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LOGICAL_ATOM_GOLF

                                             April 18, 2022

Here, Bertrand Russell is displaying some envy for the work
of Sheffer, who showed you didn't need to start with the two
logical operations of "not" and "or" as Principia
Mathematica did, you could actually just start with
something like "not", specifically "incompatibility".

    One assumption rather than two!  Twice as good!

    (Provided you believed there was much point in
    the project to begin with...)



Lecture 3, "Atomic and Molecular Propositions"
from "The Philosophy of Logical Atomism" (1918):
                                                         LOGICAL_ATOM

    "Suppose you want 'p or q', that means that the falsehood
    of p is incompatible with the falsehood of q. If p is
    false, q is not false, and vice versa. That will be: (p/p)/(q/q)."



    "Suppose you want 'p and q are both true'. That will mean
    that p is not incompatible with q. When p and q are both
    true, it is not the case that at least one of them is
    false. Thus, 'p and q are both true' = (p/q)/(p/q)."

    "The whole of the logic of deduction is concerned simply with
    complications and developments of this idea. This idea of
    incompatibility was first shown to be suffcient for the
    purpose by Mr. Sheffer, and there was a good deal of work
    done subsequently by M. Nicod. It is 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'. Here you can get on with
    only a single premise for deduction."




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