ABSTRACT

Material implication is useful to test validity. But why treat it as a logical constant in its own right? The equivalent formula not (P and not Q) represents validity too. When P is the conjunction of an argument's premises and Q is its conclusion, not (P and not Q) says it is not the case that this argument's premises are true and its conclusion false'. And we already have its constants, 'and' and 'not'. Do we really need more? Well, try it in a truth-table.

Suppose you want to show that this form (that of Randolph Argument I) is valid. What validity-formula should you test by truth-table, using 'Not (...and not...)' instead of'If-then'?