Thomas and Scotus on a question of divine infinity

The objection:*

If God existed, (i) he would have to be infinite in being and perfection, but (ii) no being is infinite in being and perfection. Proof for (ii) what is here and not somewhere else is finite in place and position; what is today so that it was not yesterday nor will be tomorrow is finite in time and duration; and what does one thing and not another is finite in action and power, and so whatever is this thing and not another is finite in being and perfection. But if God existed, he would be this divine thing and not something else, like a man, a stone, or a piece of wood. 

St. Thomas’s response:

The fact that the being of God is self-subsisting, not received in any other, and is thus called infinite, shows Him to be distinguished from all other beings, and all others to be apart from Him. Even so, were there such a thing as a self-subsisting whiteness, the very fact that it did not exist in anything else, would make it distinct from every other whiteness existing in a subject.

Scotus’s Response (As given in Scotus academicus, etc. By Claude Frassen)**

Scotus responds in 1. dist. 1. q. 2. n. 36 “I deny the consequent, for the place and time in which a thing would be not in another place or another time is finite – for if it were infinite, the antecedent would be false… If, per impossibile, there were some infinite place where something was (ubi) it would fill up any other place where something could be; so that it would not follow that this body is here in such a way as to not be there.  Therefore it is finite according to the place in which it is, for the “here” cannot be shown to be the case except in finite things. Thus Aristotle says that if a motion were infinite and the time were infinite it would not be the case that the motion would be in this time and not in another, and so [Aristotle thought] it must be finite in time. [moreover, it does not follow] from the fact that a thing is this singular and determinate being that it is finite; for the determinate is opposed to the indeterminate and not to the finite, because something can be infinite and also determinate – for if there were an infinite line, it would still be a determinate thing since it would be a quantity and not a quality, relation, or substance; but it would nevertheless not be less infinite.

The responses share considerable overlap, especially if we compare STA’s first response with the second Scotistic response, but there is an obvious note of difference: St. Thomas wants to immediately shift the consideration away from the infinite to the self-subsistent and unrecieved-into-another, whereas as Scotus doesn’t. The crucial difference seems to be that St. Thomas argues that the mere fact that a form would not be received in matter would suffice to make it infinite, and so all we need to do to account for the infinity of some form is point out that it is not in matter (see the response in the link given). Scotus seems to think that one needs more than mere separation from matter to establish infinity.

One could, however, read the “per impossibile” in Scotus’s response as meaning that all material places are finite precisely as material, and so separation from matter is formally what constitutes [the relevant sort of] infinity, which would put him in agreement with STA. But my suspicion is that St. Thomas does not think we have a distinct concept of the infinite whereas Scotus does. Existing infinite things, for STA, are nothing other than self-subsistent things, whereas for Scotus we seem to be able to understand existing infinite things formally as infinite.


*I take the Scotist formulation of the objection because it is more fleshed out.

**Respondet Doctor in 1. dist. 1. q. 2. n. 36, negando consequentiam , et rationem disparitatis profert, quod locus et tempm in quibus res esset, et non alibi, aut alio tempore, sint finita : nam si essent infinita, falsum esset antecedens: etenim, inquit Doctor : Si esset aliquod ubi infinitum, per impossibile, et corpus inflnitum, repleret illud ubi ; non scqueretur: hoc corpus est hie ita quod hon sit alibi : ergo est finitum secundum ubi, quia ly hic non demonstrat nisi in finitum. Ita secundum Philosophum, si motus esset infinitus et tempus infinitum , non sequeretur: iste motus est in hoc tempore, et non in alio : ergo est finitus secundum tempus. Ita ad propositum oportet probare illud quod demonstratur per hoc ens, esse finitum…. ex eo quod sit hoc ens, singulare et dcterminatum, non sequitur exindc quod sit ens fini- tum ; determinatum enim opponitur quidem indeterminato, non autem finito ; quia aliquid potest esse ens infinitum et simul dcterminatum, etenim si dsretur linea infinita, esset ens determinatum, quia esset quautitas, et non qualitas, nec relatio, nec substantia ; propterea tamen non minus esset infinita.


  1. Negationes etiam non summe amamus said,

    November 28, 2014 at 1:19 pm

    I was having a conversation with a Thomist theology prof. a couple weeks back about this very passage from ST. I think it’s a bad argument (as does Scotus) because it would seem to bring angels into the mix. They are by nature immaterial and incapable of receiving bodies, or body cannot receive them I should say. By STA’s reasoning they would be infinite. And the absurdities flow on from there.

    • November 28, 2014 at 8:36 pm

      Aquinas does indeed conclude that angels are infinite; he explicitly states this on occasion, citing precisely this reason. (He doesn’t think, of course, that they are infinite in every respect; unlike God, they are finite in actual being, for instance. But he does think that as forms they are infinite, precisely because they cannot be received into matter.)

      • Negationes etiam non summe amamus said,

        November 29, 2014 at 5:11 pm

        Where does he state that, Brandon. Thanks for the info.
        Granting then that he does say that, I am wondering how something can be infinite with respect to one aspect of its nature yet still a finite being. For this one part of angels to be infinite, it seems that the whole nature of the angels need to be infinite. It seems to be the case that being infinite in one aspect (necessarily, by nature) means it is infinite in every aspect, which must include being.
        Just thinking out loud. Help?

      • November 29, 2014 at 7:18 pm

        An example would be ST 1.7.2 (on the infinity of God); he also says it at 1.50.2 ad 4 (on the substance of angels).

        I think Aquinas just regards “not received into matter” as being in itself one of the things meant by ‘infinite’ (i.e., unlimited) in the first place. He likes to use the example of whiteness — if whiteness could subsist on its own without being received into matter, it just would be infinite whiteness itself, because it wouldn’t have matter to contract it to one subject. But he also always insists that this is just relative infinity, because absolute infinite would have to be uncontracted being itself, which whiteness and angels are not, since their actual being is contracted to a particular nature.

        It could also be in part because he’s already quite generous about what counts as relatively infinite — matter is relatively infinite (as potential to all forms receivable in matter), sensation is relatively infinite (as related to all sensible things), human intellect is relatively infinite (as related to all intelligible things and as not completely received into matter), so just adding angels to the list wouldn’t look strange at all.

      • Negationes etiam non summe amamus said,

        November 30, 2014 at 4:44 pm

        Ok. So let me ask it this way. What is the limiting principle of angel? It’s not matter, and Aquinas denies the individuality of angels since matter is the principle of individuation. So what is it? What keeps an angel from being infinite? What’s the limiting principle.

      • November 30, 2014 at 6:55 pm

        I’m not sure I follow — for Aquinas, nothing keeps an angel from being infinite; that’s why he says they’re infinite. But the reason for their infinity is the limited reason that they have a determinate form not received into matter; the determinate form itself, however, is such that it can only participate in actual being. In the angel, the form itself contracts the actual being or existence, since it is that which is potential for actual being. God, however, has no contracting form; it is his nature actually to be, so He is infinite being itself, not just a being that is infinite in a certain way.

      • Negationes etiam non summe amamus said,

        November 30, 2014 at 8:23 pm

        So existence is the limiting principle.

      • December 1, 2014 at 7:36 am

        Assuming I understand what you mean by ‘limiting principle’, I think Aquinas thinks the form is. The limiting principle is found in what serves as potential in the composition — matter in the case of hylomorphic composition, but in the case of immaterial substance, it is the form that is potential to actual being, and thus contracts or limits actual being. Actual being or existence cannot be a limiting principle.

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