PHIL 210 Chapter Notes - Chapter 5: Logical Truth, Natural Deduction, Truth Table
Document Summary
Truth table limitations: 2n rows is too many rows for arguments with many atomics, and more importantly, truth tables cannot be easily extended to reasoning to more than truth- functional connectives. Instead, proof methods can be used to show validity when it depends on more than just. Valid patterns of inference that generally go unmentioned in informal proofs (are obvious): conj elim, conj intro, disj intro. Informal proofs are a method of discovery and of communication. A good proof should be easily understood (see that each step is valid) and be significant (each step is informative, does not waste time). So need a balance between easy and hard depending on audience. Proof by cases is how disj elim works: s follows from every case (of a disjunction), therefore s. Logical impossibility: cannot possibly be true; if and only if its negation is logically necessary. If s is a tautology then s is a contradiction.