This is for my Philosophy of Religion class. Sorry about that fact that I could not figure out how to get both modal logic symbols and symbolic logic symbols on this post.
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PLANTINGA’S [1]MODAL ARGUMENT ON FOREKNOWLEDGE AND FREE WILL
(See: Internet Encyclopedia of Philosophy [IEP], "Foreknowledge and Free Will")
Consider these two statements:
- A) God knows that Paul will eat an orange.
- B) Paul will eat an orange for lunch tomorrow.
Each of these propositions, by itself, could be true and could be false.
But if A is true then B cannot be false. For if A is true (i.e. if it is true that God knows that Paul will eat an orange for lunch tomorrow) then B is also true.
Put another way: the truth of A guarantees the truth of B. This is to say that:
(1) It is impossible (for A to be true and for B to be false).
The compound sentence, A and not-B , is impossible (i.e. is necessarily false).
It reads: It is not possible that: God knows that Paul will eat an orange tomorrow and that Paul will not eat an orange tomorrow.
So, that entire statement is: TRUE.
"Now it is a curious fact about most natural languages – English, French, Hebrew, etc. – that when we use modal terms in ordinary speech, we often do so in logically misleading ways. Just see how natural it is to try to formulate the preceding point this way" (IEP):
That is, because (1) is true, it seems that (2) is also true. And (2) is:
(2) If A is true, then it is impossible for B to be false.
It reads: If [God knows that Paul will eat an orange tomorrow], then it is not possible that [Paul not eat an orange tomorrow].
Statement (2) is: FALSE
NOW NOTE: the proposition expressed by (1) is not equivalent to the propositions expressed by (2).
So (1) is true. But (2) is false and commits the modal fallacy.
The fallacy occurs in its assigning the modality of impossibility (necessity), not to the relationship between the truth of A and falsity of B as is done in (1), but to the falsity of B alone.
AGAIN (1) states: It is not possible that [God knows that Paul will eat an orange for lunch tomorrow and Paul choose to not eat an orange for lunch tomorrow]. THAT’S TRUE.
BUT (2) DOES NOT FOLLOW LOGICALLY: If [God knows that Paul will eat an orange for lunch tomorrow] then it is not possible [that Paul can choose to not eat an orange for lunch tomorrow].
If (2) was true, then it would be NECESSARY that Paul chooses to eat an orange tomorrow.
But the statement “Paul will eat an orange tomorrow” is a contingent, not a necessary, statement. Therefore (2) is false, and not logically equivalent to (1).
[1] In formal logic, a modal logic is any system of formal logic that attempts to deal with modalities. Traditionally, there are three 'modes' or 'moods' or 'modalities' of the copula to be, namely, possibility, probability, and necessity.
(See: Internet Encyclopedia of Philosophy [IEP], "Foreknowledge and Free Will")
Consider these two statements:
- A) God knows that Paul will eat an orange.
- B) Paul will eat an orange for lunch tomorrow.
Each of these propositions, by itself, could be true and could be false.
But if A is true then B cannot be false. For if A is true (i.e. if it is true that God knows that Paul will eat an orange for lunch tomorrow) then B is also true.
Put another way: the truth of A guarantees the truth of B. This is to say that:
(1) It is impossible (for A to be true and for B to be false).
The compound sentence, A and not-B , is impossible (i.e. is necessarily false).
It reads: It is not possible that: God knows that Paul will eat an orange tomorrow and that Paul will not eat an orange tomorrow.
So, that entire statement is: TRUE.
"Now it is a curious fact about most natural languages – English, French, Hebrew, etc. – that when we use modal terms in ordinary speech, we often do so in logically misleading ways. Just see how natural it is to try to formulate the preceding point this way" (IEP):
That is, because (1) is true, it seems that (2) is also true. And (2) is:
(2) If A is true, then it is impossible for B to be false.
It reads: If [God knows that Paul will eat an orange tomorrow], then it is not possible that [Paul not eat an orange tomorrow].
Statement (2) is: FALSE
NOW NOTE: the proposition expressed by (1) is not equivalent to the propositions expressed by (2).
So (1) is true. But (2) is false and commits the modal fallacy.
The fallacy occurs in its assigning the modality of impossibility (necessity), not to the relationship between the truth of A and falsity of B as is done in (1), but to the falsity of B alone.
AGAIN (1) states: It is not possible that [God knows that Paul will eat an orange for lunch tomorrow and Paul choose to not eat an orange for lunch tomorrow]. THAT’S TRUE.
BUT (2) DOES NOT FOLLOW LOGICALLY: If [God knows that Paul will eat an orange for lunch tomorrow] then it is not possible [that Paul can choose to not eat an orange for lunch tomorrow].
If (2) was true, then it would be NECESSARY that Paul chooses to eat an orange tomorrow.
But the statement “Paul will eat an orange tomorrow” is a contingent, not a necessary, statement. Therefore (2) is false, and not logically equivalent to (1).
[1] In formal logic, a modal logic is any system of formal logic that attempts to deal with modalities. Traditionally, there are three 'modes' or 'moods' or 'modalities' of the copula to be, namely, possibility, probability, and necessity.
