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Notes+on+Translation

Notes+on+Translation - LPS/Philos 29 Some notes on...

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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 ϕ and ψ be any wffs: 1. ϕ and ψ : ( ϕ ψ ) 2. Both ϕ and ψ : ( ϕ ψ ) 3. Not both ϕ and ψ : ( ϕ ψ ) 4. ϕ although ψ : ( ϕ ψ ) 5. ϕ even though ψ : ( ϕ ψ ) 6. ϕ but ψ : ( ϕ ψ ) 7. Either ϕ or ψ : ( ϕ ψ ) [understood inclusively] 8. ϕ alternatively ψ : ( ϕ ψ ) 9. ϕ or ψ , where °or± is intended exclusively (i.e. ° ϕ or ψ ± is false when both disjuncts are true): (( ϕ ψ ) ( ϕ ψ )) 10. Neither ϕ nor ψ : ( ∼ϕ ∼ψ ) or use ( ϕ ψ ) 11. Not either ϕ or ψ : ( ϕ ψ ) 12. ϕ is equivalent to ψ : ( ϕ ψ ) 13. ϕ means the same as ψ : ( ϕ ψ ) 14. ϕ is defined as ψ : ( ϕ ψ ) 15. ϕ just if ψ : ( ϕ ψ ) 16. ϕ if and only if ψ : ( ϕ ψ ) 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 (John²s drinking and his throwing up) and that there is an order to the events³first 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 °you²ll pass but it won²t 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 ϕ then ψ . Recall that we call ϕ the antecedent, ψ the consequent³the truth of ψ is consequent upon the truth of ϕ . Here are some examples of conditional expressions in English and their respective translations: If ϕ , ψ : ( ϕ ψ ) ϕ provided ψ : ( ψ ϕ ) ψ , if ϕ : ( ϕ ψ ) ϕ on condition that ψ : ( ψ ϕ ) ϕ implies ψ : ( ϕ ψ ) ϕ is implied by ψ : ( ψ ϕ )
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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.
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  • Winter '08
  • Updike
  • sufficient condition, Necessary and sufficient condition, If and only if, necessary condition, stock market crashes

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