Some simple arguments showing God knows both singulars and things that are not. I don’t think there will any dispute about the contentions, so in the Notes we do a little wandering. Next week is more controversial material.
 …For it has been shown that God knows other things in as much as He is their cause. Now God’s effects are singular things: because God causes things in the same way as He makes them to be actual; and universals are not subsistent, but have their being only in singulars, as is proved in 7 Metaph. Therefore God knows things other than Himself not only in the universal but also in the singular.
Notes In re “universals are not subsistent”. St Thomas means universals don’t exist actually as some ideal to which singulars are compared. Plato’s forms are not real. We are Aristotelians here.
 …Moreover. The nature of a genus cannot be known perfectly unless its first differences and proper passions be known: thus the nature of number would not be perfectly known if odd and even were unknown. Now universal and singular are differences or proper passions of being. Therefore if God, in knowing His essence, knows perfectly the common nature of being, it follows that He knows perfectly the universal and the singular. But, just as He would not know the universal perfectly, if He knew the intention of universality without knowing the thing in the universal, such as man or animal, so too He would not know the singular perfectly if He knew the nature of singularity without knowing this or that singular thing. Therefore God must needs know singulars.
Notes Like we said last week, there is little—really, no—dispute that God knows singulars, and these proofs are therefore adequate. The tidbit to note here is about numbers. Two points. The first is what we might call the commoner’s fallacy, which might also be called the we-now-know fallacy, and which is the practice whereby anything that is known by one of us (human beings) it is therefore knowledge for or of all of us, knowledge any of us might claim to know. As Wilhelmsen says in his delightful Man’s Knowledge of Reality: An Introduction to Thomistic Epistemology, “What is the difference between a master sergeant reading the Articles of War to a company of recruits and a lawyer citing the same in a court-martial?”
So just because there may be some person out there who knows all about the nature of number—and this is the second point—that knowledge does not belong to you or me, too by default. Plus, as much knowledge about numbers that exists among us, it’s unlikely anybody knows all about the nature of number. Readers who are mathematicians will probably agree with this.
 Ch. xlix.
 D. 6. xiii., xiv.
 In the next place we must show that God lacks not the knowledge of things that are not.
 …Again. The knowledge of God’s intellect stands in the same relation to other things as the knowledge of a craftsman to the works of his craft: since He is cause of things by His knowledge. Now the craftsman by the knowledge of his art knows even those things which are not yet produced by his art: since the forms of his art pass from his knowledge into external matter so as to produce the works of his art: and consequently nothing prevents forms which have not yet materialized outwardly from being in the craftsman’s knowledge. Therefore nothing prevents God from having knowledge of things that are not.
 …Moreover. Our intellect, in respect of the operation by which it knows what a thing is, can have knowledge of those things also that are not actually: since it is able to comprehend the essence of a lion or horse, even if all such animals were slain. Now the divine intellect knows, as one who knows what a thing is, not only definitions but also enunciations, as shown above. Therefore it can have knowledge of those things also that are not.
Notes The difficulty here is that we had to have some experience of actual lions or horses before we can know what they were like would they were all gone. Think dinosaurs.
 Again. An effect can be foreknown in its cause even before it exist: even so an astronomer foreknows a future eclipse by observing the order of the heavenly movements. Now God’s knowledge is of all things through their cause: for by knowing Himself, Who is the cause of all, He knows other things as His effects, as we proved above. Nothing, therefore, prevents Him from knowing those things also that are not yet.
Notes Predictions, like all probability and all statements of logic, are conditional. As long as we grasp the conditions, the deductions follow, and we can know them. But some predicitons (as regular readers know) are probabilitistic. Given the normal conditions, the probability of a head in a coin flip is 1/2. We know this 1/2 and not the outcome; but this is still knowledge (in the strong sense of that word).
And now another tidbit for our mathematical friends (only the first part of the argument is given).
 Moreover. There is no succession in God’s act of understanding, any more than there is in His existence. Hence it is all at once everlasting, which belongs to the essence of eternity, whereas the duration of time is drawn out by the succession of before and after. Wherefore the proportion of eternity to the whole duration of time is as the proportion of the indivisible to the continuous, not indeed of the indivisible that is the term of the continuous, and is not present to each part of the continuous—for such is likened to an instant of time—but of the indivisible that is outside the continuous, and yet synchronizes with each part of the continuous, or with each point of a signate continuous: because, since time does not exceed movement, eternity, being utterly outside movement, is altogether outside time…
Notes Math can be done without symbols! Although symbols are eminently useful, they do tend to tempt one into the Deadly Sin of Reification.
 By these arguments it is made clear that God has knowledge of not-beings. Nevertheless not-beings have not all the same relation to His knowledge. For those things which neither are, nor shall be, nor have been, are known by God as possible to His power. Wherefore He knows them, not as existing in themselves in any way, but as merely existing in the divine power. Such things are said by some to be known to God according to His knowledge of simple intelligence.
Notes Even God can imagine. That’s enough for us. I don’t think there is any dispute, used as we are to mathematical-like proofs, that God knows singulars or things that are not. Next week we ask whether God knows future contingents, which is a juicier question.
 Ch. lxi.
 Categ. v. 18.
 Bk. II., xxiv. See above, ch. lxv.: Moreover. God’s intellect . . . p. 137.
 Chs. xlix., liv.
 Ch. xliii.
 Ch. xlvii.
 Chs. lviii., lix.
 Ch. xlix.
 Ch. xlv.
 Ch. xv.