# If it is verisimilar that A, is it verisimilar that it is verisimilar that A?

Truthlikeness, AKA verisimilitude or a function of "proximity to the truth," is such as when we might say, "The number of planets (in the Earth's solar system) is 10," vs., "The number of planets is 222": the former is "closer to the truth" than the latter. Or, "The number of planets is between 5 and 15," being narrower than, "The number of planets is between 0 and 1000," is "closer to the truth" than the latter, even though overall either is plainly true.

Now, in axiomatic theories of truth, there are axioms for a truth operator or truth predicate that can be varied with peculiar results, and which must be varied in certain contexts (on pain of inconsistency). However, we could go ahead and be alethic pluralists if we wished to say that there are separate operators for every alternation over the various axioms. For example, we might say that there is one operator that iterates but for which negation isn't commutative, another for which negation is commutative but which doesn't iterate, and so on and on. The SEP article says that those two principles (iteration and commutativity-of-negation) are inconsistent over weak theories of syntax (I don't know what that means, though), so we'll just focus on them, here.

Letting "it is verisimilar that" be a verisimilitude operator, what then of a proposition such as, "It is verisimilar that it is verisimilar that A"? One might start out by saying that maximal verisimilitude is equivalent to plain truth, i.e. two truths are perfectly verisimilar when their truthlikeness is complete and equivalent ("the number of planets is 9" = "the number of planets is the square of 3"). So "it is true that it is verisimilar that" is a trivial equivalent of "it is verisimilar that it is verisimilar that." What, then, of nontrivial iterations of "it is verisimilar that"? Or does the verisimilitude operator not iterate like that, but is e.g. such that negation commutes for it? I.e. does "It is not verisimilar that" = "it is verisimilar that not" instead? Which truth axiom is a better fit for verisimilitude, of the two relatively inconsistent ones?

• Are you asking specifically about the particular formalization of the concept of "versimilitude" outlined in the article you referenced? If so, you should make that clear, and outline the relevant parts of the extensive logical calculus from the article. If not, there may not be any fact of the matter with regards to your question, since this isn't a topic around which a wide consensus exists. Dec 21, 2023 at 14:48