Version: v1, Published online: 1998
Retrieved May 31, 2020, from https://www.rep.routledge.com/articles/thematic/consequence-conceptions-of/v-1
The idea of one proposition’s following from others – of their implying it – is central to argument. It is, however, an idea that comes with a history attached to it, and those who blithely appeal to an ‘intuitive’ or ‘pre-theoretic’ idea of consequence are likely to have got hold of just one strand in a string of diverse theories. This entry introduces the main alternatives – to call them rivals would be too strong, since it suggests that they are necessarily in competition with one another. Simply put, consequence may be conceived as a relation that is or is not modal in character, and is or is not formal. Thus for Aristotle, consequence is both necessary and formal; for Chrysippus it is necessary but not formal; for Bolzano and Tarski it is formal but not necessary; and for Philo and Russell it is neither necessary nor formal. Conceptions of consequence that are neither necessary nor formal are also needed if justice is to be done to deduction in science, the law and daily life. Cutting across all these other differences there is a perennial controversy about relevance. Does implication always require a full-blooded connection between premises and conclusion, or may it hold simply because of some property of either separately, for example, because the premises are impossible?
Smiley, Timothy. Consequence, conceptions of, 1998, doi:10.4324/9780415249126-Y022-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/consequence-conceptions-of/v-1.
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