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

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Boolean logics with strict truth values are the most familiar, partly because they have proven useful for a variety of applications, and because their implications are easy to formalize in an unambiguous way. However, there are many ways in which they don't capture the subtleties of the real world.

To address that gap, philosophers have created a variety of modal logics with different variations on truth values. Some of those are fairly well-known, elaborated, and useful. Others, like the logic of "truthiness," are still in a largely unformed state.

All this to say, there's no one currently acclaimed answer to your question. The article you referenced from the Stanford Encyclopedia goes into a fair amount of technical detail on a possible "truthlike" operator. If you are not using that one, then, in essence, you are creating and defining your own new logical operator. As such, it's up to you to define its behaviors, work out its implications, and address the ways it does or does not successfully formalize an intuitive concept of natural language.

  • I wasn't sure if there was an analysis of the idea of a truthlikeness operator... The SEP article on axiomatic theories of truth contains the phrase, "In order to treat truth like other predicates," and I wondered if maybe that was pertinent to truthlikeness otherwise so-called. Like maybe truthlikeness had been formalized with a different axiom for induction or something. But so if the phrasing is just a coincidence... Dec 21, 2023 at 15:01
  • The article you referenced goes into deep technical detail on a possible truthlikeness logic, but I haven't seen that particular system referenced anywhere else. There must be hundreds of different modal logics that various philosophers have experimented with over the years. // The sentence you are referencing should be read as "In order to treat 'truth' like other predicates," and NOT as "In order to treat 'truthlike' other predicates." Dec 21, 2023 at 16:34
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    Thank you for clearing that up! I thought for some reason they just left a hyphen out. Dec 21, 2023 at 17:17

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