William M. Briggs

Statistician to the Stars!

Summary Against Modern Thought: God Knows Infinite Things

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles. All posts are under the category SAMT.

Previous post.

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Chapter 69 That God Knows Infinite Things (alternate translation)

[1] WE must next prove that God knows infinite things. For in knowing that He is the cause of things He knows things other than Himself, as was shown above.[1] Now He is the cause of infinite things, if there be infinite things, since He is the cause of whatever is. Therefore He knows infinite things…

Notes Infinity, as I’m frequently pointing out, is not a very large, or even unimaginably large number. It is way beyond any conception of any number; indeed, it is infinitely beyond. We cannot—we are dealing in an impossibility, and not in the modern sense of that word, but in its old-fashioned definition of cannot be done no matter what—have any true conception of all that infinity is. We cannot because our minds are finite. God’s mind is not. Only an infinite mind can create something from no-thing.

[3] Moreover. If God’s knowledge extends to all things that exist, in whatever way they exist, as we have shown,[4] it follows that He knows not only actual being but also potential being. Now in natural things there is the infinite potentially although not actually, as the Philosopher proves in 3 Phys.[5] Therefore God knows infinite things: even as unity, which is the principle of number, would know infinite species of numbers, if it knew whatever is potentially in it; for unity is every number potentially…

Notes Back to basics. What is potential is not actual (and it takes something actual to turn a potentiality into actuality), but what is potential is unbounded. And since God is the ultimate or first cause of everything, it follows He knows all potentialities, hence He can known infinite things.

[6] Moreover. According to the Philosopher (3 De Anima)[10] an intellect which knows the supremely intelligible knows the less intelligible not less but more: and the reason for this is that the intellect is not corrupted by the excellence of the intelligible, as the sense is, but is the more perfected. Now if we take an infinite number of beings, whether they be of the same species–as an infinite number of men–or of an infinite number of species, even though some or all of them be infinite in quantity, if this were possible; all of them together would be of less infinity than God: since each one and all together would have being confined and limited to a certain species or genus, and thus would be in some way finite: wherefore it would fall short from the infinity of God Who is infinite simply, as we proved above.[11] Since, therefore, God knows Himself perfectly,[12] nothing prevents Him from also knowing that infinite number of things…

Notes We haven’t discussed this topic much, but according to St Thomas that whereas each man belongs to mankind, each angel is its own species. Angels are also immaterial, and thus there is no difficulty in stacking them up from here to forever. Now put you and me together: the sum of our intelligences is not arithmetic, as is obvious from any reading of history. Simply putting more of us together is not going to increase our “joint” mind to infinity. Infinity is infinitely far away. Whereas God is in a different unapproachable class altogether.

[9] Again. Since our intellect is cognizant of the infinite in potentiality, for as much as it is able to multiply the species of numbers indefinitely; if the divine intellect knew not also the infinite in act, it would follow either that our intellect knows more things than the divine intellect knows, or that the divine intellect knows not actually all the things that it knows potentially: and each of these is impossible, as proved above…[15]

Notes The tidbit here is that we can, as any mathematician already knows, be aware of the infinite in potentiality, as admitted in the first note. But a proof that a thing exists does not imply that we understand fully the thing.

[13] From the foregoing it is clear why our intellect knows not the infinite, as the divine intellect does. For our intellect differs from the divine intellect in four respects, which constitute this difference. In the first place, our intellect is simply finite, whereas the divine intellect is infinite. Secondly our intellect knows different things by different species: wherefore it cannot grasp infinite things by one knowledge, as the divine intellect can. The third difference results from the fact that our intellect, since it knows different things by different species, cannot know many things at the same time, so that it cannot know an infinite number of things except by taking them one after the other. Whereas it is not so in the divine intellect, which considers many things simultaneously, as seen by one species. Fourthly, because the divine intellect is about things that are and things that are not, as we proved above.[19]

Notes Ponder this well. Memorize it.

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[1] Ch. xlix.
[2] Ch. xlvii.
[3] Ch. xliii.
[4] Cf. ch. l.
[5] iv. seqq.
[6] Ch. xlix.
[7] Ch. xliii.
[8] Ch. xlv.
[9] Ch. xliii.
[10] iv. 5.
[11] Ch. xliii.
[12] Ch. xlvii.
[13] Ch. xlv.
[14] Ch. xlv.
[15] Cf. chs. xvi., xxix.
[16] Ch. xlvi.
[17] 1 Phys. ii. 10.
[18] Ps. cxlvi. 5.
[19] Ch. lxvi.
[20] Cf. ch. lxiii.: The fifth . . . p. 134.
[21] 1 Phys., l.c.
[22] Sum. Th. P. I., Q. xiv., A. 12 ad 1.
[23] Cf. ch. lxvi.

7 Comments

  1. Sander van der Wal

    August 16, 2015 at 9:08 am

    It is impossible for numbers to change to a different number. 1 doesn’t become 2, nor does it become ?. Otherwise, if you added 1 to 1, you could never have a single instance of something unique, like the Eiffel Tower or the American President, ever again. By adding 1 to 1, you would instantly have 2 Eiffel Towers, and two American Presidents. The world will be fine with 2 Eiffel Towers, but it won’t survive two American Presidents.

    further, there is just one infinity for natural numbers. So if there is an infinite number of species, then God is as big as that number, not bigger. In other words, the infinity of God will fit in Hilbert’s Hotel.

  2. It’s interesting that St. Augustine also thought about the infinite knowledge of God, as did the mathematician Cantor. See my post (shameless self-promotion time again) that promotes “Beyond Infinity: Augustine and Cantor”, a book by Adam Drozdek, Associate Professor of Computer Science at Duquesne University:

    http://rationalcatholic.blogspot.com/2012/05/mathematics-handmaiden-of-theology.html

  3. Seems strange, given God’s infinite all-knowingness, that the Pope sees fit to have people pray to God to save the planet, & such. If God knows so much, what’s the need for prayer to alert Him to fix his own creation.

    http://www.climatedepot.com/2015/08/12/holy-co2-pope-declares-sept-1-to-be-annual-global-warming-prayer-day-pope-francis-announces-world-day-of-prayer-for-the-care-of-creation/

  4. Semiotic Animal

    August 17, 2015 at 9:17 am

    @Ken
    Aquinas wondered the same thing:

  5. swordfishtrombone

    August 17, 2015 at 10:52 am

    By this point in Thomas’s arguments, God has been so hyper-inflated into infinite power and ‘know-it-all-ism’, he might just as well be an abstract mathematical object, Max Tegmark-style. It’s certainly hard to see by definition how he could muster any enthusiasm for our infinitely uninteresting lives.

    “Know-it-all-ism? That’s not even a word!” Lisa Simpson.

  6. Still waiting for theodicy.

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