After critiquing the arguments against using formal logic to teach critical thinking, this paper argues that for theoretical, practical, and empirical reasons, instruction in the fundamentals of formal logic is essential for critical thinking, and so should be included in every class that purports to teach critical thinking.

Background Logic, Critical Thinking, and Irrational Language Games.

In the general theory of logic built up by Whitehead and Russell to furnish a basis for all mathematics there is a certain subtheory which is unique in its simplicity and precision; and though all other portions of the work have their roots in this subtheory, it itself is completely independent of them. Whereas the complete theory requires for the enunciation of its propositions real and apparent variables, which represent both individuals and propositional functions of different kinds, and as a (...) result necessitates- the introduction of the cumbersome theory of types, this subtheory uses only real variables, and these real variables represent but one kind of entity—which the authors have chosen to call elementary propositions. The most general statements are formed by merely combining these variables by means of the two primitive propositional functions of propositions Negation and Disjunction; and the entire theory is concerned with the process of asserting those combinations which it regards as true propositions, employing for this purpose a few general rules which tell how to assert new combinations from old, and a certain number of primitive assertions from which to begin. (shrink)

In formal logic there is a premium on clever paraphrase, for it subsumes troublesome inferences under a familiar theory. (A paradigm is Davidson's analysis 1967 of inferences like ?He buttered his toast with a knife; so, he buttered his toast?.) But the need for paraphrase in formal logic runs deeper than the odd recalcitrant inference, and thus, I shall argue, commits logicians to some interesting consequences. First, the thesis that arguments are valid in virtue of their form must be severely (...) qualified (?4). And second, it is misleading to view a formal logical theory as a standard for justifying and criticizing inference (?7). The latter point depends on the nature and role of paraphrase, which permit a range of conflicting logical theories. Conflicting logical theories arise from the conflicting goals of logical theorists and the promiscuous nature of paraphrase makes reconciliation impossible. (shrink)

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1973.

Over the last two decades, William Lycan’s work on the semantics of conditionals has been distinguished by his careful attention to the connection between syntax and semantics, and more generally by his impeccable methodology. Lycan takes compositionality seriously, so he requires that the meaning of compound expressions like ‘even if’ be a combination of the constituent expressions, here ‘even’ and ‘if’. After reading his work, it’s hard to take seriously work that does not share this methodology.

The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its (...) decision procedure is almost as efficient as that of the classical logic. It therefore provides a rational and convenient system in which to formalize English arguments. (shrink)

The present text book is intended as an introduction to elementary logic. Its content, structure, and manner have been determined in large measure - perhaps 'caused' is the better word- by certain desiderata about which the reader should be informed at the outset. The leading idea is that even an introductory treatment of logic may profitably be fashioned around a rigorous framework.

A plausible and popular rule governing the scope of truth-functional logic is shown to be indequate. The argument appeals to the existence of truth-functional paraphrases which are logically independent of their natural language counterparts. A more adequate rule is proposed.

"One of the most careful and intensive among the introductory texts that can be used with a wide range of students. It builds remarkably sophisticated technical skills, a good sense of the nature of a formal system, and a solid and extensive background for more advanced work in logic.... The emphasis throughout is on natural deduction derivations, and the text's deductive systems are its greatest strength. Lemmon's unusual procedure of presenting derivations before truth tables is very effective." --Sarah Stebbins, The (...) Journal of Symbolic Logic. (shrink)

This definitive survey of the hottest issues in inductive logic sets the stage for further classroom discussion.