PHIL 110 Lecture 15: Note 9.2
16 Mar 2017
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Dr mc"s philosophy 110 (1171) part notes 9#2 . This is the expansion of (x)fx, with respect to that domain. ( x) fx. Expansion for the same domain: fa v fb. We could try to construe quantified sentences this way always but: Some domains are infinite (and we don"t want infinitely long sentences!) We might not have names for every thing in even a finite domain. Nonetheless, the idea of expansion is useful for understanding what a sentence with a quantifier is saying. A sentence whose logical form guarantees it is false. This is the conjunction of two sentences that cannot be true at the same time. They also cannot be false at the same time. If one is false, the other is true. They are contradictories. (i) all a are b. (ii) some a are not b. If it is false that: (x)(ax bx) ( )(ax ~bx) then it is true that: _____________________ (and vice versa)
