Examples 8.2

Examples 8.2 - Notes 8.2 Using the Rules of Inference The...

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Notes 8.2 Using the Rules of Inference! The main reason we’ve retained the truth-functional operators (dot, wedge, etc.) is to allow predicate logic symbolizations to be used in natural deduction. The main problem, however, with this method is that the first 8 rules of inference must apply to whole lines. That means we’ve got to come up with a way of losing those quantifiers (existential and universal) or we won’t be able to apply those rules. So, the main things we’ve got to be familiar with are 4 new rules. Here they come: 1. Universal Instantiation (UI) Consider the following argument: All economists are social scientists. (x)(Ex Sx) Milton Friedman is an economist. Em Therefore, Milton Friedman is a social scientist. Sm Intuitively, it seems like this conclusion follows from the premises. That is, the argument seems valid. But, as we see it above, none of the rules of inference apply. We really need the first line to look like: Em Sm If this were the case, we could do a simple modus ponens and we could have our conclusion. But, think about it: if the first premise means that, for anything in the world, if it’s an E, then it’s an S . . . then surely if Milton (m) is an economist (E), then he (m) has got to be a social scientist (S). This is just an instance of our universal premise. A line that states just this would then be a case of universal instantiation. All we need to do is to introduce an instantial letter , and the derivation looks like this:
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This note was uploaded on 05/04/2008 for the course PHIL 2203 taught by Professor Barrett during the Spring '08 term at Arkansas.

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Examples 8.2 - Notes 8.2 Using the Rules of Inference The...

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