Aristote - Organon: Topics (2)

The Topics, in their practical applications, provide the means to determine which of these classes a given attribute belongs to; for example, an attribute will only be recognized as a genus of the subject if it is verified that it belongs to all the species included under the subject, that everything that belongs to the subject also belongs to it (Book IV, Chapter 1). These are, as we see, rules allowing us to discuss whether an attribution accepted by the respondent is valid, whether what they have posited as a genus is not rather a proper noun, etc., but not at all to discover such attributions[1]. Such is the nature of the famous rules of definition given in the Topics; dialectic is incapable of answering the question “what is it?” For the only questions admissible are those that can be answered with yes or no: unable to establish a definition, it can test a proposed definition, by examining, for example, whether the definition applies exclusively to what is being defined, whether the proper has not been surreptitiously introduced alongside the proximate genus and the specific difference, whether homonymous or metaphorical terms have been used, as those who define only by comparison did[2].

It is the practice of these discussions that leads Aristotle to pose three problems that will dominate his logic: that of the conversion of propositions, that of categories, and that of opposites. The first arises from the spontaneous use made in discussion of the reciprocal propositions of those that have been accepted by the respondent; if, for example, one has admitted that all pleasure is a good, one will be inclined to consider it agreed that all good is a pleasure. Now, such reciprocity is possible only if the attribute belongs exclusively to the subject, that is, if it is one of its own or the formula of its definition; but, in the general case, since the attribute can belong to terms that are not in the subject, the universal affirmative is converted into a particular one. On the other hand, the universal negative and the particular negative do not change in their conversion.

The second problem, that of categories, is also posed for the purposes of the discussion[3]. The ten categories are the various meanings that terms (subjects or attributes) can take: they can indicate either a substance (man, horse), or when or where a being is located (adverbs and complements of place and time), or the quality of a thing (qualifying adjectives), or what it relates to (double, half), or its situation (he is sitting or lying down), or its possession (he has shoes or weapons), or its action (he cuts or burns), or its passion (he is cut or burned). Although this classification is aided by the analysis of language, it is not entirely reducible to it, since, for example, despite the linguistic formula, the noun “whiteness” can designate a quality and not a substance. These distinctions arose rather from dialectics. It is not enough, for the discussion to be clear, to know whether an attribute is genus, difference, species, proper, or accidental; It is still necessary to know into which of the ten categories it falls; for if a term is a genus, and if this genus is, for example, a quality (color), its difference and its species must also be qualities[4]. This precaution is all the more necessary since the same word can have several meanings, each belonging to a different category: the term “good,” for example,* can fall into the category of producing (the remedy that produces health), or of quality (virtuous), or of time (the right opportunity), or of quantity (the right measure). It is, in certain cases, thanks to the categories that the dialectician can maintain the distinction between the proper and the accidental; if I am alone sitting in a gathering, although sitting is, in itself, an accident, it becomes a proper in relation to the others present and for as long as their gathering lasts[5].

The problem of oppositions is, par excellence, that of Platonic dialectic. For a discussion to be even possible (since every problem consists of asking for a yes or a no), the no must at least have meaning in relation to the yes, the error in relation to the truth, the other in relation to the same: this is Plato’s question in the Sophist. Aristotle, having in mind above all the practice of discussion, seeks to determine which theses are mutually rebuttable and which are mutually exclusive. When one proposition affirms about the whole subject what the other denies about the whole subject (Every man is just, no man is just), they are said to be contrary and cannot be true at the same time: two propositions are contradictory when one affirms what the other denies (Every man is white; it is not true that every man is white or: some man is not white); of two contradictory propositions, it is necessary that one be true and the other false[6]. It was also necessary to determine which pairs of attributes one governs or excludes the other; there are four oppositions of terms: relatives (double and half), opposites (good and bad), possession and privation (clear-sighted and blind), contradiction (sick and not sick)[7]. Of these oppositions, the meaning of the first and fourth is easy to grasp; for two relatives imply each other, and two contradictories exclude each other, one of the two necessarily having to belong to the subject. On the other hand, the use of the other two groups of opposites requires a thousand precautions; first, it is necessary to determine in which category the opposites are taken (white and black in the category of color; even and odd in the category of number) and relate the discussion exclusively to that category; Then, we must distinguish between two cases: the first, where opposites have no middle ground, and the position of one entails the exclusion of the other (even, odd), and the opposite case (white and black; non-white not necessarily being black). In this latter case, determining opposites will be difficult. If the opposite of white is black and not another color, it is because, in the category of colors, black is the furthest removed from white: the most distant possible terms. This is the rather imprecise definition of opposites that Aristotle arrives at. As for possession and privation, it is understood that they only have meaning if they are related to a subject that possesses by nature that which it can be deprived of; it is man who is blind, not the stone. Otherwise, the sophism that claims man has horns because one cannot say when he lost them would be true.