On Necessity in Aristotle's De Interpretatione IX

"How dreadful to possess the knowledge
that does not benefit the one who knows it."
Teiresias, King Oedipus, Sophocles.

From Antiquity, through the Middle Ages and right up to the XX century Aristotle'sDe Interpretatione IXhas been provoking discussions. They concern not only the interpretation of the passages in the chapter, but question what exactly is Aristotle maintaining - what is he affirming and what exactly is he refuting. Aristotle's arguments in the famous chapter about the inevitability of the future follow the laws of logic, and the deterministic viewpoint is put forward again by the means of logic. If certain propositions about the future are true, then all future events, and our will as well, are determined. If a prediction belongs to the present, and the event will happen at another present, which at the time of the prediction belongs to the future, at the time when the statement is made what can be actually said about the statement? Can a statement about the reality of a future event be not a possibility, or a probability, but a certainty? Then, what is it to live in the present? The things passing through one's mind - what time do they belong to? What will happen can be interpreted in many ways as to the meaning of the event, but the statements about the event as such, as a "fact", are either true or false. Whatever the prediction has been at the moment of its being pronounced, when the event occurs, with the occurrence itself, makes things come true or not come true. The battle tomorrow will be or will not be - and this is not a hypothesis. On the other hand, how is it possible, that something is and at the same time is not? How can this be true? What are the qualities of our knowledge about the future? Is our knowledge about the future homogeneous? Fragmentary? Unwrapping in sequences? Are not some things extremely clear while others remain hidden? If the future cannot be influenced, it will follow the same course of events, independently of our actions. After making this point Aristotle goes on to say that this conclusion contradicts experience, and gives a solution to the problem. Before offering a reading to the chapter, I will make a brief overview of the main points that commentators disagree about.

Most of the authors agree the chapter falls into three parts: Part I (18a28-34) - that a certain claim does not apply to future singulars; part II (18a34-19a6) - that if this claim did apply to future singulars, then everything that happens would happen of necessity; part III (19a7-b4) - Aristotle's denial of the deterministic approach, and his own solution about future singulars . For Hintikka the typical strategy of the Aristotelian argument (proceeding dialectically) is clearly present in this chapter: Aristotle argues first for one side and then for the other. The clash between the two gives rise to an aporiato be solved, usually by a conceptual analysis of the arguments which were at the basis of the aporia, and it is often in pointing out the different senses of some word or phrase [19, p.468]. For Hintikka the scheme follows a presentation of Aristotle of the deterministic view (18a34-18b16), a refutation of this view, on the grounds of its impossibility (19a7-22), and a solution from 19a23 on.

There are some discussions over the way Aristotle uses the word "necessary" in different senses according to various observations. Ackrill distinguishes the following senses: first, that there is a possibility that in this chapter Aristotle fails to distinguish between that "necessarily", which modifies a proposition, and the "necessarily", which marks the connection between a premise and a conclusion (a distinction made clear otherwise, in Prior Analytics, but confused here). Then, Aristotle, according to Ackrill, does not draw a line between logical and causal necessity, and laws of logic are treated as on a par with laws of nature, and, moreover, that "necessity" is used here to cover up for temporal necessity as well [1, p.133]. I think that Aristotle makes this distinction at 18b36-19a6, and even if this is not so, logical necessity still may be necessary naturally (especially in a "correspondence" theory of truth).

There are various views on the nature of Aristotle's problem in De Interpretatione IX. Upon the "traditional" or "the oldest" interpretation bivalence implies determinism, and, therefore, universal bivalence should be abandoned. This view is opposed to the "second oldest interpretation", which reconciles bivalence with indeterminism. Another major point of disagreement is between the philosophers in the XX century. It is concerned with the point whether Aristotle is rejecting as false the sentence "necessarily (p or -p)", which is the "standard" interpretation. This view is typical for the first half of our century. The "non-standard" interpretation, introduced by E. Anscombe in 1956 [3], holds that Aristotle is denying "necessarily p or necessarily -p".

