Faculty of Arts
Logical consequence is a key methodological notion in the cognitive, mathematical and hard sciences, as well as in computer science and philosophy. Arguably, we need to appreciate it in order to understand how any conclusion should be drawn from premises, since probabilistic, abductive and default reasoning might best be explained as systematic deviations from, or generalisations of, the consequence relation. When introduced to logic, one is told that a conclusion is a logical consequence of some premises when it is impossible for those premises to be true with the conclusion false, or when the truth of the premises guarantees the truth of the conclusion. Many questions arise. Are these (and other common definitions of consequence) equivalent? What sorts of things are premises and conclusions: sentences, propositions, or something else? Is consequence fundamentally a formal notion? That is, if a conclusion is a consequence of some premises, must this be because of facts about the logical structure, rather than the content, of the premises and conclusion? If logical theory undermines our intuitions, for instance, by telling us that every conclusion is a consequence of a contradiction, under what conditions should we abandon the intuitions? We know that there are many different logics-classical, intuitionistic, paraconsistent and more-that share a language but yield different sets of theorems. Should we conclude that there are many different consequence relations, or that different logics aim to capture the same consequence relation, or that consequence is only one of the relations that interest logicians, or all of the above?
Not taught in 2012
Lecturer(s) Professor Fred Kroon
PHIL 737: 15.0 points