PL 330 Advanced Symbolic Logic
Betrand Russell claims that logic is to philosophy as mathematics is to physics. Others claim that logic is to language and reasoning as mathematics is to physical science. Logic provides both the language with which we evaluate reasoning and inferences, and the standards by which they are judged. In order to understand how sentences work, it is necessary to learn to find their logical structure. This doesnít tell us everything about the sentence, but it does provide a skeleton on which the other parts of the sentence can be fleshed out, the same way E=MC2 doesnít tell you how matter converts into energy, just that it does.
Logic is all about relationships between chunks of meaning, which are called Propositions. Propositions are composed of Predicates and Varaibles. Roughly speaking, Propositions are the skeletons of sentences; Predicates are the skeletons of verbs (or adjectives), and Variables are the skeletons of nouns (or pronouns). Almost everything else in a sentence is pretty much ignored in logic; itís only interested in the skeletal parts.
This course introduces several different formal techniques for evaluating propositions and the relations that exist between them. Each technique illucidates an important aspect of formal systems.