May_14 [Compatibility Mode]

May_14 [Compatibility Mode] - Thursday, May 14 ● Today,...

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Unformatted text preview: Thursday, May 14 ● Today, we'll talk about: ore logic!- More logic!- 8.7 Common Argument Forms- 8.8 Statement Forms and Material Equivalence- 8.9 Logical Equivalence- 8.10 Three “Laws of Thought”- 9.1 Formal Proof of Validity Review ● Yesterday we looked at the basic structure of logical statements. ● We talked about simple statements and how they, combined with (truth-functional) connectives, make up compound statements. ● We also discussed truth tables, by which we can examine simple statements that comprise compound statements in order to determine such compound statement's validity ● We have, as we went along, discussed translating natural language to symbolic logic. Common Invalid Forms ● Affirming the consequent – p → q; q; Therefore, p enying the antecedent → q; ~p; Therefore, q ● Denying the antecedent – p → q; ~p; Therefore, q ● As stated yesterday, a given argument can be a substitution instance of a number of different argument forms – some of these forms will probably be invalid. The question is whether or not the SPECIFIC form of the argument is valid. Only that form matters. 8.8 Statement Forms ● We've talked about argument forms , where there's only statement variables, and we can sub in statements to make an argument. There are also statement forms , which are comprised of sequences of variables, but no statements. For example: p v q p • q p → q ~q ● All of these are statement forms – the forms of statements but, because they only contain statement variables but no statements, they are not actually compound statements. ● We can substitute in statements as “substitution instances” and we have specific forms Statement Forms (con't) ● So, p • q is the specific form of: Elvis is alive and Elvis is in Vegas. ● And p → q is the specific form of: If it is raining, then the streets will be wet....
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May_14 [Compatibility Mode] - Thursday, May 14 ● Today,...

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