First formula unless e p only if s 4 main connective

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Unformatted text preview: connective unless E, P only if S 5. standard or non-standard non-standard, so we paraphrase it unless = if not if not E, then P only if S 11 Example 2 c if not E, then P only if S 4. 5. main connective if not E, then P only if S standard or non-standard standard, so we symbolize it ( not E ) ( P only if S ) work on constituents ( not E ) ( P only if S ) 6. E ( not P if not S ) ( if not S, then not P ) ( S P) 12 6 Example 2 d 7. Substitute constituents E ( S P) 8. Translate formula back into English if the exam is not easy, then if I do not study, then I will not pass 13 Example 3 if I am HAPPY only if I am DRUNK, then I am not HAPPY unless I am DRUNK. 1. simple sentences: H = I am happy D = I am drunk 2. connectives: if...then only if not unless (standard) (non-standard) (standard) (non-standard) 14 7 Example 3 b 3. first formula: if H only if D, then not-H unless D main connective: if H only if D, then not-H unless D standard or non-standard: standard, so we symbolize it ( H only if D ) ( not-H unless D ) 15 4. 5. Example 3 c 6. Work on constituents ( H only if D ) ( not-H unless D ) ( not H if not D ) (if not D, then not H ) ( D H) ( H only if D ) ( not-H unless D ) ( not-H if not D ) ( if not-D then not H ) ( D H) 16 8 Example 3 d 7. Substitute constituents ( D H) ( D H) 8. Translate formula back into English IF if I am not drunk then I am not happy THEN if I am not drunk then I am not happy 17 Example 4 if I CONCENTRATE well only if I am ALERT, then provided I am WISE I will not FLY an airplane unless I am SOBER 1. simple sentences: C = I concentrate well A = I am alert W = I...
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This note was uploaded on 02/04/2012 for the course PHIL 110 taught by Professor Bohn during the Fall '08 term at UMass (Amherst).

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