The distinction between the "standard" and the "non-standard" interpretations is commented upon by Ackrill [1, p.133] . Ackrill talks about it as a possibility to acknowledge there being a "strong thesis" , on the one hand: that of two contradictories one is necessarily true and one is necessarily false, that is either "necessarily p or necessarily -p". On the other hand, it might be the "weak thesis" - of any two contradictories necessarily one is true and one is false, that is "necessarily either p or -p". For Ackrill Aristotle denies the strong variation (which entails determinism), but accepts the weak one. Or even there exists the possibility that Aristotle introduces and denies the "weak thesis", though he does maintain that of two contradictories it is necessary that one should at some time be true and one false.

The standard interpretation applies to the last part of the chapter and rejects the possibility here of either the law of bivalence or the law of the excluded middle to future contingents, or both. Then future contingents need not be true/false and no determinism follows. J.Saunders suggests that Aristotle's solution not only makes future contingents neither true or false, but the whole law does not apply to future contingents [33, p. 367-377]. Upon this reading it remains unclear whether Aristotle did follow the determinist argument presented in the second part of the chapter and accept it.

In Jan Lukasiewicz's variation (of the standard interpretation) Aristotle is said to have accepted the principle of the excluded middle, but rejected the applicability of the law of bivalence to future contingents [26, p.36]. Every proposition, then, has to be either true or false and we can assume one and only one of the two truth values: true or false, which Lucasiewicz called the principle of bivalence. In this context Lukasiewicz developed the semantics for a system of three-valued logic. There are thus three possible "truth-values", one being "indeterminate" , besides the two traditional ones. Determinism does not follow from truth, because there is no truth proposition to lead on to determinism. Future contingents are neither true or false; and if both p and -p are indeterminate, then so is their disjunction. (Though Lukasiewicz holds that the disjunction of a future contingent and its negation is necessarily true. But when disjunction is not a truth-functional connective, how can logic determine the truth-value of the compound, even if the truth-value of the components is known ?)

Another commentator of the standard line is D. Williams, who speaks directly about truth-values. He holds that Aristotle maintained that the principle of excluded middle or a whole instance of it is true and necessarily true, and even about the future, but a simpler or existentional proposition like "there is a sea-fight" or its contradictory cannot be true about the future at all [48, p.253]. Then R.Taylor holds that Aristotle is saying that future contingents are, antecedently, not true and yet not false, but that any disjunction of such a proposition with its denial is necessarily true [39, p.2]. Similarly, J. King-Farlow maintains that certain assertions about future events can be neither true or false, yet the disjunction of such assertions and their denials must be necessarily true [23, p.36] . In all cases Aristotle is interpreted to exclude future contingents from the classical two-values propositions.

It seems that there is a major disagreement among the commentators what the principle of excluded middle is. Everyone seems agreeing that Aristotle accepted statements like "either p or -p" as necessarily true, for any p, including contingent statements about future events . Why do then some reject the applicability the principle of the excluded middle and some do not? The formulation "either p or -p" is too general and does not give the meaning of the principle, unless some conditions are added. If either bivalence or the classical definition of negation do not hold, then "either p or -p" does not express the principle of the excluded middle. So if "either p or -p" is necessarily true according to Aristotle, it does not follow that he thought the law of the excluded middle held when dealing with future contingents. It must be also the case that bivalence and the classical definition of negation hold. So Aristotle held that "either p or -p" is true and rejected bivalence (according to all commentators), it seems that the problem lies in the interpretation of what the principle of excluded middle is about [20, pp.46-53].

