Diodorus Cronus

Diodorus Cronus (4th century B.C.E.) was a Greek philosopher of the Megarian school. Most notable for logic innovations, in particular the paradox of future contingents, little is known of his life.

Diogenes Laertius tells a story that, while staying at the court of Ptolemy Soter, Diodorus was asked to solve a dialectical subtlety by Stilpo. Not being able to answer on the spur of the moment, he was given a nickname by Ptolemy meaning the God, equivalent to slowcoach. The story goes that he died of shame at his failure. Strabo, however, says that he took the name from Apollonius, his master.

Like the rest of the Megarian school he revelled in verbal quibbles, proving that motion and existence are impossible. The impossible cannot result from the possible; a past event cannot become other than it is; but if an event, at a given moment, had been possible, from this possible would result something impossible; therefore the original event was impossible. This problem was taken up by Chrysippus, who admitted that he could not solve it.

The problem of the future's contingents

The problem of the future's contingents is a logical paradox first posed by Diodorus Cronus from the Megarian school of philosophy, under the name of the "dominator", and then reactualized by Aristotle in chapter 9 of De Interpretatione. It was later taken on by Leibniz. It concerns the contingency of a future event. Deleuze used it to oppose a "logic of the event" to a "logic of signification". Diodorus' problem concerned the question: "Will there be a sea battle tomorrow?" According to this question, two propositions are possible: "yes, there will be a sea battle tomorrow" or "no, there will not be a sea battle tomorrow." This was a paradox in Diodorus' eyes, since either there would be a battle tomorrow or there wouldn't be one: according to the basic principle of bivalence (A is either true or false), one of the two proposition had to be right and therefore excluded the other. But this poses a problem, since the judgment on the proposition (whether it is right or wrong) can only be made when the event has happened. In Deleuze's words, "time is the crisis of truth" . This problem thus concerns the ontological status of the future, and therefore of human action: is our future determined or not? The future, putting in stakes the category of possibility, here poses problems to logic which are discussed to the present time.

Aristotle's solution

According to the principle of bivalence, something concerning reality is either true or false (A is B or A is not B). Logic is thus based on disjunctive syllogism. But this poses a problem when logic is applied to future possibilities instead of present reality. Diodorus' famous propositions are: "Will there be a sea battle tomorrow?" and/or "Will there not be a sea battle tomorrow?" This problems concerns the ontological statute of the future, and therefore of human action: is future determined or not? Logical necessity seems to be defeated by real necessity.

One can either say that the proposition is neither true nor false: some possible futures make it true and others wrong; this may be called "indeterminacy intuition". Or one can say that the truth-value of the proposition will be only given in the future, that is until the future unfolds. Thus, it is always will be given but never presently given.

Aristotle solved the problem by asserting that the principle of bivalence found its exception in this paradox of the sea battles: in this specific case, what is impossible is that both alternatives can be possible at the same time: either there will be a battle, or there won't. Both options can't be simultaneously taken. Today, they are neither true nor false; but if one is true, then the other becomes false. According to Aristotle, it is impossible to say today if the proposition is correct: we must wait for the contingent realization (or not) of the battle, logic realizes itself afterwards:

One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial, one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. (§9)

For Diodorus, the future battle was either impossible or necessary. Aristotle added a third term, contingency, which saves logic while in the same time leaving place for indetermination in reality. What is necessary is not that there will or that there won't be a battle tomorrow, but the alternative itself is necessary:

A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow." De Interpretatione' 9, 19 a 30.

Thus, the event always comes in the form of the future, indetermined event; logic always come afterwards. Hegel would say the same thing by claiming that wisdom came at the dusk. For Aristotle, this is also a practical, ethical question: to pretend that future is determined would have unacceptable consequences on man.

Leibniz

Leibniz gave another response to the paradox in §6 of Discourse on Metaphysics: "That God does nothing which is not orderly, and that it is not even possible to conceive of events which are not regular." Thus, even a miracle, the Event by excellence, does not break the regular order of things. What is seen as irregular is only a default of perspective, but does not appear so in relation to universal order. Possible exceeds human logics. Leibniz encounters this paradox because according to him:

Thus the quality of king, which belonged to Alexander the Great, an abstraction from the subject, is not sufficiently determined to constitute an individual, and does not contain the other qualities of the same subject, nor everything which the idea of this prince includes. God, however, seeing the individual concept, or haecceity, of Alexander, sees there at the same time the basis and the reason of all the predicates which can be truly uttered regarding him; for instance that he will conquer Darius and Porus, even to the point of knowing a priori (and not by experience) whether he died a natural death or by poison,- facts which we can learn only through history. When we carefully consider the connection of things we see also the possibility of saying that there was always in the soul of Alexander marks of all that had happened to him and evidences of all that would happen to him and traces even of everything which occurs in the universe, although God alone could recognize them all. (§8)

If everything which happens to Alexander derives from the haecceity of Alexander, then fatalism threatens Leibniz's construction:

We have said that the concept of an individual substance includes once for all everything which can ever happen to it and that in considering this concept one will be able to see everything which can truly be said concerning the individual, just as we are able to see in the nature of a circle all the properties which can be derived from it. But does it not seem that in this way the difference between contingent and necessary truths will be destroyed, that there will be no place for human liberty, and that an absolute fatality will rule as well over all our actions as over all the rest of the events of the world? To this I reply that a distinction must be made between that which is certain and that which is necessary. (§13)

Against Aristotle's separation between the subject and the predicate, Leibniz states: "Thus the content of the subject must always include that of the predicate in such a way that if one understands perfectly the concept of the subject, he will know that the predicate appertains to it also." (§8). The predicate (what happens to Alexander) must be completely included in the subject (Alexander) "if one understands perfectly the concept of the subject". Leibniz henceforth distinguish two types of necessity: necessary necessity and contingent necessity, or universal necessity vs singular necessity. Universal necessity concerns universal truths, while singular necessity concerns something necessary which could not be (it is thus a "contingent necessity"). Leibniz hereby uses the concept of compossible worlds. According to Leibniz, contingent acts such as "Caesar crossing the Rubicon" or "Adam eating the apple" are necessary: that is, they are singular necessities, contingents and accidentals, but which concerns the principle of sufficient reason. Furthermore, this leads Leibniz to conceive of the subject not as a universal, but as a singular: it is true that "Caesar crosses the Rubicon", but it is true only of this Caesar at this time, not of any dictator nor of Caesar at any time (§8, 9, 13). Thus Leibniz conceives of substance as plural: there is a plurality of singular substances, which he calls monads. Leibniz hence creates a concept of the individual as such, and attributes to it events. There is a universal necessity, which is universally applicable, and a singular necessity, which applies to each singular substance, or event. There is one proper noun for each singular event: Leibniz creates a logic of singularity, which Aristotle thought impossible (he considered that there could only be knowledge of generality).

See also

• In Borges' The Garden of Forking Paths, both alternatives happen, thus leading to what Deleuze calls "incompossible worlds"

External links

• Ephilosopher, Sea Battles, Futures Contingents, and Relative Truth and Future Contingent and Relative Truth by John MacFarlane, The Philosophical Quarterly 53 (2003), 321-36
• CERPHI (French)

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