thmt - Philosophy 140A Take-Home Mid-Term Branden Fitelson...

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Unformatted text preview: Philosophy 140A Take-Home Mid-Term Branden Fitelson 03/20/07 You are to answer all six (6) exercises on this take-home exam. Your solutions are due on Tuesday, April 10 at 4pm . You may work in groups on this exam (with the usual rules and procedures for group work). 1 Formalizing Some of the Metatheory of P in Q 1.1 The Formal System PS for P Consider the following formal system for P , which I will call PS . The system PS has the same three axiom schemata (PS1)(PS3) that Hunters formal system PS has, and it has the following single rule of inference: (MP ) From PS A and PS A B , infer PS B . So, the only difference between PS and PS is that the (MP) rule of PS does not require its premises to be theorems of PS , whereas the (MP ) rule of PS does require its premises to be theorems of PS . Exercise #1 . Explain why PS and PS have exactly the same set of theorems. Exercise #2 . Explain why PS and PS are (nonetheless) not the same formal system. 1.2 Formalizing Some of the Metatheory of PS in Q Consider the following four universally quantified WFFs of Q : (1) V x V x 00 F *0 f **0 x f **0 x 00 x (2) V x V x 00 V x 000 F *0 f **0 f **0 x f **0 x 00 x 000 f **0 f **0 x x 00 f **0 x x 000 (3) V x V x 00 F *0 f **0 f **0 f *0 x f *0 x 00 f **0 x 00 x (4) V x V x 00 (F *0 x (F *0 f **0 x x 00 F *0 x 00 )) Now, consider the following interpretation I of Q . 1 The domain D of I is the set of WFFs of P ....
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This note was uploaded on 08/01/2008 for the course PHIL 140A taught by Professor Fitelson during the Spring '07 term at University of California, Berkeley.

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thmt - Philosophy 140A Take-Home Mid-Term Branden Fitelson...

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