The Two-Knowledge View
Aquinas, ST 1.14.9:
Whatever therefore can be made, or thought, or said by the creature, as also whatever He Himself can do, all are known to God, although they are not actual. And in so far it can be said that He has knowledge even of things that are not. Now a certain difference is to be noted in the consideration of those things that are not actual. For though some of them may not be in act now, still they were, or they will be; and God is said to know all these with the knowledge of vision: for since God's act of understanding, which is His being, is measured by eternity; and since eternity is without succession, comprehending all time, the present glance of God extends over all time, and to all things which exist in any time, as to objects present to Him. But there are other things in God's power, or the creature's, which nevertheless are not, nor will be, nor were; and as regards these He is said to have knowledge, not of vision, but of simple intelligence. This is so called because the things we see around us have distinct being outside the seer.
(Quaecumque igitur possunt per creaturam fieri vel cogitari vel dici, et etiam quaecumque ipse facere potest, omnia cognoscit Deus, etiam si actu non sint. Et pro tanto dici potest quod habet etiam non entium scientiam. Sed horum quae actu non sunt, est attendenda quaedam diversitas. Quaedam enim, licet non sint nunc in actu, tamen vel fuerunt vel erunt, et omnia ista dicitur Deus scire scientia visionis. Quia, cum intelligere Dei, quod est eius esse, aeternitate mensuretur, quae sine successione existens totum tempus comprehendit, praesens intuitus Dei fertur in totum tempus, et in omnia quae sunt in quocumque tempore, sicut in subiecta sibi praesentialiter. Quaedam vero sunt, quae sunt in potentia Dei vel creaturae, quae tamen nec sunt nec erunt neque fuerunt. Et respectu horum non dicitur habere scientiam visionis, sed simplicis intelligentiae. Quod ideo dicitur, quia ea quae videntur apud nos, habent esse distinctum extra videntem.) [L]
Aquinas, SCG 1.66:
Things that neither are, nor shall be, nor have been, are known by God as possible to His power: hence He does not know them as being anywise in themselves, but only as being within the compass of divine power. These sort of things are said by some to be known by God with the 'knowledge of simple understanding'. But as for those things that are present, past, or future to us, God knows them as they are within the compass of His power; and as they are within the compass of their own several created causes; and as they are in themselves; and the knowledge of such things is called the 'knowledge of vision'.
(Ea enim quae non sunt nec erunt nec fuerunt, a Deo sciuntur quasi eius virtuti possibilia. Unde non cognoscit ea ut existentia aliqualiter in seipsis, sed ut existentia solum in potentia divina. Quae quidem a quibusdam dicuntur a Deo cognosci secundum notitiam simplicis intelligentiae. Ea vero quae sunt praesentia, praeterita vel futura nobis, cognoscit Deus secundum quod sunt in sua potentia, et in propriis causis, et in seipsis. Et horum cognitio dicitur notitia visionis.) [L]
God has two kinds of knowledge:
(1) Knowledge by Simple Intelligence
(2) Knowledge of Vision: "according to which He is said to know those things which are in act in some period of time" (ST 1.14.15 ad 2).
The Three-Knowledge View (Molinism)
Molina, Concordia IV qXIV a13 d52:
Unless we want to wander about precariously in reconciling our freedom of choice and the contingency of things with divine foreknowledge it is necessary for us to distinguish three types of knowledge of God. One type is purely natural knowledge, and accordingly could not have been any different in God. Through this type of knowledge He knew all the thigns to which the divine power extended either immediately or by the mediation of secodnary causes....The second type is purely free knowledge, by which, after the free act of His will, God knew absolutely and determinately, without any condition or hypothesis, which ones from among all the contingent states of affaris were in fact going to obtain and, likewise, which onese were not going to obtain. Finally, the third type is middle knowledge, by which, in virtue of the most profound and inscrutable comprehension of each faculty of free choice, He saw in His own essence what eac such faculty would do with its innate freedom, were it to be placed in this or in that or, in deed, in infinitely many orders of things--even though it would really be able, if it so willed, to do the opposite....
(Triplicem scientiam oportet distinguamus in Deo, nisi periculose in concilianda libertate arbitrii nostri et contingentia rerum cum divina praescientia hallucianri velimus. Unam mere naturalem, quae proinde nulla ratione potuit esse aliter in Deo, per quam omnia ea cognovit ad quae divina potentia sive immediate sive interventu causarum secundarum sese extendit....Aliam mere liberam, qua Deus post liberum actum suae voluntatis absque hypothesi et conditione aliqua cognovit absolute et determinate ex complexionibus omnibus contingentibus, quaenam re ipsa essent futurae, quae non item. Tertiam denique mediam scientiam, qua ex altissima et inscrutabili comprehensione cujusque liberi arbitrii in sua essentia intuitus est, quid pro sua innata libertate, si in hoc, vel illo, vel etiam infinitis rerum ordinibus collocaretur, acturum esset, cum tamen posset, si vellet, facere re reipsa oppositum....)
The three kinds of knowledge are (X in each example is a future contingent):
(1) Natural Knowledge (God has this in virtue of His nature): God knows X as possible. = Knowledge by Simple Intelligence
(2) Free Knowledge (God has this in virtue of His choices): God knows X as it actually will be (simply, in itself). = Knowledge of Vision.
(3) Middle Knowledge (God has this in virtue of His pre-choice deliberation): God knows X as it will be (on supposition of God's choosing this or that order of things). Not natural (because it involves contingents); not free (because it is logically prior to willing).
Molina, Concordia IV qXIV a13 d52:
[T]he knowledge through which God, before he decides to create a being endowed with free choice, foresees what that being would do on the hypothesis that it should be placed in a particular order of things--this knowledge depends on the fact that the being would in its freedom do this or that, and not the other way around. On the other hand, the knowledgeby which God knows absolutely, without any hypothesis, what is in fact going to happen because of created free choice is always free knowledge in God, and such knowledge depends on the free determination of His will, a determination by which He decides to create such-and-such a faculty of free choice in such-and-such an order of things.
Inde vero creare, praevidet quid sit factura, ex hypothesi quod in eo rerum ordine collocetur, pendere ex eo quod ipsa pro sua libertate hoc vel illud sit factura et non e contrario. Scientia vero qua Deus absque ulla hypothesi absolute scitquid per liberum arbitrium creatum sit reipsa futurum semper est in Deo libera, pendetque a determinatione libera suae voluntatis, qua tale liberum arbitrium in tali vel tali ordine rerum creare statuit.
The standard objection to Molinism (the grounding objection): How does God know what a free creature would do under a given set of circumstances that would distinguish it from knowledge of what the free creature could do and from knowledge of what the free creature actually does? (A closely related question: Are there true counterfactuals of freedom?)
MOLINA, ARMINIUS, PLAIFERE, GOAD, AND WESLEY ON HUMAN FREE-WILL, DIVINE OMNISCIENCE, AND MIDDLE KNOWLEDGE by Barry E. Bryant
MOLINA, LUIS DE by Alfred Freddoso
MOLINISM by Alfred Freddoso
THE DECREES OF GOD by Francis Turretin (a seventeenth-century Calvinist)
UPDATE (August 5): Expanded first Molina quote; replaced second Molina quote; added Latin for Aquinas and Molina. The English quotations for Molina are from:
Luis de Molina, On Divine Foreknowledge: Part IV of the Concordia, Alfred Freddoso, tr. Cornell University Press 1988.