"There are many reasons to get interested in nonclassical logic, but one exciting one is the belief that classical logic is wrong--that it provides an inadequate model of (genuine) logical truth and logical consequence." (92) The argument is that classical logic, by assuming the principle of bivalence
, assumes one too many logical truths.
The realist holds the idea of truth as subject to the principle of bivalence
, that is, that reality renders statements either true or false independently of whether anyone can make that determination.
Introductory chapters one and two present different forms of the liar paradox and two kinds of approaches to solving it: one is by suspending the principle of bivalence
, the other by introducing hierarchy of languages.
Sections XVII-XX concern the implications for the principle of bivalence
, the law of excluded middle, and the principle of noncontradiction.