1002 Lecture Notes - Complex Differential Form, Sentence Clause Structure, False Premise
5 Feb 2013
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During this course, i have made claims that are not obviously true. I have simply asked you to take these claims for granted. I will also, in coming classes, make further claims of a like nature: Sd is sound: if yields p in sd, then t-f entails p. We cannot go through all the sentences, sets, and arguments of sl and verify that there are no exceptions, because there are infinitely many of them. We might try to prove the claims by reductio ad absurdum (that is, by showing that if you suppose that they are false you get caught in a contradiction), but it is not obvious how to do that. A better way to prove these claims and others like them is to employ a special form of argument called mathematical induction. They are not inductive arguments at all, and you won"t learn anything about them if you study accounts of induction.
