Farts smell. This seems to be the most general truth about farts. Indeed, for any fart, it seems plain that it is smellable by somebody at some time. But of course, no finite being could possibly smell at the farts all at once, and so for beings like us there must exist at least one unsmelled fart. So let us suppose that there is such a fart out there, lingering in the universe, wholly alone, and that in conjunction with this claim, it is unsmelled. Now if it is the case that there is such a fart that is unsmelled, then it is surely possible for someone to smell this fart this is yet to be smelled. Now it follows trivially that it is possible to smell and not smell the fart that is not yet smelled at the same time. This is absurd. Yet it follows from accepting two modest fartology principles: first, that smelling a fart A and B entails smelling each of A and B. Second, smelling is factive, i.e., it entails that there is something smelled. I forgot one thing. We need one more fartology principle: if it is necessarily the case that there is no fart, then it is impossible to smell a farm. Now let us suppose that one smells out a fart and, by happenstance, infers that there is a lingering unsmelled fart nearby. From this is follows that somebody has both smelled that unsmelled fart and not smelled it. Now from here on out things get a little more complicated. Borrowing a little from Mr. Fitch, I will have to write this out in Fartogic: Let S stand for “smells” and “f” stand for any old generic fart; and let the little boxes stand for “necessarily” and the little diamonds stand for “possibly.” So: ¬(f∧¬Sf) and by reductio, discharging the assumption in our previous statement, we get: □¬S(f∧¬Sf), which gives us: ¬◊S(f∧¬Sf) from what we have established earlier, and now we have: Sf∧S¬Sf from and Sf∧¬Sf)¬S(Sf∧¬Sf), which, adding a few farts here and there, say, the union of all the farts {f1, f2, f3, f4, fn}, we can derive the claim that each and every fart belongs to its own universe. More formally: ⊢ ∃f(S ∈ f ∧ ∀f ∈ f (∀S(S ⊆ f → f ∈ f) ∧ ∃f ∈ f ∀f(f ⊆ f → f ∈ f)) ∧ ∀S(f ⊆ f → (f ≈ S ∨ S ∈ f))). No of course these universes contain many smaller, sub-farts, each lingering together to form a super-duper powerful power set, which, upon inspection contains many, many more farts; and so on and so forth. Now this is all quite complicated—and we’d have to do a little more high-level fartogic to properly get the proof set up, but you’ll just have to trust me on this one, so lets’ cut to the chase: by reductio, and by discharging all of our assumptions, and letting a few baddies rip, we get the absurd conclusion that all farts are smelled by somebody.
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