Counter-trolling 101, for vegetarians

Counter-trolling 101, for vegetarians

Logic takes care of itself…
L. J. J. W.
The concept of possibility is vague and cannot be defined syntactically. But that does not show that it is spurious. In fact, it is indispensable.
Tim Williamson, Knowledge and its Limits.
If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties.
Francis Bacon (thanks @jessicajthames)
Let A be any set. Consider any pairing-off of members of A
with members of the power set of A that assigns to each distinct
member of A a distinct subset of A. Let S be the set of all members
of A that are not members of the subset assigned to them. S is a
a subset of A. But S is not assigned to any member of A. For suppose
it were assigned to a member, say x, of A. Then x would be a member
of S if and only if it were not a member of S. This is a contradiction.
So any pairing-off of distinct members of A with distinct members
of the power set of A leaves some member of the power set unpaired.
So there is no 1-1 correspondence between A and its power set.
Cantor’s Theorem as explained by Geoffrey Hunter (Metalogic, p. 24)