On 7 Nov. at ScIn I asked how to represent "and" in formal logic. Shortly after that, while reading Nagel's and Watson's Gödel's Proof, which in fact spurred my inscitia, they showed me how )on pg. 76).
p • q ≡ ¬(¬p V ¬q).
In other words, "It is not the case that 'not p' or 'not q'." Hence, it is the case that p and q.
So if I said, "John is tall and fat," I could formalize it, I think, as
(p is 'tall')(q is 'fat') → ∃x J(x) if x is ¬(¬p V ¬q).
Presumably, defining "or" in this way would happen thus:
p V q ≡ ¬(p • ¬p) ∧ ¬(q • ¬q)
which means, "It is not the case that both 'p' and 'not p' and 'q' and 'not q'."
As always, I stand wide open for correction.
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