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NOT_INCOMPATIBLE

                                  September  2, 2020

As I commented before, Russell comments approvingly
on a system developed by Sheffer & Nicod in
which "and" and "not" can both be derived from
a *single* operation, a test for "incompatibility".

Bertrand Russell, "The Philosophy of Logical Atomism" (1918):

    "Suppose you want 'if p and q', that simply
    means that you cannot have p without
    having q, so that p is incompatible with
    the falsehood of q."

    "Suppose you want 'p or q', that means that
    the falsehood of p is incompatible with
    the falsehood of q."


    Russell likes this, calling it "a good deal simpler when
    it is done this way than when it is done in the way of
    Principia Mathematica, where there are two primitive ideas
    to start with, namely 'or' and 'not'."


At first glance, though, I can't see what Russell is talking
about: his derivation of "and" and "or" from "incompatibility"
seems to require the use of negation, it presumes the "not"--
he's talking about incompatibility with "the falsehood of q".

So he's replacing "or" and "not" with "incompatible" and "not".

Perhaps the idea that a test for "incompatibility" is actually
a negation, so everything is derivable from "not"?

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