A three-valued propositional logic is presented, within which the three values are read as ?true?, ?false? and ?nonsense?. A three-valued extended functional calculus, unrestricted by the theory of types, is then developed. Within the latter system, Bochvar analyzes the Russell paradox and the Grelling-Weyl paradox, formally demonstrating the meaninglessness of both.

In this paper I am concerned with two questions: What is sexist humor? and what is wrong with it? To answer the first question, I briefly develop a theory of humor and then characterize sexist humor as humor in which sexist beliefs (attitudes/norms) are presupposed and are necessary to the fun. Concerning the second question, I criticize a common sort of argument that is supposed to explain why sexist humor is offensive: although the argument explains why sexist humor feels offensive, (...) it does not place responsibility for the offense in the humorist or audience that enjoys sexist humor. I develop an alternate account of the offense in sexist humor that places responsibility for offense in precisely those quarters. (shrink)

Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical (...) systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems. (shrink)

This outstanding book is a leading text for symbolic or formal logic courses. All techniques and concepts are presented with clear, comprehensive explanations and numerous, carefully constructed examples. Its flexible organization (all chapters are complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose.

A wealth of literature has been devoted to the problem of developing an adequate semantic analysis of sortally incorrect statements. The motivation is clear, albeit controversial: sortally incorrect statements appear to exhibit an unusual behavior when coupled with other statements in logically complex statements. For instance, two senses of negation are distinguishable when the operation is applied to sortally incorrect statements. In this paper, I shall reopen the question of the "correct" semantic analysis of sortally incorrect statements.

The typical rules for truth-trees for first-order logic without functions can fail to generate finite branches for formulas that have finite models–the rule set fails to have the finite tree property. In 1984 Boolos showed that a new rule set proposed by Burgess does have this property. In this paper we address a similar problem with the typical rule set for first-order logic with identity and functions, proposing a new rule set that does have the finite tree property.

In 1987, Crispin Wright argued that degree-theoretic solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.

In 1987, Crispin Wright argued that degree-theoretic (fuzzy) solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.