THE SEA BATTLE TOMORROW AND FATALISM
Consider: (1) Either there will be a sea battle tomorrow or there will
not be. (2) N (If it is true that there will be a sea battle tomorrow, then there will be a sea
battle tomorrow) and N (If it is false that there will be a sea battle tomorrow, then there will
not be a sea battle tomorrow.) 1
Suppose (3) It is true that there will be a sea battle tomorrow.
(4) Thus, N (There will be a sea battle tomorrow) (From 2
and 3). (5) Thus, future events are predetermined (this is simply a generalization of 4,
since the inference from 2 and 3 can be carried out for any future event).
This argument has been philosophically famous since Aristotle, but (I hope to show)
undeservedly so. But first let us make sure we have the right argument. Aristotle does not in his De
Interpretatione present a closely argued version of the sea battle tomorrow puzzle, his discussion
taking place throughout the Dze Interpretatione. I do not propose to examine the text of Aristotle to
justify the above version as a faithful reconstruction of the argument, for this has already been done
by others more competent than myself. According to J. Hintikka 2 and M. Kneale,3 among others,
the argument I have formulated is Aristotle's; accordingly, we assume that this is a correct version
of the puzzle. In what follows, I shall sketch some of the reactions to this argument, propose a rather
simple solution, and show that my solution, if adequate, undermines the more complicated
"solutions" to the puzzle.
Reactions to the argument have been considerably varied and I can survey only some of
them. First, a word about Aristotle's proposed
1 Here I use 'N' to abbreviate 'It is necessarily true that.' 2 'The Oce and Future Sea Fight,"
Philosophical Review, LXXIII (1964), 463. 3 The Development of Logic, New York: Oxford, 1962,
47-48. Kneale's version differs only slightly from mine.
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solution. There is some controversy concerning how Aristotle's remarks should be interpreted.
According to Kneale, Aristotle distinguished the logical law of the excluded middle from the semantic
law of bivalence. The first says that any proposition of the form Pv--P is logically true. The second
says that every proposition is either true or false, or, equiv- alently, that one of P and U-.P is true,
the other false. In the case of future contingencies, Kneale claims, Aristotle denies the law of
bivalence while retaining the law of the excluded middle.4 But how is this supposed to bear on the
argument? Presumably, we are to distinguish (1) from (1'):
(W) Either There will be a sea battle tomorrow is true and its
negation is false, or vice versa.
1) is true, as is (2), but (11) is false. And without (1'), the assumption (3) cannot be made.
Now this is an interesting interpretation of Aristotle, but whether it is historically accurate or not is
not now to the point. According to this interpretation,, we cannot suppose that a future contingency is true, but if it were, it would follow that it is necessarily true. To avoid this consequence,
we deny that the future contingency is either true or false. This point should be emphasized. This
interpretation has it that if (3) is allowed, then the fatalistic conclusion (4) would follow from
(2) and (3). Since we obviously want to block this inference, the inter- pretation continues, we
cannot allow (3). I show later that the above conditional is false; we can permit the assumption (3)
without being forced to the fatalistic conclusion, for (4) does not follow from (2) and (3). Hence,
there is no reason to suppose that future contingencies are neither true nor false.
J. Lukasiewicz & and A. N. Prior 6 provide a somewhat different inter- pretation of
Aristotle's remarks. They have Aristotle rejecting both the law of excluded middle and the law of
bivalence in the case of future contingencies. Such-propositions are neither true nor false, but
have a neutral or indeterminate truth-value. The consequence here is almost the same. Both (1)
and (1's) are false, and (3) cannot be assumed as a premise, blocking the deduction of the
fatalistic conclusion. The difference between this interpretation and Kneale's is that according to
Kneale, future contingencies have no truth-value at all, while according to Lukasiewicz and Prior,
they have a third neuter truth-value. Indeed, this view of the matter was the basis from which
Lukasiewicz pioneered his system of many-valued logics. Now many-valued logics are interesting
i their own right. But Lukasiowicz is mistaken in sinking that they are necessary in order to avoid
the fatalistic conclusion (4). For he too thinks that if (3) is allowed, the fatalistic conclusion would
follow. And this is not true.
