PHL145H5 Lecture Notes - Lecture 5: Venn Diagram, Propositional Calculus, If And Only If
Document Summary
Propositional logic has little to say about arguments like: Logically equivalent if every value in truth table is true under exact same conditions. Not connectives: all p"s are q"s. This argument is intuitively valid (and valid in virtue of its form), but impossible to symbolize with , , , : none of these sentences have connectives, and so we need to symbolize them as follows: No logical structure to represent argument with. So validity, unsurprisingly, is more expensive than truth tables. We are interested in the logic of categorical propositions: propositions that assert relationships of quantity between two classes of entities. All blend a quantifier (some all), a subject s, a copula (is/are, is/are not), and predicate p. Treating s and p as variables, we can think of categorical propositions as substitution instances of these forms. We can represent the four forms of cps with venn diagrams. Venn diagram examples: some s is not p.
