Examples 6.5

# Examples 6.5 - Examples 6.5 Indirect Truth Tables These...

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Examples 6.5 Indirect Truth Tables These things are useful, but not somewhat tricky to catch on to. The basic idea is as follows: instead of doing an entire truth table for an argument with lots of components and lots of premises, we’ll just do a short cut by assuming the argument’s invalid (premises are true while the conclusion is false), then working backward we’ll see whether it’s possible to fill in the truth values to make such a row (in a truth table). Intuitively, if it’s possible to make such a row (where the premises are true and the conclusion is false), then we know that argument is invalid. If it’s not possible, then we know the argument is valid. So, instead of explaining, let’s just look at this concept in action, and maybe it will make more sense. Start with this argument: If ~A then (B v C) ~B If C then A First, lay out the argument like a truth table: If ~A then (B v C) | ~B || If C then A Then lay out the truth values under the operators to make the argument invalid. If ~A then (B v C) | ~B || If C then A T T F Now, since the conclusion can only be falsified by ONE arrangement of truth values (i.e., where the antecedent is true and the conclusion is false—according to the truth function for conditionals), we can fill out the truth values for the components. (I’m gonna bold the TVs under the main operators so things don’t get (more) confusing). If ~A then (B v C) | ~B || If C then A T T T F F Now, all we have to do is go back and fill in the rest of the table. We know that all of the ‘C’s have to be T, and all of the ‘A’s have to be false—so go do it. Also, we’re can flip

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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 6.5 - Examples 6.5 Indirect Truth Tables These...

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