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Back to Aristotle!

100%

Slater H.

Logic and Logical Philosophy

2011

tom 20

nr 4

275-283

There were already confusions in the Middle Ages with the read- ing of Aristotle on negative terms, and removing these confusions shows that the four traditional Syllogistic forms of statement can be readily gen- eralised not only to handle polyadic relations (for long a source of diffi- culty), but even other, more measured quantifiers than just ‘all’, ‘some’, and ‘no’. But these historic confusions merely supplement the main con- fusions, which arose in more modern times, regarding the logic of singular statements. These main confusions originate in the inability of the mainline modern tradition to supply the ‘logically proper names’ which alone have the right to replace individual variables; an inability which has resulted in the widespread, but erroneous replacement of individual variables with or- dinary proper names, i.e. names for contingent beings, in many if not most contemporary logic texts. The paper includes the exhibition and grammat- ical characterisation of the logically proper names that are required instead, specifying just how they differ syntactically from ordinary proper names. It also shows how ontologically significant is the distinction, since not only do logically proper names refer to necessarily existent objects (showing there are no ‘empty domains’ for Classical Logic to fail to apply to), but also thereby central features of Realism become considerably clarified.

Logický čtverec a otázka existence

100%

Vlasáková M.

Filosofický časopis (Philosophical Journal)

2015

tom 63

nr 1

77-93

The aim of this article is to challenge a time-honoured myth which claims that the Aristotelian demarcation of the mutual relations between particular types of categorical judgements, as represented in the “square of opposition”, and also a part of Aristotelian syllogistics, are not valid from the point of view of modern logic without the assumption of the non-emptiness of the concepts under consideration. In reality, however, the Aristotelian tradition works with empty concepts and the square of opposition is valid for those concepts. The only problem is with the inadequate formal transcription of categorical judgements which modern logic usually offers: it assumes, that is, an “existential import” (if the judgement is true then there must exist an instance of the subject’s concept) in partial judgements, while the Aristotelian logic assumes it in positive judgements. On this Aristotelian assumption, the relations of the square of opposition, and syllogistics in general, function without difficulties, even for empty concepts. This had been quite explicitly formulated by medieval logicians. In the following part of the article, some traditionally controversial expressions of Aristotle concerning just this question of existential import are analysed. Some of these controversies probably stem from the confusion of two different problems – on the one hand, the question of the mutual logical relations of the categorical judgements under analysis, on the other hand the problem of the possibility of a truthful account of non-existent objects. To this second problem the Aristotelian tradition takes a different approach than modern logic, which considers existence as a second-order property and identifies it with presence in the universe.