You have probably seen these types of arguments before on incompatibility of omniscience and free will. The question is are these arguments valid and what can be a good refutation?

Let G= x is known by God T= x occurs

1.[](G -> T)

2.[]G -> []T

3.[]G

4.[]T

• One option is to distinguish this matter in temporal logic, via a distinction between an at-eternity tense and a future tense, where AE operates somewhat like a past tense relative to your x's. So to say: for all G-statements, we would preface them by AE, then write something like AEGx → PTx (if something is known at eternity, then relative to in-time tense, it has "already happened"). This probably isn't fully sufficient to blocking omniscience = fatalism, but it might be a decent start on such an effort. It is, for example, apparently how Dante tried to reconcile things, here. Nov 16, 2023 at 15:30
• I believe Dante was following Aquinas in this, and IIRC the poet writes something somewhere like, "All time is time present in God's eyes," and regarding contingency says, "Contingency, whose action is confined to the few pages of the world of matter, is fully drawn in the Eternal Mind; but it no more derives necessity from being so drawn than a ship dropping down the water derives its motion from a watcher’s eye." Nov 16, 2023 at 15:43
• General considerations are already addressed in detail in SEP, Foreknowledge and Free Will. The short summary is that one can define "omniscience" and "free will" so that they are compatible. Questions here are expected to be more specific. Nov 16, 2023 at 20:53

Let's work in a temporal logic with five tenses Pa, Pr, F, N, and Æ: "It was true that," "It is true that," "It will be true that," "It is never true that," and, "It is true at eternity that." Suppose that the three in-time operators all collapse into Pa relative to Æ, via a principle like:

• ÆxΨxÆPaxΨx

I.e., if something is true at eternity, then it is true at eternity that it is true "in the past." But we could go on to:

• ÆxΨxÆPrxΨx
• ÆxΨxÆFxΨx

But we will block writing down:

• ÆxΨxÆNxΨx

I.e., we are not saying that if something happens at eternity, then it never happens. But so instead we have:

• ÆxΨxÆÆxΨx

I.e., the at-eternity tense operator conforms to something akin to the knowing-that-one-knows principle in epistemic logic. This means that:

• ÆÆxΨxÆÆÆxΨx

... and so on and on. Now, what we have overall with regards to representation of things intratemporally is that eternity implies sempiternity, i.e. if something exists at eternity, then it exists at all times also. So if something is known at eternity, then it is known at all times. Is this the same as being known in all times, however? For if we hold that the divine intellect is not inside of anything besides Itself (so to speak), we will want to distinguish knowledge of a time from knowledge in a time; hence we will look for a formalization of the Aquinas-Dante thesis whereby God's knowledge of future contingents (of free will, say, or quantum flux, or whatever else we countenance as partially indeterministic) is like someone looking on as a ship flows down a river, seeing the ship at all its locations without being the (direct/sufficient) cause of the ship's being at said locations.

I don't want to say that the above really clearly solves the occurrent problem. I'm not competent enough with symbolic temporal logic in particular, or symbolic logic as usual/in general (FOL), to proclaim such a thing with much confidence. However, from reading through myriads of formal systems over the years, I am rather confident that a way can be found to formalize the at-eternity tense that would clearly solve the omniscience-to-fatalism-pipeline problem (even were the solution to raise new issues, but that is the way of these things, is it not? that every answer evokes another question, whose answers evoke further questions, of the demesne of which there will be no end...). So otherwise, I would recommend reading the SEP article on temporal logic as well as Martin[88] and Meyer[??] (see pg. 86 et seq.).

• in simple words, what's the conclusion? Nov 16, 2023 at 17:33
• @IoannisPaizis that there is a balancing act in temporal logic where the symmetries and asymmetries of eternity-and-sempiternity mean that what is contingent is contingent on one side of things in one way, and is contingent on the other side of things in another. It is the reciprocity of these ways that then constitutes divine knowledge from-eternity-to-eternity vs. this knowledge sempiternally-to-sempiternally, such as is consistent with the contingency of free will, in part because of the contingency of God's own will! Nov 16, 2023 at 18:24
• I find myself struggling to follow the logic here, specifically the concept of "at eternity", as it seems that eternity does not denote any "location" on the timeline. I did see that you mentioned that if we are speaking about "eternity" in intratemporal terms, then eternality simply collapses into sempiternity, resulting in "at eternity" denoting the whole of the timeline. I do not see how introducing this remedies the issue, for if it is true at some time (x) before occurrence (y) that God knows (y), then it seems that the fatalist conclusion trivially follows. Nov 16, 2023 at 19:04
• @MaxMaxman I was trying to imagine that the past/present/future that AE goes with is relative to a special set of points AE (how e.g. Meyer seems to introduce the at-eternity tense), which sometimes includes talk of "eternal duration." So what is eternally true is also always true inside of eternity, but the opposite does not hold: not everything sempiternal is eternal, the symmetry is broken and the broken symmetry of contingency itself, here, must come into play. Nov 16, 2023 at 19:08