Truth Tropic Language I
By way of investigating one of the more important truth-tropic properties of language, today I introduced a formal logic.
As we see in specifying its vocabulary, syntax, and semantics, the Propositional Calculus (PC) is a lean, some might say simplistic, logic. Nevertheless, it provides us with lots of room to develop a more sophisticated understanding of validity.
Today we defined PC by specifying its syntax and semantics. We used the semantics to develop a method of displaying in a table precisely how the truth of a Well Formed Formula (WFF) of PC--that is, a syntactically correct formula or sentence of PC--depends on the truth of its constitutive sentence letters.
You should in this regard be familiar with the mechanical method of filling out a truth table so as to systematically exhaust all the possible combinations of truth values of constitutive sentence letters. (We call the result a 'standard truth table'.)
Next time we'll use truth tables to define validity for PC arguments, we'll spend time practicing on the board, and (time permitting) I'll introduce a second way of defining validity for PC arguments that is not nearly so clunky or time-consuming (albeit, far less mechanical) than the method of truth tables.