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Lecture 3

# PHL105Y5 Lecture 3: Logic Ch. 2

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University of Toronto Mississauga

Philosophy

PHL105Y5

Bernard Katz

Fall

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C HAPTER 2 T RUTH A ND V ALIDITY 2.1 Validity and Soundness It is useful to distinguish deductive arguments, which purport to be demonstrative, from inductive arguments, which do not. In both cases, one is given reasons for accepting some conclusion. In deductive arguments, however, the premises are supposed to be strictly sufficient for establishing the conclusion; in other words, the premises are offered as providing conclusive support. Consider, for example, the argument below: (a) Ottawa is the capital of Canada. Alfred has never visited Ottawa. Therefore, Alfred has never visited thecapital of Canada Clearly, if both of the premises are true, the conclusion must be true as well. In inductive arguments, on the other hand, the premises are supposed only to provide good evidence for the conclusion; the premises are offered as providing probable support. Consider, for example, the following argument: (b) Alfreds fingers are nicotinestained. Therefore, Alfred is a smoker. The premise of this argument gives a good reason for the conclusion, but it is by no means conclusive. (Perhaps Alfred was conducting a chemistry experiment and accidentally stained his fingers.) Inductive reasoning plays an important role both in science and in ordinary life, but the standards for evaluating inductive reasoning are quite different from those used in deductive reasoning. For now, we shall confine our attention exclusively to deductive reasoning. Somearguments aregood,andothers arenot.Whetheraparticularargumentisgooddepends onanumber of different factors. There is one consideration, however, which is logically salient: in a good argument there must be a connection of the right sort between the premises and the conclusion. The premises and conclusions that make up an argument are sentences and, so, are either true or false. The point of the premises, of course, is to provide support for the conclusion. Accordingly, one mark of a good deductive argument is that the premises, if true, ensure that the conclusion is as well. An argument is valid if and only if it is not possible for all of its premises to be true and its conclusion false. An argument is invalid if and only if it is not valid. In other words, an argument is valid just in case the relation between the premises and conclusion is such that given that all of the premises are true, the conclusion must be true as well. Thus, if an argument is valid and all of its premises are true, then its conclusion will be true as well. It follows that if you know that an argument is valid and you know that all of its premises are true, you may infer that the conclusion is true. What happens if one or more of the premises is false? What if anything can you infer concerning the truthvalue of the conclusion? Not much. If one or more of the premises of a valid argument is false, then the conclusion of that argument may be true or it may be false. Each of the arguments below is valid:

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