Symbolic Logic: At Home In Natural Language

This text introduces all the basic components of symbolic logic, including multiple quantifiers, properties of relations, enthymemes, identity, and paradoxes based on properties of properties. No technical background is presupposed in math or logic. The text has enough material for a 2-semester course, though by skipping certain sections most of the book could be covered in one semester. It is shown multiple times how putting English statements into symbolic notation reveals the complexity (and sometimes ambiguity) of natural language. Many examples are given of the usage of logic in life, including playtime (like working a Sudoku). Examples to translate are taken from musicals, from legal documents, etc. Despite the attention to natural language, there is no sacrifice of depth and precision in the problems. Symbolizing the operator symbols as relations (i.e., Cxy, x conjuncted with y is true) allows formulas to be expressed whose truth value requires precise understanding of what the formula is saying in natural language. The book ends with a careful presentation of Richard’s Paradox, challenging those who dismiss the problem because it is not strictly mathematical. This paradox is used to construct a valid symbolic logic proof that Cantor’s procedure does not prove there are nondenumerable sets, with a challenge to the reader to identify and prove which premise (or premises, if any) of the argument are false.