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Glances Ahead: More to Think About

II. Philosophical Analysis
        A philosophical analysis of a concept is a collection of conditions that are individually necessary and jointly sufficient for the application of that concept.  The biconditional (phrased as “if and only if” and having truth conditions satisfied if both parts being tested have identical truth values) can be used in this process, and philosophical analysis is a common technique used to simplify the determination of truth values for a biconditional with numerous characterizing consequents.  One straightforward example of philosophical analysis would be (in which S is an agent):    
  Ex. S is a bachelor if and only if       (a) S is a man, and    
                                                         (b) S is unmarried.    
       In this case, upon examination of the two consequents supplied, we find that, alone, each is a necessary condition for being a bachelor—that is, S cannot be a bachelor without being (a) a man and, separately, (b) unmarried.  In combination, the consequents are sufficient conditions for the antecedent—that is, if S is a man and S is unmarried, then S must be a bachelor (for those two conditions are satisfactory in defining the notion of a bachelor).    
       A more famous and debated example of the technique of philosophical analysis is the following.    
            Ex. S knows that p if and only if         (a) S believes that p.    
                                                                       (b) p (is true).    
                                                                       (c) S has good reason to believe p (S                                                                       is justified in believing p).    
       The claim was that these conditions were individually necessary and jointly sufficient for “S knows that p.”  However, this example was challenged by Edmund Gettier, then reformulated by Fred Dretske and Robert Nozick, and then challenged again by Saul Kripke. 

I. Introduction to Symbolic Logic: Using Truth Tables   

III. Logic and Natural Language

IV. The Law of the Excluded Middle