The non-standard interpretation does not put the major importance on the truth value of propositions, but on their necessity. The determinist kind of necessity does not follow from the truth of propositions, and the principle of bivalence and the principle of the excluded middle still apply to future contingents, but not the necessity which follows. The non-standard interpretation belongs to E.Anscombe [3], and has several followers, like C. Strang , J. Van Eck, M. Lowe. Strang holds that not everything is temporally necessary and not everything is causally necessary, and that some things are neither and hence are possible [38, p.459]. M.Lowe and J. Van Eck hold that Aristotle is not denying the principle of the excluded middle to statements about future events, but only the inference from that principle to the necessity of all events. [26, p.58 and 41, p.37]. Thus, Aristotle is not rejecting, on this interpretations, any of the determinist's premises, or just one, he is agreeing with them, but what follows is something different. It is not that from the truth of future contingents follows the necessity of events (determinism). There exist different kinds of necessity. Past and present events are necessary in the sense that they cannot be other than what they are, but this is not a consequence of the truth from the statements made about them. Necessity comes from the events context in time relative to "now". Necessity resulting from statements about the future is different. The true propositions corresponding to some state of affairs are necessarily true, but this necessity does not rub off on the state of affairs itself - it may be necessary or contingent. This interpretation suggests we distinguish between the different uses of "necessary" and "contingent". And there is a mistake in going from the necessity of a proposition to the necessity of the state of affairs it describes [20, 53-56]. From here follows the dispute about the possibility of Aristotle being worried about things true "from eternity" (the problem of infinite past truth, as Hintikka calls it [19, 483], and not so much as about the problem of future truth: Aristotle is trying to draw a distinction between what is sometimes true and sometimes not true and what is always true. For Hintikka Aristotle equates possibility with sometime truth and necessity with omnitemporal truth (Categoriae V, 3a34-b2, 4a23-30; Metaphysics IX, 10, 1051b13 ff.), and Aristotle's problem for him springs specifically as soon as he starts to consider sentences like 'p at time to,' where to is independent of the moment of utterance of the sentence in question, in addition to sentences like 'p now'.

We are facing here a couple of separate questions, which are essential for the clarification of the issue: Does Aristotle argue from present to future ? Does truth and falsity apply to future statements ? If not - then not allevents are necessary, but only past and present ones. Does the truth of a statement entail the necessity of the event whose occurrence it asserts? Is it true that, as Ryle says: "Whatever anyone ever does, whatever happens anywhere to anything, could not not be done or happen, if it was true beforehand that it was going to have to be done or was going to happen. So everything, including everything that we do, has been definitively booked from any earlier date you like to choose. Whatever is, was to be." [32, 15]. Further - is there a possibility of the solutions: (a) neither P nor -P may be true where P is about the future (a denial of the Principle of the Excluded Middle); (b) both P and -P (a denial of the Law of Contradiction)? It is important to take a close look at some of the passages, in order to be able to suggest some answers to these questions, the difficulty being in Aristotle's unclear treatment of the argument and the solution to it. In the first part of the chapter, Aristotle holds, according to some interpretations [1] that with statements about what is and what has been, each member of a contradictory pair is either true or false, but with future singulars it is different - Aristotle is denying that it holds of future singulars that each of a contradictory pair must be either true or false, which expresses the determinist conclusion (rejected later in 19a7-10):

"For if every affirmation or negation is true or false it is necessary for everything either to be the case or not to be the case. For if one person says that something will be and another denies this same thing, it is clearly necessary for one of them to be saying what is true - if every affirmation is true or false; for both will not be the case together under such circumstances" (18a34 -38).

If every affirmation or negation has a truth-value, the truth of whichever of the pair being true makes it necessary that the event predicted comes to be (or does not, if predicted truly not to), and everything that comes to be must come to be, must of necessity take place. With contradictory future singulars necessarily one of them is true, if every affirmation or negation is true or false: "So it is necessary for the affirmation or the negation to be true" (18b4). Determinism follows clearly from here - since either the affirmation or the negation is true, nothing is or can take place by chance, and there are no real alternatives. Because when an event occurs by chance, it might as easily happen, as not happen. The distinction between necessity and chance is that when the second holds true reality is so constituted that it may issue in either of two opposite directions (18b7).Aristotle's arguments concerning necessity, though, are given not of things or events, but of statements , thus if it is true to say that something is white, than it is necessary for it to be white. Aristotle makes his argument from truth to necessity:

"Again, if a thing is white now, it was true to say earlier that it would be white; so that it was always true to say of anything that has happened that it would be so. But if it was always true to say that it was so, or would be so, it could not not be so, or not be going to be so. But if something cannot not happen it is impossible for it not to happen; and if it is impossible for something not to happen it is necessary for it to happen. Everything that will be, therefore, happens necessarily. So nothing will come about as chance has it or by chance; for if by chance, not of necessity" (18b10-17).

