Stanislav of Znojmo (died 1414), a professor of the Prague Theological Faculty, first a teacher and friend to Jan Hus, but then his decided opponent, wrote a comprehensive treatise, probably around 1403, entitled De vero et falso. The subject of my article is an analysis of the content of this work. In it, Stanislav deals with the question of the truth of a proposition and the problem of its truth-maker. The question of the truth-maker falls into the area of metaphysics, and so the author speaks of metaphysical truth. In so far as metaphysical truth is concerned, Stanislav of Znojmo defends a decidedly realist standpoint, judging that categorematic expressions are not alone in having real counterparts in the world, but syncategorematic expressions (for example, statement conjunctions, words expressing negations and so on) also have such counterparts. Stanislav’s treatise, in its overall orientation, belongs to propositionalism, a trend in logical thought widespread at the end of the Middle Ages. Although the author of the treatise De vero et falso does not cite contemporary authors, he shows a knowledge of some exponents of propositional logic (namely Gregory of Rimini, for example). His main inspiration, however, is undoubtedly the work of John Wyclif.
We investigate how to formalize reasoning that takes account of time by using connectives like “before” and “after.” We develop semantics for a formal logic, which we axiomatize. In proving that the axiomatization is strongly complete we show how a temporal ordering of propositions can yield a linear timeline. We formalize examples of ordinary language sentences to illustrate the scope and limitations of this method. We then discuss ways to deal with some of those limitations.
This article is intended for philosophers and logicians as a short partial introduction to category theory (CT) and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, which, in general, is an intuitionistic logic. We next present two families of toposes whose tautologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies.
This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and especially the presence of the rule of reverse substitution, requires certain change the definition of structurality.
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