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Unformatted text preview: 1 LPS/Philos 29 Some notes on translations: First note that the following rules of translation are really just rules of thumb: they guide our practice of translation and they usually work very well, but there is room for controversy. Let and be any wffs: 1. and : ( ) 2. Both and : ( ) 3. Not both and : ( ) 4. although : ( ) 5. even though : ( ) 6. but : ( ) 7. Either or : ( ) [understood inclusively] 8. alternatively : ( ) 9. or , where &or is intended exclusively (i.e. & or is false when both disjuncts are true): (( ) ( )) 10. Neither nor : ( ) or use ( ) 11. Not either or : ( ) 12. is equivalent to : ( ) 13. means the same as : ( ) 14. is defined as : ( ) 15. just if : ( ) 16. if and only if : ( ) To indicate how rough these translations may be, consider the English connective &and, which we translate as & . One might say something like &John got drunk and threw up, by which we express two facts (Johns drinking and his throwing up) and that there is an order to the eventsfirst the drinking, then the throwing up. PL is not sensitive to this causal or temporal ordering. We translate the highlighted sentence as &(D T), which you can check is equivalent to &(T D). Likewise, the word &but, as in &youll pass but it wont be easy indicates some sort of subjective factor, perhaps surprise. Again, PL is not able to express, in any obvious way, these subjective factors. Conditionals: There are many expressions in English that may be characterized as conditional, roughly, of the basic form if then . Recall that we call the antecedent, the consequentthe truth of is consequent upon the truth of . Here are some examples of conditional expressions in English and their respective translations: If , : ( ) provided : ( ) , if : ( ) on condition that : ( ) implies : ( ) is implied by : ( ) 2 There are several instances of a conditional form in English that are particularly problematic: &only if, &unless (which may also be translated as a disjunction) and the giving of necessary and sufficient conditions. giving of necessary and sufficient conditions....
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This note was uploaded on 04/12/2008 for the course LPS 30270 taught by Professor Updike during the Winter '08 term at UC Irvine.
 Winter '08
 Updike

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