Let us assume (1) and (3), for the moment. If we do this, then we must show that either (2k)
is false or (4) does not follow from (2) and (3) if we are to avoid the fatalistic conclusion. It is easy
to show that (4) does not follow from (2) and (3). The logical form of the inference from (2) and (3)
to (4) is the following:
(2a) N (P-*Q). (3a) P. (4a) Thus, N (Q).
This inference-pattern is just not valid. The following is a substitution- instance with all true
premises and a false conclusion:
(6) N (If Paul is dead Paul is dead). (7) Paul is dead. (8) Thus, N
(Paul is dead).
Suppose Paul is dead. Then (6) and (7) are true while (8) is false. Hence, (8) does not follow from
(6) and (7). But the inference from (2) and (3) to (4) has exactly the same form. By parity of
reason, the conclusion of the sea battle argument does not follow from the premises. Hence, we
are free to reject the puzzle whether or not the premises are true.
As far as I can see every argument with a fatalistic conclusion rests upon the above fallacy.
For example, once we translate the talk of logic- ally necessary and sufficient conditions into
necessarily true conditionals, R. Taylor's 7 unjustly celebrated fatalistic argument rests upon the
same fallacy. An interesting variant is the argument formulated and discussed by N. Pike 8
concerning Divine Omniscience and free will. Pike's argu- ment goes like this:
(A) N (If S knows that p is true, then p). (B) God is, by definition, One who knows every
true proposition. (C) Suppose that I will wash my house tomorrow. (D) Thus, God knows that I will
wash my house tomorrow.
(From B and C). (E) Thus, N (I will wash my house tomorrow) (From A and D).
This argument had considerable interest for medieval philosophers. Just as Lukasiewicz, Prior,
and others developed many-valued logics in reaction to Aristotle's sea battle argument, some of
the medievals were concerned with the bearing of three-valued logics on the doctrine of God's
omniscience. Ockham, for instance, seeks the following way out of the puzzle. Since whatever is
known can be expressed in a true proposi- tion, if there are matters about which it is not at present
possible to formulate either a true or false proposition, it would seem that there are some
propositions that God does not know concerning future contingen- cies. For example, where A is a
future contingent event, the proposition "A will occur" has a neuter truth-value and the proposition
"God knows that A will occur" is false. On Ockham's view the conditional "If God knows that A will
occur, then A will occur" is true, since false proposi- tions imply neuter propositions. Now how
does Ockham deal with the above argument? Ockham seems to allow A) and (B). But he denies
(C) and thereby rejects (D). He is then free to deny the fatalistic conclusion (E). This is an
interesting but unnecessary reaction to the argument. Ockham conceeds, wrongly, that (E) follows
from (A) and (D). It'is obvious that this inference has the same invalid form as the inference from
(2) and (3) to (4), in the sea battle tomorrow argument. Hence, we may reject the fatalistic
conclusion whether or not the premises are true. ,A noteworthy feature of the divine omniscience
argument for the fatal- istic conclusion is that it enables us to formulate an important claim with
respect to God's Omniscience. It has been shown that the fatalistic con- clusion (1) does not
follow from (A) and (D) as the argument requires if it is to be valid. But there is a perfectly
straightforward way to make the inference valid. We may reformulate (D) as follows:
(Dl) Thus, N (God knows that I will wash my house tomorrow). Then the inference from (A) and
(Dl) to (E) has the logically valid modal form:
(i) N (P->Q). (ii) N (P). (iii) Thus, N (Q).
Now (D) follows from (B) and (C). Is there any reason for thinking that the stronger premise (DI)
might follow as well? I believe there is. (B)
says that God, by definition, knows every proposition. And this claim can be understood as
saying that God necessarily knows every true pro- position, or, equivalently:
(Bi) N (God knows every true proposition). And (Dl) does follow from (Bi) and (C). So
the argument can be made valid. But we get validity only at the cost of unsoundness. For there
are, I believe, compelling reasons for the falsity of both (Bi) and (Dl). Take the more specific
premise (Dl). The proposition God is said to neces- sarily know here is I will wash my my house
tomorrow. But this prop- osition is contingent. Hence, it is possible that the proposition is false.