This way what is truly predicted cannot but happen. The force of the argument, though, is in that this does not depend on whether a true prediction has been made or not, but only that it could have been: circumstances are not influenced by an affirmation or a denial from anyone. Only this - if a true prediction is made, the event cannot fail to take place, and of that which takes place, it was always true to say that it will be. (18b33-19a6). There follows a refutation of this position (19a7ff.) All arguments above lead to an impossible conclusion - because we know from our experience and our senses that both deliberation and action are causative with regard to the future, and that in those things that are not continuously actual there is a possibility in both directions: things may be or not be, events may take place or not take place, and in some instances there are real alternatives. Then the affirmation is no more true and no more false than the denial. Now follows the most difficult section of Aristotle's chapter. This section can be divided into two parts, as Ackrill suggests [1, 137] - 19a23-30 and 19a30-39. Both parts are presented by Aristotle as they should be making the same point - in one case regarding things and events, in the other - regarding statements. Conclusions for contradictory propositions are to be drawn corresponding to the conclusions for things and events ("In the case, also, of contradictory propositions this holds good",19a27). What is Aristotle saying exactly? In the first part he talks that there is a major difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be (and similarly in the case of that which is not). It is not just a qualification or a condition that Aristotle is warning us to beware and not drop out - but it is a qualification that relates to time and repetition or continuity in time ( the necessity of what is "when it is" as contrasted to the necessity of "simply . . . all"). In the second part he is drawing a line, on the one hand, between the absence of necessity of something happening at precisely toor the absence of necessity of something not happening at precisely to, and, on the other hand, the necessity of the event happening or not happening at to . But, if this warning that is given here, in the second part concerns the drawing of inferences from "it is necessary for P to occur or it is necessary for P not to occur", then the fallacy in this inference is not the same as the one in the first part. It does seem, on Ackrill's suggestion [1, p.138], that the move Aristotle wants to make here is by rejecting the inference from "necessarily: P or -P" to "necessarily P" or "necessarily -P" to reject the inference from "necessarily: P or -P" to "necessarily P or necessarily -P".

What is it Aristotle is asserting: the distinction between "necessarily (p or -p)" and "necessarily p or necessarily -p" or does he want to underline the distinnction between "necessarily (p is true or -p is true)" and "necessarily (p will be true or -p will be true)"? Is it the case where Aristotle accepts that of any two contradictions necessarily one is true and one is false (does not regard it as determinism), denying that of any two contradictories one is necessarily true and one is necessarily false ( because it entails determinism)? Or is Aristotle's discussion turned onto another point altogether? Is it that Aristotle first introduces that of any two contradictions necessarily one is true and one is false, denying it as it entails determinism, but accepting something else about future singulars - that of two contradictories it is necessary, that one should at some time be true and one false? If we take the first possibility to be Aristotle's intended meaning, then, according to Ackrill, we should read that the truth-value of all statements about the past are inescapably settled, though we may not know how, but the truth value of some statements about the future are not inescapably settled, though it is settled that either the affirmation or the negation is true (something awaits to happen or not to happen). To say a statement about the future is true is to say that it will happen, but to say that it is necessarily true - it is to say that the present state holds proofs that it will be so. There are true predictions that are necessarily true, and others are not - until the time comes for them to occur - they become necessary only after the event has taken place. The truth of a statement does not change with time, though statements can be neither necessary nor impossible and become one of these things later, when the event takes place or does not [1, p.139].

There is another possibility to interpret Aristotle's puzzle: all true statements are necessary, but truth is not a timeless value, but could become such later on, and every statement is at some time true or false. Then if something is true it cannot not happen, but then it does not hold true that for all future singulars (as for other statements) either the affirmation or the negation is true. True statements do mean that the facts are there necessarily, but it does not follow from here that since every statement is true or false, then all the facts are there, determined to be as they turn out to be. Precisely because many future events are not yet determined the statements about such events cannot yet be true or false - though in due time they will be [1, p.140]. One of the difficulties with this interpretation is that if: "With these [things that are not always so or are not always not so] it is necessary for one or the other of the contradictories to be true or false - not, however, this one or that one, but aas chance has it; or for one to be true rather than the other, yet not already true or false."(19a36-38). But on this interpretation Aristotle leaves only that it is necessary for one of the two contradictories to be true at some time. But if it were necessary for this one to be true at some time, it would follow, things being already necessary, that this one was already true. So "one of the two" turns out to have to mean "neither is yet true".

