Aquinas Day By Day


Aquinas’s topic: Logic of concepts: relation 2

Scripture:  “The days will come when the bridegroom is taken away from them, and then they will fast.” Matthew 9:15

Aquinas’s text: Sententia super Metaphysicam, Bk. 5, lec. 17

Here is Aquinas’s commentary on the first part of Aristotle’s fuller treatment of relation.

Here the Philosopher determines about the relative. …  And first he enumerates the ways in which things are said in themselves to be relative. ... Therefore, he first posits three ways in which things are said to be relative.  (1) The first of these is relative based on number and quantity, such as double to half and triple to one-third. ... (2) The second is as things are said to be relative based on action and passion, or on active potency and passive potency, such as heating to heated, which pertains to natural actions, and cutting to being cut, which pertains to using an artifact, and, in general, whatever is active to whatever is passive. (3) The third sense of relative is as the measurable is relative to the measured.  Not measured and measurable in quantity—for this pertains to the first sense of relative, as double is called relative to half and half to double—but based on the measurement of being and truth. For the truth of knowledge is measured by the knowable object; since because a thing is or is not, a claim is known to be true or false, but not the reverse.  And the same relation holds for the sensible object and sensation.  This is why the relation of measure to measurable and the reverse relation are not reciprocal, as they are in the other senses of relation; but this sense concerns only the relation of measurable to measure.  And an image is said to be related to that of which it is an image in the same way that the measurable is related to its measure; for the truth of an image is measured by the thing of which it is an image.

He then proceeds to treat the three senses of relation that have been enumerated. ... In regard to the first sense, he does two things, (1a) first describing relations that follow on number as such, then describing relations that follow on unity as such.  Therefore, he says that the first mode of relation based on number is divided this way:  into relations comparing one number to another number and relations comparing a number to unity. ... Now one must know that every measure found in continuous quantities is derived in some way from number.  Therefore, relations based on continuous quantity are also attributed to number. One should also know that numerical proportions are divided into equality and inequality.  But there are two kinds of inequality, namely, the larger and the smaller, the more and the less. ... (1b) He then treats relatives that are based on unity, but not on comparison of a number to one or to another number.  He says that “equal,” “similar,” and “same” are said to be relative in a way different from the previous kinds of relations.  For these are based on unity.  For the “same” are those whose substance is one; the “similar” are those whose quality is one; and the “equal” are those whose quantity is one.  Since the one is the principle of number and its measure, it is clear that these are relative “according to number,” that is, according to something pertaining to the genus of number.

(2) He then proceeds to treat the second type of relations, which are found in active and passive things. ...  Now one must know for relatives based on active and passive potency, one finds differences regarding time.  For some of these are called relative based on past time, such as what made as related to what was made.  For example, father to son, since the father generated him but he was generated.  These differ as action and passion. But others are called relative based on future time, as what will make is related to what will be made.  And relations based on privation of potency, such as the impossible and the invisible, are reduced to this kind of relation.  For something is called impossible for this or that thing; and the same is true for visible.

[Introductions and translations © R.E. Houser]