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I understand that I am waiving issues like the absolute/relative simplicity/complexity distinction, the difference between the logic of existence and the logic of nonexistence per se, etc., so I understand that this line of reasoning is (relatively!) naive. However:

  1. Even if a necessary being doesn't exist, then there is an explanation why (a reason why the force of necessity was blocked, despite necessity's essential character).
  2. An explanation of why a necessary being does exist would be trivial: it exists by necessity.
  3. An explanation as to why it doesn't exist would be less trivial, and hence more complicated.
  4. The object of an explanation for why some specific necessary being doesn't exist would itself be a specific object, whose own existence would be necessitated so as to explain why the other necessary being doesn't exist [emphasis added; see below].

So, to no longer waive the issue of the difference between existence and nonexistence, is this where (4) goes awry?

  1. All points of an identity function are fixed points; all points of a nonidentity function are critical points. Identity functions are indistinguishable, since they always have the same outputs no matter what as such, whereas nonidentity functions can differ by mapping their inputs to disparate non-identical outputs (id(x) always goes to exactly some x but not(x) can go to a, b, c, ... generally-speaking).
  2. An explanation as to why something doesn't exist is like a nonidentity function; but so reifying the request for an explanation, here, would also mean reifying the explanation as to why a specific failure of existence accrued to some necessary being, rather than some other failure.
  3. This might be "more complicated" than the alternative, but if the issue is explaining a concrete/more-particular fact, not explaining the abstract possibility of explanation more-in-general, then this is unavoidable.

Is the nontriviality of nonidentity the reason why the (1)-through-(4) cosmological(?) argument for a necessary being fails to justify a specific conclusion about whichever necessary beings are supposed to be inferred via the argument? (I don't find the (1)-through-(4) argument especially compelling, and perhaps it reflects some memory I have of someone else's such argument, but if it is already an argument of others' making, I would like to understand where they're coming from, I suppose.)

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  • As per my understanding, if it's possible for a necessary being to not exist, then it's not a necessary being, by definition (although I haven't found any claims of the necessity of a being to be justified far beyond merely asserting it to be so).
    – NotThatGuy
    Commented Aug 29, 2023 at 15:31
  • @NotThatGuy the linked SEP article stresses a proposed difference between logical and metaphysical necessity to handle this complication. This might be the right idea, but it seems wrongly executed in the end if we go on to appeal to explanations-of-explanations here (some confusion of orders/types being involved), or if we omit the difference between general and particular explanations (such as this difference is). Commented Aug 29, 2023 at 16:49
  • Surely going from exists prior state to prior state includes a being to includes exactly one being each require additional evidence?
    – g s
    Commented Aug 29, 2023 at 17:10
  • @gs I think that that's sort of/one of Kant's (and the SEP article's) conclusions, that arguments for necessary beings are "so far" too abstract to justify specific descriptions of such beings/claims as to how many such beings there are. One might be able to get an indestructible being out of it, but if every abstract object is indestructible, then one has not gotten a God out of it, it would seem. Commented Aug 29, 2023 at 17:15
  • One could pull a Gaunilo and quip, "So the explanation for the existence of a necessary unicorn would be simpler than an explanation for such a unicorn's nonexistence." I suppose the Anselmian might reply, "Ah, but it is simpler to explain the necessity of a being whose quintessential characteristic is its necessity, than it would be to explain the necessity of a unicorn," but now all we have is some pure necessitarian flotsam mucking about, not a living God with infinitely complicated attributes like maximal goodness and knowledge. Commented Aug 29, 2023 at 17:19

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