In Aristotle's famous sea battle argument, he argues from bivalence (or something like it) to determinism. Stalnacker has an argument to determinism using standard logical laws, as well. My question is: if you are a determinist, is it a problem if logical laws necessitate determinism? It seems that most people think it is.

Intuitively, I want to say that there is something wrong with logical laws entailing determinism, even though I am a determinist-- I feel like they shouldn't be dependent on the metaphysical state of the universe. I just do not have a good way of articulating this sentiment. Does Stalnacker address this issue? Is there any nice philosophical quote out there, or person on Stack Exchange, that can perhaps articulate my sentiment?

  • The Laws of Logic are concepts created by human beings that are used to describe the very nature of things. If these laws deduced determinism, it would be provisionally logical to follow it to its conclusion, but one must realize that there is always room for fallible interpretation. However, I am incredibly skeptical that the laws of logic do, in fact, show determinism to be true, albeit I am not necessarily a determinist so I may have a bias. – Goodies Dec 16 '14 at 7:16
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    At most, the laws of logic seem able to show the laws of logic are deterministic. I'm not sure you're reading the sea battle correctly... – virmaior Dec 16 '14 at 8:51
  • Aristotle's argument is that if it is true today that the sea battle either happens or does not happen tomorrow then it it is predetermined today which will happen tomorrow. From modern perspective he is committing the modal fallacy by assuming “if a is the case, then necessarily, a is the case”. en.wikipedia.org/wiki/… – Conifold Dec 16 '14 at 21:11

First, one should distinguish determinate and determined. Being determinate means having a truth value. Being determined means being deducible from present or past states and the laws of nature. Determinism (the latter) does not follow from logic, only determinateness does. The difference is important because the fact that something will occur does not mean strictly speaking that it will occur as a matter of physical necessity. A determinate future does not imply fatalism (or at least this is a contentious issue).

Second, it is possible to resist the view that all future events are determinate as a matter of logic. Your intuition is right that we cannot learn something about the world by pure a priori reasoning. This intuition can be implemented here by noting that determinateness of propositions is a linguistic principle (that all sentence have a truth value). The ontological counterpart would be: all objects have determinate properties. While the linguistic principle can be accepted a priori, its ontological counterpart can only be known by experience.

Let us take an example from quantum mechanics: an electron can have no determinate position. Then it is true that all sentences of the form "this electron has such position" are determinate. Actually, they are all false. The linguistic principle is true, yet the ontological principle fails. One possible interpretation would be that in this case, our language is not adapted to reality (the appropriate language would be a language that would attribute a wave-function to the electron). Perhaps a proper language would restore determinacy in the case of electrons. However then determinacy is language-dependent: it does not mean much if our language is not adapted to the world; you'll end up with a bunch of false, but really uninformative sentences.

The lesson is this: a logical or linguistic principle can teach us nothing about the world, because further, we need to assume that there is a certain correspondence between language and reality, which does not go without saying.

Finally there are other avenues for the one who wished to deny that future events are determinate. One can for example deny the principle of logical bivalence and add a new logical constant: indeterminate. One can also assume that truth is intrinsically tensed ('it will be true' cannot be translated into a tenseless, atemporal statement such as 'it is (atemporally) true at time t'), or that only the present (and maybe the past) exists.


Yes, it is wrong to deduce determinism from logic, because logic is a branch of deductive reasoning, and "deduction tells you what follows from your premises, but does not tell you whether your premises are true."*

Determinism is a scientific conclusion. It is based on such empirical observations as opium will have certain effects on behaviour, and "constitution" is hard to say when one is drunk. All scientific conclusions are tentative, subject to revision based on new evidence.

Edit: There is no such thing as logical law; there are only premises.

*Russell, Bertrand. The Art of Philosophizing. New York: Philosophical Library: 1968


I'm afraid that determinism (determinate future) is a consequence of unrestricted bivalence, as Aristotle points out. If either "there will be a sea battle tomorrow" or "there won't be a sea battle tomorrow" is true today, then the future is already fixed today i.e. in advance.

As to the wonder, how a logical principle might have metaphysical consequences, I think the answer is that for Aristotle (and for many others) logic is related to metaphysics. Logic is only partially an independent realm. Some if its principles are based on metaphysical considerations, and have metaphysical consequences.

Thus concerning the sea battle problem, Aristotle concludes that bivalence does not hold for potential existence, only for actual existence. This is a metaphysical distinction.

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. (On Interpretation part 9)

Another example of the intermingling of logic and metaphysics concerns the principle of non-contradiction. It is a case in point that Aristotle defends this logical principle in The Metaphysics, of all places.

  • Ok, but if we are fine with determinism, then is determinism being a consequence of bivalence at all an issue? Or can we just be like, ok, cool, bi valence implies determinism,,which is totally fine since determinism holds anyway. – MathTeacher Dec 20 '14 at 22:37
  • Yes, If you are fine with causal determinism, then logical determinism (the kind that is implied by bivalence) should be fine for you as well. Personally I am not fine with determinism, just finding it difficult to avoid. – Ram Tobolski Dec 21 '14 at 17:40
  • It should be, but it doesn't, even though I think I am fine with causal determinism. – MathTeacher Dec 22 '14 at 7:33

From a Kantian idealist perspective, if something like determinism were true in a definitive way, we should be able to deduce it from logical laws.

For a certain stripe of idealist, forms of intuition and categories are not physical facts, they are ideals, so something so completely defined in terms of two things, one a category (causation) and the other a form (time) should be equally ideal, and not affected by phenomenal wrapping.

This is still a relatively respectable philosophical perspective, so I cannot see where we can agree it would be wrong to find such a deduction. What is more likely, from this point of view, is that such a construct is not relative or contingent, and therefore must be either provable or false. If we can prove by more concrete means that we cannot prove determinism, it indicates that determinism itself is false, and not just unattainably complex.

This is important from an ethical point of view, because it determines whether duty is well-determined but relative due to our embedding in the world, or whether it is not well-determined, and might vary for different species.

Basically, if duty is not well-determined, the agendas of different sorts of intelligence cannot be aligned or explained to one another, and we cannot "all just get along". The categorical imperative cannot really mean anything categorically.

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