Daily Lessons from St. Thomas

Aquinas Day By Day

Aquinas’s topic: Logic of concepts: relation 1

Scripture: “You have made him little less than the angels, and crowned him with glory and honor. You have given him rule over the works of your hands, putting all things under his feet.” Psalm 8

Aquinas’s text: Sententia super Physicam, Bk. 3, lec. 1, n 6; De veritate 21.1.

Of all the categories, “relation has the weakest kind of being” [De potentia, 8.1 ad 4m] and so is the hardest to understand. But this metaphysical deficiency does not prevent it from playing an exceedingly important role in logic. Every relation has four features, the subject where the relation starts, the term where it ends, the ground or basis for the relation, and the relation itself. Aristotle had treated relation in his Categories. In his commentary on the Physics Br. Thomas gives a succinct version of his own understanding of relation, in the context of treating motion. He also refers to Aristotle’s more developed treatment of relation in his philosophical dictionary at Metaphysics 5. In the second text below, Br. Thomas again succinctly sums up his view of Aristotle, calling the relation running from knower to known a “real relation,” the relation proceeding from known to knower a “relation of reason.”

From Aquina’s commentary on the Physics:

The third division pertains to one of the genera of beings, namely, relation. For in a way motion seems to belong to this genus, as the mover is referred to the mobile object. In order to understand this, one must consider that, since relation has the weakest kind of being because it consists only in this, that there is a referring to another, it is necessary that relation be founded on some other accident. For the more perfect accidents are closer to substance and by means of them the other accidents are present in a substance. Now relation, which is order to another, is especially founded upon two things, namely, quantity and action. For quantity can be the measure of something external and an agent transfers its own action to another. Therefore, some relations are founded on quantity, and especially on number, to which belongs in the first place the notion [ratio] of measure. This is clear in the double and the half, the multiplied and the divided, and other such things. In addition, same and similar and equal are founded upon unity, which is the principle of number. Now other relations are founded upon action and passion, either based on an act, as heating is said in reference to what is heated, or based on what has acted, as father is referred to son because he has begotten him, or based on the power of the agent, as lord is referred to servant because he can order him. The Philosopher explains this division fully in Metaphysics 5.

Tertia divisio est unius generis entium, scilicet eius quod est ad aliquid. Nam motus aliquo modo ad hoc genus pertinere videtur, inquantum movens refertur ad mobile. Ad huius igitur tertiae divisionis intellectum, considerandum est quod, cum relatio habeat debilissimum esse, quia consistit tantum in hoc quod est ad aliud se habere, oportet quod super aliquod aliud accidens fundetur; quia perfectiora accidentia sunt propinquiora substantiae, et eis mediantibus alia accidentia substantiae insunt. Maxime autem super duo fundatur relatio, quae habent ordinem ad aliud, scilicet super quantitatem et actionem: nam quantitas potest esse mensura etiam alicuius exterioris; agens autem transfundit actionem suam in aliud. Relationes igitur quaedam fundantur super quantitatem; et praecipue super numerum, cui competit prima ratio mensurae, ut patet in duplo et dimidio, multiplici et submultiplici, et in aliis huiusmodi. Idem etiam et simile et aequale fundantur super unitatem, quae est principium numeri. Aliae vero relationes fundantur super actionem et passionem: vel secundum ipsum actum, sicut calefaciens dicitur ad calefactum; vel secundum hoc quod est egisse, sicut pater refertur ad filium quia genuit; vel secundum potentiam agendi, sicut dominus ad servum quia potest eum coercere. Hanc igitur divisionem manifeste expressit philosophus in V Meta.

From Aquinas’s De veritate:

According to Aristotle in Metaphysics 5, that relation is said to be merely a relation of reason in which that is called relative which does not depend on that to which it refers but the converse is true, since relation itself is a kind of dependence, as is clear in knowledge and the knowable object, and in sensing and the sensible object. For knowledge depends on the knowable object, but the converse is not true. Therefore, the relation in which knowledge is referred to the knowable object is a real relation, but the relation in which the knowable object is referred to knowledge is only a relation of reason. For according to the Philosopher, the knowable is relative, not because it refers but because another thing is referred to it. And this is true of all other things that are related as measure to thing measured or as perfective to what is perfected.