• By My Lights
    2
    There are a number of fun paradoxes which seem assertible despite seemingly lacking any possible truth-maker to really make sense of why they would be true or false. For example, "This proposition is true." Nothing really seems wrong with saying it's true, but if it were false, nothing seems like that would be wrong either, and as it only refers to itself, what resources could we really use to decide between the two. Now, maybe the liar's paradox has made you suspicious of such explicitly self-referential statements, but like the liar's paradox, explicit self-reference isn't really necessary you can get the same effect. For instance, consider the following logical construction: Proposition n: "Proposition n+1 is true" for all n such that n is a natural number. None of the propositions in this construction will refer to themselves, but all of them seemingly could be true, or all of them seemingly could be false. Personally, I think the simplest and possibly most virtuous solution to this paradox by my lights is just to say that the truth-value of such paradoxical propositions is a brute fact, as to whether they are actually are true or false, I think this is most likely unknowable. The question I want to ask is: does this suggest brute facts are logically necessary? I kinda hope it might because it could be a helpful resource to really support a metaphysical view of the world where brute facts place a significant role. The problem I suspect is that paradoxes are notorious for leading to all sorts of unintuitive consequences, so we probably should be cautious resting too much upon, however this does seem like a relatively nice paradox, so maybe we could away with it.
  • Relativist
    2.6k
    I think the simplest and possibly most virtuous solution to this paradox by my lights is just to say that the truth-value of such paradoxical propositions is a brute fact, as to whether they are actually are true or false, I think this is most likely unknowable.By My Lights
    I don't think such propositions have a single truth value: they are dialetheia, sentences that are both true and false.

    does this suggest brute facts are logically necessary?By My Lights
    No. First of all, because they don't actually have a single truth value. Second (assuming you choose to assign only one truth value), there is no logical necessity to your choice.

    On the other hand, I do think it is logically necessary that there is at least one brute fact* The PSR suggests there's a chain of explanations, but the chain must end somewhere - at an unexplained brute fact.

    * I do not actually think that propositions actually exist unless they are articulated by a mind, so I'm talking about their hypothetical existence: hypothetically, everything about the world is explainable in some set of propositions.
  • By My Lights
    2
    I don't think such propositions have a single truth value: they are dialetheia, sentences that are both true and false.
    As far as I know, they definitely could be dialethia, however I do think a when choosing between theories, I feel like posting dialethia probably should come with a greater theoretical cost then positing brute facts, but admittedly that's just an intuition.
    Second (assuming you choose to assign only one truth value), there is no logical necessity to your choice.
    I think I agree; what I suspect could be necessary is that the choice has to be made, but what the resulting choice actually will be I expect would indistinguishable from chance. Maybe, I'm misunderstanding something here.
    On the other hand, I do think it is logically necessary that there is at least one brute fact* The PSR suggests there's a chain of explanations, but the chain must end somewhere - at an unexplained brute fact.
    I might be talking past you, but I feel like I would more think of stuff like the PSR as concerning metaphysical possiblity rather then logical possiblity as I don't think there is anything inconsistent about denying or modifying the PSR. The hope with trying to secure brute facts within the realm of propositions and logic is that it might be a path towards really fleshing out resources that could be useful when wrestling with the problems found at the foundation of metaphysics.
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