And (A) says that it is necessarily true that no person knows any false proposition. It is certainly
true that we can (and do) know propositions that are possibly false - we know ever so many
contingent propositions. But it should be equally clear that if a proposition is possibly false, then no
person, including God, necessarily knows it. To see this, consider the contrapositive of (A):
(Al) N (If p is false, then S does not know p).
Both (A) and (Al) seem to be obviously true principles about knowledge. Now the proposition
I will wash my house tomorrow is possibly false, or:
(a) It is possible that I will wash my house tomorrow is false.
And (Al) and (a) entail the following:
(b) It is possible that no person knows I will wash my house
tomorrow.
The inference here from (Al) and (a) to (b) has the valid modal form: N (P->Q); Possibly P);
therefore, possibly (Q). So (b) follows from (Al) and (a), and both (Al) and (a) are true. But (b) entails
the negation of (Dl). Hence, (Dl) is false. And if (Dl) is false, then (B1) is false. This shows, among
other things, that either God is not omniscient or God does not have all His properties necessarily.
For if God is omniscient, then He has some contingent properties, i.e., the property of knowing
contingent propositions, since no person can necessarily know any contingent prop- ositions. If, on
the other hand, He has every property He has necessarily, then God is not omniscient, since He
does not know any contingent prop- osition. Thus, God's omniscience is logically incompatible with
the fre- quently encountered claim that every property God has He has neces- sarily. Let me briefly
summarize what I have said about the argument from God's omniscience for fatalism. Either this
argument is invalid or it is valid, but unsound. And in either case we are free to reject the fatalistic
conclusion. A corollary to the second case is that God cannot be both omniscient and have all His
properties necessarily.
In the face of the fantastic interest in the sea battle and other fatalistic puzzles since
Aristotle, it requires considerable temerity to suggest that fatalistic puzzles admit of such an easy
solution. In conclusion, then, let me defend my treatment against several possible objections. One
possible objection to my treatment is that some other sense of 'necessity' besides that of logical
necessity is involved in fatalism. Now I will concede that there may well be other versions of
fatalism that proceed in terms of some nonlogical senes of 'necessity,' but it remains true that
logical necessity is intended in the arguments considered here. In the case of the sea battle
argument, for example, Aristotle makes it clear that it is logical necessity he is concerned with.
And R. Taylor speaks of logically necessary and sufficient conditions in his version of fatalism.
Finally, if the sense of 'necessary' intended in the argument from divine omniscience is not logical
necessity, I am completely unable to find any reason why anyone would ever think (E) follows
from (A) and (D). Now one who believes the inference from (2) and (3) to (4) in the sea battle
argument valid might contend that the inference from (6) and (7) to (8), offered as a
counterexample, is equally valid. Why? Because they are both substi- tution-substances of the
inference-pattern (2a), (3a), therefore (4a), and this is a valid inference form! This would commit
such a person to the truth of (8). But then a hard-core fatalist would not find this an especially
unwelcome result. Indeed, he would likely reply that this merely shows that fatalistic implications
cannot be avoided. Is there a reply to this? I am convinced that such a rejoinder by the fatalist is
inadequate, for several reasons. First, the fatalist, e.g., Richard Taylor, has often accused his
critics of question-begging, and he has expressed confidence that his fatalistic conclusions follow
from (more or less) uncontroversial premises, e.g., the Law of Excluded Middle. But this is surely
false. For the argument-form from (2a) and (3a) to (4a) is valid only if every prop- osition is either
necessarily true or contradictory. Of course, the fatalist is arguing, in effect, that every proposition,
if true, is necessarily true. But then he can hardly use this argument-form to argue for such a conclusion, since that conclusion is the very assumption required for the inference to the conclusion
to be valid. It seems that the fatalist is guilty of the very charge he has so frequently leveled
against his critics, viz., question-begging.