Basics of Argument III

Basics of Argument III - PHI 108.04 Logical and Critical...

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PHI 108.04 Logical and Critical Reasoning Spring 2008 Hurley, Logic, and Munson and Black, The Elements of Reasoning were used as sources for the above information. 1 The Basics of Arguments III 1. NECESSARY AND SUFFICIENT CONDITIONS A necessary condition is a condition which must be present in order for a given result to follow. For example, there are a number of necessary conditions that govern whether or not our car will start moving when we press the accelerator. There must be gas in the car, the car must be turned on, the engine must be working, etc. A necessary condition is necessary to bringing about a result, but does not guarantee that result. A sufficient condition is one which, whenever it is present, always produces a given result. If my Saturn SL2 lacks an engine, this is a sufficient condition for knowing that it will not work properly. A sufficient condition is just that it is sufficient , it is all that is needed, to bring about a certain result. These terms can be applied to some of the statement forms we ve looked at so far. For example, in the statement P → Q” , we know that if P is true then Q must also be true. Therefore, P is sufficient to guarantee Q; in other words, P is a sufficient condition for Q. On the other hand, Q is a necessary condition for P: Q must be true, in order for P to be true. Q is necessary for P. 2. EQUIVALENT FORMS In evaluating arguments symbolically, we must use the following rules establishing equivalent (and therefore substitutable) argument forms. An equivalent form is another way of stating the same thing. Many of these will look like common sense, but it is necessary to know them in their standard forms. a. Double Negation (DN) --P P This is certainly common sense: a thing is the opposite of its opposite; P is not the opposite of P; P is not not-P. b. Commutation (Com) (P • Q ) (Q • P) This allows us to switch the two terms of a conjunction: P and Q is the same as Q and P . It also applies to disjunctions, either/or statements. We can switch their terms because the order of terms in and and either/or statements doesn t matter. (On the other hand, this is not true in the case of implication: If Q then P is not the same as If P then Q. ) For example, Albert has a pet lizard and a pet monkey. is equivalent to Albert has a pet monkey and a pet lizard. or (P v Q) ↔ (Q v P ) Either James will win the game or Marie will. is equivalent to Either Marie will win the game or James will.
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  • Spring '08
  • Logic, Necessary and sufficient condition

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