Version: v1, Published online: 1998
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1. Aristotle’s logic: general
Aristotle was the first great logician (see Aristotle §§4–5, 7). His logical writings are traditionally grouped together as the Organon, comprising Categories, De interpretatione, Prior Analytics, Posterior Analytics, Topics and On Sophistical Refutations.
Categories and Topics share a concern with distinguishing different types of predication. In Categories beings are classified into substances, quantities, qualities, relatives, places, times, positions, states, actions and affections. Within any one category, beings are related to one another in tree-structures linked by the ‘said of’ relation; for example, in the category of substance, animal is said of swan and of horse. Between categories there are relations of ‘inherence’: for example, colour (a quality) inheres in body (a substance). The ‘said of’ and inherence relations underlie all true predications. Substances are either ‘primary’ (for example, this horse) or ‘secondary’ (for example, horse). Among all beings, primary substances are basic: all others are said of or inhere in primary substances, whereas primary substances neither are said of nor inhere in anything. Though Categories is concerned mainly with ontological questions, it also states a few principles of inference, including the following: ‘When one thing is predicated of another as subject, everything said of the predicate will also be predicated of the subject’.
Topics divides predications into four types: (1) essential and convertible, (2) essential and non-convertible, (3) non-essential and convertible, (4) non-essential and non-convertible. Any predicate thus stands to its subject as (1) a definition (for example, ‘biped land-animal’ is the definition of man), (2) a ‘genus’ or ‘differentia’ (for example, colour is the genus of white, biped is the differentia of man among land-animals), (3) a ‘peculiarity’ (for example, ‘walking in the gymnasium’ would be a peculiarity of a particular man if he were the sole walker there) or (4) an ‘accident’ (for example, evil is an accident of chance). These four types of predication are traditionally known as the ‘predicables’, and Topics formulates a large number of principles (or, commonplaces, ‘topoi’) concerning them, for example, ‘the genus is predicated essentially of whatever the species is predicated of’ (IV 2).
The ninth book of Topics is known by the separate title On Sophistical Refutations. Aristotle there distinguishes fallacies that depend on linguistic factors (such as lexical or syntactic ambiguity) from those that do not.
Fallacies not depending on linguistic factors are seven. The fallacy of ‘accident’ attributes to a thing what belongs only to an accident of the thing, for example, supposing Coriscus happens to be approaching, it would be wrong to infer that you do not know Coriscus, given the premise that you do not know who is approaching. The fallacy of ‘secundum quid’ argues from a qualified to an unqualified statement, for example, supposing you have a belief about a non-being, it would be wrong to infer that a non-being is, given the premise that a non-being is-an-object-of-belief. The fallacy of ‘ignoratio elenchi’ argues to the wrong point, for example, by showing that something is double in height when required to show that it is double in width. The fallacy of ‘petitio principii’ or begging the question is committed when someone ‘tries to prove by means of itself what is not known by means of itself’ (Prior Analytics II 16). The fallacy of ‘affirming the consequent’ is committed when the direction of implication is confused, for example, by confusing the statement that whatever is created has a beginning with the statement that whatever has a beginning is created. The fallacy of ‘false cause’ arises from the inclusion of redundant material in a reductio argument, for example, arguing that the diagonal is incommensurable with the side of a square because if it were commensurable, and if traversing a distance entailed first traversing half the distance, then we would be committed to the absurd statement that motion is impossible. The fallacy of ‘many questions’ occurs when what in fact are several questions are treated as if they were just one. (See Fallacies.)
De interpretatione contains a semantic theory of categorical statement-forms. Prior Analytics contains the theory of the syllogism. Posterior Analytics applies the syllogistic to the special case where a syllogism embodies scientific knowledge. It deals with the orderly exposition of a body of scientific knowledge in an axiomatic deductive system: the axioms of such a system will state how things are in themselves and necessarily, and the deductions’ premises will explain the truth of their conclusions.
Thom, Paul. Aristotle’s logic: general. Logic, ancient, 1998, doi:10.4324/9780415249126-Y032-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/logic-ancient/v-1/sections/aristotles-logic-general.
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