science

Problem of future contingents

Problem of future contingents is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Problem of future contingents rather than just read about it. In short: Future contingent propositions (or simply, future contingents) are statements about states of affairs in the future that are contingent: neither necessarily true nor necessarily false. The problem of future contingents seems to have been first discussed by Aristotle in chapter 9 of his On Interpretation (De Interpretatione), using the famous sea-battle example.

Key takeaways

Problem of future contingents belongs to science; place it in that map before memorising details.
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Connect Problem of future contingents to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Problem of future contingents from memory before moving on to harder problems.

Reference excerpt

Future contingent propositions (or simply, future contingents) are statements about states of affairs in the future that are contingent: neither necessarily true nor necessarily false. The problem of future contingents seems to have been first discussed by Aristotle in chapter 9 of his On Interpretation (De Interpretatione), using the famous sea-battle example. Roughly a generation later, Diodorus Cronus from the Megarian school of philosophy stated a version of the problem in his notorious master argument. The problem was later discussed by Leibniz. The problem can be expressed as follows. Suppose that a sea-battle will not be fought tomorrow. Then it was also true yesterday (and the week before, and last year) that it will not be fought, since any true statement about what will be the case in the future was also true in the past. But all past truths are now necessary truths; therefore it is now necessarily true in the past, prior and up to the original statement "A sea battle will not be fought tomorrow", that the battle will not be fought, and thus the statement that it will be fought is necessarily false. Therefore, it is not possible that the battle will be fought. In general, if something will not be the case, it is not possible for it to be the case. "For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time" (De Int. 18b35). This conflicts with the idea of our own free choice: that we have the power to determine or control the course of events in the future, which seems impossible if what happens, or does not happen, is necessarily going to happen, or not happen. As Aristotle says, if so there would be no need "to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow".

Aristotle's solution 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 will not be a battle tomorrow, but the dichotomy itself is necessary:

A sea-fight must either take place tomorrow or not, but it is not necessary that it should take place tomorrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place tomorrow. (De Interpretatione, 9, 19 a 30.)

Islamic philosophy What exactly al-Farabi posited on the question of future contingents is contentious. Nicholas Rescher argues that al-Farabi's position is that the truth value of future contingents is already distributed in an "indefinite way", whereas Fritz Zimmerman argues that al-Farabi endorsed Aristotle's solution that the truth value of future contingents has not been distributed yet. Peter Adamson claims they are both correct as al-Farabi endorses both perspectives at different points in his writing, depending on how far he is engaging with the question of divine foreknowledge.

Al-Farabi's argument about "indefinite" truth values centers around the idea that "from premises that are contingently true, a contingently true conclusion necessarily follows". This means that even though a future contingent will occur, it may not have done so according to present contingent facts; as such, the truth value of a proposition concerning that future contingent is true, but true in a contingent way. al-Farabi uses the following example; if we argue truly that Zayd will take a trip tomorrow, then he will, but crucially:There is in Zayd the possibility that he stays home....if we grant that Zayd is capable of staying home or of making the trip, then these two antithetical outcomes are equally possibleAl-Farabi's argument deals with the dilemma of future contingents by denying that the proposition P "it is true at t 1 {\displaystyle t_{1}} that Zayd will travel at t 2 {\displaystyle t_{2}} " and the proposition Q "it is true that at t 2 {\displaystyle t_{2}} that Zayd travels" would lead us to conclude that necessarily if P then necessarily Q. He denies this by arguing that "the truth of the present statement about Zayd's journey does not exclude the possibility of Zayd’s staying at home: it just excludes that this possibility will be realized".

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, and thus possibility exceeds human logics. Leibniz encounters this paradox because according to him:

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Problem of future contingents

Start with the simplest possible case. Write down what Problem of future contingents claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Problem of future contingents before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Problem of future contingents ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Problem of future contingents

In research: Problem of future contingents appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Problem of future contingents in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Problem of future contingents is common in secondary-school and first-year university syllabi. It links to neighbouring topics Ancient Greek logic, Future, Modal logic, so understanding it makes those chapters shorter.
In everyday life: Look for Problem of future contingents outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Problem of future contingents in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Problem of future contingents means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Problem of future contingents out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Problem of future contingents in simple terms?

Why does Problem of future contingents matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Problem of future contingents?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Problem of future contingents.