Having stated my “Axioms of God’s Foreknowledge vs. Human Freedom”, I have gradually realized that what is for me self evident, and therefore axiomatic, is not so for many people. This is so, I suspect, in particular for Protestant Christians, in particular of Calvinist ascent. Anyway, I realize that it is necessary to demonstrate what to me is obvious, either directly, or by disproving the opposite, viz. the position that is referred to as "compatibilism", that is:
God’s total foreknowledge is compatible with genuine human freedom.
A typical example can be found in this article by
Norman Swartz,
Foreknowledge and Free Will @ The Internet Encyclopedia of Philosophy.
You can read the article, in detail, for yourselves. At some point it gets rather technical, and requires a certain familiarity with Symbolic Logic.
I will only concentrate on the essential for my present purpose. The author of the article, Norman Swartz (professor emeritus of philosophy, retired 1998, Simon Fraser University) gives immediately the clearest possible formulation of the problem, the one that goes back in the 12th century and to the Jewish philosopher Moses Maimonides:
… "Does God know or does He not know that a certain individual will be good or bad? If thou sayest 'He knows', then it necessarily follows that man is compelled to act as God knew beforehand he would act, otherwise God's knowledge would be imperfect. …"
(The Eight Chapters of Maimonides on Ethics [Semonah Perakim]), edited, annotated, and translated with an Introduction by Joseph I. Gorfinkle, pp. 99-100, New York: AMS Press, 1966)
The objection of
Norman Swartz to the validity of Moses Maimonides’
statement has been summed up
by saying that what Norman Swartz affirms it is vitiated by a logical fallacy, the modal fallacy.
Logical Symbolism
To examine the objection that
Norman Swartz raises against Moses Maimonides, one has to become familiar with some logical symbolism used in his paper:
P,
Q,
R, ... are
propositions, that is objective statements (see
note #3 in
Swartz’ paper)
~P: it is
not the case that P (Example: It is not the case that copper conducts electricity. Note: "P" and "~P" have opposite truth-values – whichever is true, the other is false.)
P > Q:
if P, then Q (Implication. Example: If she is late, (then) the meeting will be delayed.)
gKP:
God knows that P (Example: God knows that the Mississippi River flows north to south.)
◊P: it is (logically)
possible that P (Example: It is (logically) possible that the United States was defeated in World War II. (Note: Whatever is not self-contradictory is logically possible.)
☐P: It is (logically)
necessary that P (Example: It is logically necessary that every number has a double. (Note: If
Q is not logically possible, then
~Q is logically necessary.)
∇P: It is
contingent that P (Example: It is contingent that the United States purchased Alaska from Russia. (Note: A proposition, Q, is contingent if and only if
Q and
~Q.)
∴: it
necessarily follows (It is the
conclusion, viz. the proposition that follows logically and necessarily follows one or more propositions that are called
premises. The conclusion is at the bottom, separated from the premises by a horizontal line
____ )
_______
Swartz’ exam of Maimonides’ argument and (presumed) modal fallacy
Herebelow I have copied entirely form his paper, Swartz’ exam of Maimonides’ argument and (presumed) modal fallacy (see 6b. The Modal Fallacy in Epistemic Determinism
Let's recall Maimonides's argument:
… "Does God know or does He not know that a certain individual will be good or bad? If thou sayest 'He knows', then it necessarily follows that [that] man is compelled to act as God knew beforehand he would act, otherwise God's knowledge would be imperfect."
We can symbolize the core of this argument, using "∴" for "it necessarily follows"; and "☐" for "compelled" [necessitated]; and "D" for the proposition describing what some particular person does tomorrow.
gKD [“God knows what a particular person will do tomorrow”]
____ [“implies that”]
∴☐D [“it necessarily follows what that particular person will do tomorrow]
There seems to be (at least) one missing premise. [In the terminology of logicians, the argument is enthymematic.] One tacit assumption of this argument is the necessary truth, "it is not possible both for God to know that D and for D to be false", or, in symbols, " ~ (gKD & ~D)". So the argument becomes:
gKD [“God knows what a particular person will do tomorrow”]
~ (gKD & ~D) ["it is not possible both for God to know that D and for D to be false"]
____ [“imply that”]
∴☐D [“it necessarily follows what that particular person will do tomorrow]
But even with this repair, the argument remains invalid. The conclusion does not follow from the two premises. To derive the conclusion, a third premise is needed, and it is easy to see what it is. Most persons, with hardly a moment's thought, virtually as a reflex action, will tacitly assume that the second premise is logically equivalent to:
gKD ⊃☐D [“If God knows what a particular person will do tomorrow, then what that person will do tomorrow is (not contingent but) necessary”]
and will tacitly (/unconsciously) add this further premise, so as to yield, finally:
gKD [“God knows what a particular person will do tomorrow”]
~ (gKD & ~D) ["it is not possible both for God to know that D and for D to be false"]
gKD ⊃☐D [“If God knows what a particular person will do tomorrow, then what that person will do tomorrow is (not contingent but) necessary”]
____ [“imply that”]
∴☐D [“it necessarily follows what that particular person will be compelled to do tomorrow”]
[Swartz’ conclusion]
But this third premise, we have seen above, is false; it commits the modal fallacy. Without this premise, Maimonides' argument is invalid; with it, the argument becomes valid but unsound (i.e. has a false and essential premise [viz. the third one]). Either way, the argument is a logical botch.
Once the logical error is detected, and removed, the argument for epistemic determinism simply collapses. If some future action/choice is known prior to its occurrence, that event does not thereby become "necessary", "compelled", "forced", or what have you. Inasmuch as its description was, is, and will remain forever contingent, both it and its negation remain possible. Of course only one of the two was, is, and will remain true; while the other was, is, and will remain false. But truth and falsity, per se, do not determine a proposition's modality. Whether true or false, each of these propositions was, is, and will remain possible. Knowing – whether by God or a human being – some future event no more forces that event to occur than our learning that dinosaurs lived in (what is now) South Dakota forced those reptiles to take up residence there.
Criticism of Swartz’ criticism of Maimonides’ (presumed) modal fallacy
I have no objection concerning Swartz’ analysis of Maimonides’ argument, and on the "implicit premises" that Swartz extracts from Maimonides’ argument.
It is Swartz’ conclusion that, far from exposing Maimonides’ argument (complete with the three explicit premises) as “unsound” and as a “logical botch” emphasizes Swartz’ own fallacy, in the case of God.
Swartz affirms that the “third premise” (symbolically gKD ⊃☐D, viz. “If God knows what a particular person will do tomorrow, then what that person will do tomorrow is (not contingent but) necessary”, is false and essential, because … “Inasmuch as its description was, is, and will remain forever contingent, both it and its negation remain possible.”
Now, while all the above is, from a strictly logical POV, impeccable, I affirm that it cannot apply to God, if God is considered totally omniscient and omnipotent, and that, in fact, contrary to what Swartz says, in the case that God is considered totally omniscient and omnipotent, the “third premise” is essential AND true, because, if it wasn’t, then God would be either NOT omniscient, OR NOT omnipotent, OR both.
An example will be sufficient to show that Mt. Swartz' mountain is nothing but a molehill. 
