PHIL 210 Chapter Notes - Chapter 4: Negation Normal Form, Logical Truth, Logical Possibility
15 Dec 2017
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&, v, - are truth-functional connectives i. e. truth value can be determined with just the truth values of constituents. It is necessarily the case that is not a truth-functional connective because ex. knowing. X is true (for a certain condition) is not enough to know whether it is necessarily true. (see 4. 1) Boolean connectives are truth functional, so you can calculate the logical property. Definition of logical necessity: true in every logically possible circumstance. Sentences with this property are called logical truths . Logical possibility: there is some logically possible circumstance/situation/world where the claim is true. Truth tables can show that certain sentences are logically necessary; but some logically necessary sentences are so for reasons the truth table method cannot detect. Tautology: truth value is only t in truth table. Conventions for multiple conjunctions/disjunctions: rightmost is main connective. ((a&b)&c)&d. Tautologies are a subset of logical necessities; logical necessities are a subset of tw necessities.
