Tuesday, October 16, 2007

5.101 The truth-functions of every number of elementary propositions can be written out in a schema in the following way:

(T T T T)(p, q) Tautology (if p then p, and if q then q) [p  HOOK p . q  HOOK q]
(F T T T)(p, q) in words: Not both p and q. [~(p . q)]
(T F T T)(p, q) '' '' If q then p. [q  HOOK p]
(T T F T)(p, q) '' '' If p then q. [p  HOOK q]
(T T T F)(p, q) '' '' p or q. [p v q]
(F F T T )(p, q) '' '' Not q. [~q]
(F T F T)(p, q) '' '' Not p. [~p]
(F T T F)(p, q) '' '' p or q, but not both. [p . ~q :v: q . ~p]
(T F F T)(p, q) '' '' If p, then q; and if q, then p. [p  == q]
(T F T F)(p, q) '' '' p
(T T F F)(p, q) '' '' q
(F F F T)(p, q) '' '' Neither p nor q. [p . ~q or p | q]
(F F T F)(p, q) '' '' p and not q. [p . ~q]
(F T F F)(p, q) '' '' q and not p. [q . ~p]
(T F F F)(p, q) '' '' p and q. [p . q]
(F F F F)(p, q) Contradiction (p and not p; and q and not q.) [p . ~p . q . ~q]

Those truth-possibilities of its truth-arguments that verify a proposition, I will call its truth-grounds.

So, this is what those series would be. And here we have the in-between of tautology and contradiction that I doubted earlier (i.e. from the second to the penultimate line of the schema). Does this show my doubt to have been misplaced? Well, all we have here is a kind of chart. What is going to be done with it? How is it to be interpreted?

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