "n = 1," than it is to the Łukasiewiczian answers. But so here, still, "n = 2 or 3," is closer to the truth, too, than the infinitary values for n. Therefore, all the finite-valued wrong answers are closer to the right answer than any of the infinite-valued ones. So, e.g., "n = 0," is closer to the truth than, "n = |ω|."
- Or suppose that the correct answer is n = 2|ω| (fuzzy logic). Now, in the ordinal interval [0, a], for a = any countable ordinal (finite or infinite), there are fewer ordinals than in [a, 2|ω|]. So in fact, if the fuzzy-logic answer is right, then every lower answer is as far from correct as any other. Worse, if the right answer were, "n = |ω|," then the fuzzy-logic answer would be uncountably far from the truth, and all finite options would only be countably far away, so it would be as if the uncountable answer had less verisimilitude than any finite answer.
Does the concept of verisimilitude not apply to questions like, "How many truth values there are?" because either (A) that is not an empirical question or (B) even if it is, a decision (in constructing a theory) about the number of truth values will end up preceding a theory of verisimilitude itself? By comparison, perhaps the question, "Which theory of truthlikeness is most like the true such theory?" cannot be well-posed.
In case you're allergic to the alephs and omegas, substitute "2n + 1" in the recipe of the problem as of (6). E.g., if, "n = 4," is correct, then, "n = 9," is farther from the truth than, "n = 0." Or if you want to omit, "n = 0 or 1," from consideration, reformulate the (6)-problem in terms of "2n - 1" (this means e.g. that, "n = 2," is the lowest possible-but-false answer, and is two steps away from the truth, so that an answer more than two steps from the truth is more falsimilar than, "n = 2," with, "n = 7," being the minimal more-falsimilar option).
