Questions on the Metaphysics of Aristotle

Question Twelve

QUESTION TWELVE Text of Aristotle: “One type1 of relative is as double to half, and treble to a third, and in general that which contains something else many times to that which is contained many times in something else and that which exceeds to that which is exceeded. Another type of relative is that which can heat to that which can be heated and that which can cut to that which can be cut, and in general of the active to the passive; and another type is as the measurable to the measure and the knowable to knowledge and the sensible to sense perception.” (Metaphysics V, ch. 15, 1020b 26-32) Are the philosopher’s three modes of relatives suitable? Does the Philosopher aptly assume three types of relation or relatives? [Arguments Pro and Con] 1 [1] [The three modes in general] That he does not in general: These diverse modes are founded upon diverse categories; therefore, the relations are in diverse categories. Proof of the implication: if a relation is the same as its foundation, then it is evident; if it is other than its foundation, since one takes the species and distinction from the foundation, then the relations will differ as the foundations do. Why should not the relations be distinguished generically, if the foundations are? 2 Likewise, the Philosopher says in Bk. V2 that “eight may be described as a double number by use of the definition of two.” Since doubleness is only in other numbers through duality, which is the first foundation of doubleness, therefore, it follows that the unity and distinction of a relation stems from its foundation. 1 Modus = mode, i.e. a way, a manner, a style of relating things. It explains how they are related, i.e. in what way. If one speaks of the noun form “relation” however, we need something other than ‘mode.’ The Oxford translation = kind, where I prefer ‘type.’ 2 Aristotle, Metaphysics V, ch. 29, 1025a 1. 562 THE METAPHYSICS OF JOHN DUNS SCOTUS 3 Also, these modes are not sufficient, because relatives according to genus are per se relatives, and are not contained under these modes. Proof of the first: whatever is contained in the concept of the genus, pertains to the concept of the species; therefore, if the genus depends on another, so too does the species.—The Philosopher says as much about the second3 in the text.4 4 [The relations of the first type] With reference especially to the first type,5 the same thing is not related per se to diverse things, but the same container is referred to the many things i t contains [according to Aristotle]. 5 Also, all relatives are opposed according to the Categories, in the chapter ‘On Opposites’;6 but containing and contained are not opposed. Proof of the minor: in the Categories, the chapter ‘On Quantity’:7 great and small are not contraries, because the same thing is called great and small; similarly, a number may be double this and half of that. Therefore, they are not opposed. 6 Also, the second part of this [first] type is not appropriate [i.e. equal, like, and the same], because identity [or sameness] is a conceptual relation; therefore, it is not a true relation of this sort. Proof: “identity is the oneness characteristic of more than one, when the intellect uses one as two”;8 hence identity and real similarity are not in the same genus. 3 Namely, that relatives are not contained under these modes. 4 Aristotle, Metaphysics V, ch. 15, 1020b 26-1021b 11. 5 Paragraphs 4 and 5 deal with the first part concerning the first type of relatives, whereas paragraphs 6 and 7 treat of the second part concerning the first type of relatives; cf. Antonius Andreae, Expositio in libros Metaph. V, sum. un., ch. 14 n. [101] (ed. Vives VI 82b): “Ad evidentiam primae partis notandum quod relationes primi modi fundantur super aliquid de genere quantitatis, scilicet super numerum vel super continuum. Prius tamen reperitur relatio istius modi in numeris et inest dupliciter: uno modo comparando numerum ad numerum, ita quod oportet utrumque extremum esse numerum; alio modo comparando numerum ad unum, ita quod solum alterum extremum est numerus... Secundum hoc ergo, haec pars dividitur in duas: quia primo prosequitur de relativis primi modi, secundum quod consequuntur ipsum numerum. Secundo, prout sequuntur ipsum unum, quod est principium numeri.” 6 Aristotle, Categories ch. 10, 11b 25-26. 7 Aristotle, Categories ch. 6, 6a 9-10...