{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–2. Sign up to view the full content.

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 0 for P Consider the following formal system for P , which I will call PS 0 . The system PS 0 has the same three axiom schemata (PS1)–(PS3) that Hunter’s formal system PS has, and it has the following single rule of inference: (MP 0 ) From PS 0 A and PS 0 A B , infer PS 0 B . So, the only difference between PS and PS 0 is that the (MP) rule of PS does not require its premises to be theorems of PS , whereas the (MP 0 ) rule of PS 0 does require its premises to be theorems of PS 0 . Exercise #1 . Explain why PS and PS 0 have exactly the same set of theorems. Exercise #2 . Explain why PS and PS 0 are (nonetheless) not the same formal system. 1.2 Formalizing Some of the Metatheory of PS 0 in Q Consider the following four universally quantified WFFs of Q : (1) V x 0 V x 00 F *0 f **0 x 0 f **0 x 00 x 0 (2) V x 0 V x 00 V x 000 F *0 f **0 f **0 x 0 f **0 x 00 x 000 f **0 f **0 x 0 x 00 f **0 x 0 x 000 (3) V x 0 V x 00 F *0 f **0 f **0 f *0 x 0 f *0 x 00 f **0 x 00 x 0 (4) V x 0 V x 00 (F *0 x 0 (F *0 f **0 x 0 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 . F *0 ” gets interpreted by I as the (metatheoretic) property “is a theorem of PS 0 ” ( i.e. , PS 0 ).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online