Is everything necessary before it happens? Is it causally determined already, beforehand? The answers to these questions cannot be directly inferred from the true statement that something is once it is. There is a difference between predicating the potentiality of some opposite predicates and predicating the actuality of one or the other of these. As F. Sommers holds, when we deny that there will be a sea battle tomorrow, we could be asserting two things:
1. That a certain relationship is held between some thing and some predicate (expressed as "P - s" or as "P - s"), asserting the actuality of "P - s";
2. Or it could be asserted that " - ( P - s)", which denies the actuality of "P - s", with which a certain relationship is denied altogether. All that tomorrow's sea-battle is is potential, there is no necessity involved [36, p.309].

According to Horst Wessel's non-traditional predicate theory negation can be either external (classical) or internal [44]. In internal negation the predicate is neither "attributed" nor "withheld" from a subject, so that we want to say that both a sentence and its negation are false. For example, this happens in the cases when it is not possible at this time, or in principle, to determine if the assertion holds true. According to Fred Sommers Aristotle maintains the falsity of both, that "there will be a sea battle tomorrow" and of that "there will not be a sea battle tomorrow" [36, p.308]. Or: in Aristotle "S is not P" is not "not: S is P". When both "S is P" and "S is not P" are false, "not: S is P" is true. And whether "S is not P" is true or false has no bearing on the law of excluded middle, because the law is about statements of the form " P and - P". This difference corresponds to the difference between internal and external negation [20, pp.84-85]. This solution seems to hold in so far as Aristotle does not accept the possibilities of "in-between" value or no value. Statements for Aristotle are either true or false (Metaphysics , bk.4, ch.VII). But necessity follows only from truth, and not from falsity (19a1-6). So it does seem that the only real alternative to the "one true/one false" thesis is the "both false". Aristotle is not questioning bivalence, so future contingent statements must be either true or false. They cannot be both true, and the "one true/one false" thesis being rejected, it remains that they must be both false. Aristotle concludes that everything that is, is necessarily, when it is (same holds for "is not"). This type of necessity is true of actual things that were, or that are. Once something is actual, it cannot not be. But the necessity of the determinist means something else: that some event in the future is necessary, at some time, if it is determined at that time causally (before the fact). The only thing which is actual about the sea battle is that it "will be or not be", and this is necessary. But we cannot divide and say that one or the other is necessary (19a29). The sea battle is not yet determined to be or not to be, the sea battle is potential, with no actual qualities. Therefore predicting either of these will result in a false statement, since truth is saying of what is P that it is P. It is not necessary for a sea-battle to take place tomorrow, nor for one not to take place (if the object of a statement of two contraries does not exist, then both statements predicting one of a pair of contraries to that object, will be false) - though it is necessary for one to take place or not to take place (neither is true now, but one will become true, and not this one or that one, but as chance has it (19a31-37).

Determinism means that knowledge is not good for anything, because things cannot really be interfered with, since all results will remain the same. If the future is seen as the past, as something that can be described as something that has already happened, a "future retrospection", and since I know what will happen, and I am in a way analyzing after the event - the situation is closed, finished (no vain expectations are possible). I describe events as a person who recites facts, as a historian of things that will happen. But this does not explain why I should choose this particular event from the future (and not some other) for my point of view. We are motivated by our situation when we make choices, but a knowledge about the future has to be free of that, because what is known when knowledge about the future is involved is a knowledge about the total condition of the universe at this moment, a complete knowledge about the laws that run the universe - I should posses knowledge that is total and homogeneous. The supposition that a finite consciousness can come up with a perfect knowledge about future events leads to unsolvable problems.

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22 October 1994