by Corry Shores
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[The following is summary. Bracketed commentary is my own. Please forgive my typos, as proofreading is incomplete.]
is denied byThis may be rendered as ‘there are Λ’s.(Frege 19)
(3B) For every x, if x is a zombie, then x is happy.
(3B*) Choose any object you please in the domain of discourse; if that object is a zombie, then it will be also be happy.
(3E) Every zombie is happy.
(Agler 271, 272)
z is an X and z is a Pz is not an X and z is a Pz is not an X and z is not a P.
means: ‘whatever may be substituted for a, the case in which P(a) would have to be denied and X(a) affirmed does not occur.’ It is thus possible that, for some possible meanings of a,P(a) must be affirmed and X(a) affirmed; for others,P(a) must be affirmed and X(a) denied; for others again,P(a) must be denied and X(a) denied.| We can thus give the rendering: ‘If something has the property X, then it has also the property P,’ or ‘every X is a P,’ or ‘all X’s are P’s.’(Frege 19-20)
(4B) For every x, if x is a zombie, then x is not happy.
(4B*) Choose any object you please in the domain of discourse consisting of human beings (living or dead); if that object is a zombie, then it will not be happy.
(4E) No zombies are happy.
(Agler 271, 272)
This is the way causal connexions are expressed.means: ‘no meaning can be given to a such that P(a) and Ψ(a) p. 24] could both be affirmed.’ We may thus render it as ‘what has the property Ψ has not the property P’ or ‘no Ψ is a P.’(Frege 20)
deniesand may be therefore rendered as ‘some Λs are not Ps’(Frege 20)
denies that no M is a P and thus means ‘some Ms are Ps’ or ‘it is possible for an M to be a P.’(Frege 20)