Logical Determinism

I love logic.

Despite hating math during my formative school years and not having much of a formal education in logic, it's one of my favorite subjects. I know I will never be coming up with brilliant new proofs, but I nonetheless stoked a late-blossoming passing interest in it after falling into a career of writing code as a software developer. I even have a few tattoos of logic paradoxes and problems: Fitch's Paradox of Knowability, Moore's Paradox, and Moore's "Here is one hand" argument.

I started Anthony Kenny's New History of Western Philosophy recently and worked through the opening few chapters on Greek philosophers. Aristotle, the grandfather of logic, was obviously highlighted. His foray into modal logic in On Interpretations touched upon the problem of future contingents, or statements about the future, and how to ascribe truth values to them.

The state of the future is a bewildering arena. We tend to think of future events as being quasi-real; we ask questions and make assertions about them (the meeting will happen at 2 o'clock in the afternoon tomorrow, not 3). We also tend to think of ourselves as free agents with the ability to prevent future events (I will be canceling the meeting at 2 o'clock tomorrow). If an event belongs to the future, it is a necessary truth (as in, a logical necessity) that it will occur and we cannot prevent it from occuring. If we can prevent an event from occuring, then it is not a necessary truth that it will occur.

In accordance with the Laws of Thought, assertions are true or false. Time and modality, as already pointed out, complicate any simple assertion. Assertions about the past are necessarily either the case or not the case (true or false), in the same manner that 2+2=4. Try as we might, it is impossible to change any past state of affairs; they have a truth value today and will always have the same truth value. Time is the great divider of truth and falsity. It is the case that the Declaration of Independence was signed on August 2, 1776 and this assertion always will have the same truth value.

Take note that the truth of an assertion about the signing of the Declaration of Independence on a particular date is not due to the merits of our epistemic condition. In other words, we might imagine that we did not, in fact, have first hand knowledge that the document was signed; nonetheless, we may find it perfectly logical to say that the assertion has a truth value independent of our personal knowledge. The truth or falsity depends on what happened before.

Future-tensed statements do not share this luxury; truth values have a temporal directional, it would seem.

Take two sentences as stated today:

(1) There will be a sea battle tomorrow.
(2) There will not be a sea battle tomorrow.

If either 1 or 2 were true today, we would be saying that it is impossible for it take place or necessary to take place, no matter any actions taken, not due to our merits of epistemic condition (because we cannot reach into the future and grab its contents), but rather as a merit of truth.

Walking the logical line of the principle of bivalence (Either “p” is true or “p” is false) gets us to the law of the excluded middle (Either p or not-p). Taking another logical step forward begets the concept of fatalism, or the doctrine according to which nothing is contingent, that is, everything is either necessary or impossible:

Either it is necessary that p or it is impossible that p

From fatalism, we get if p it is necessary that p, and if not-p, it is impossible that p. It should be noted that "necessary" means "necessary given our past and our present" and "impossible" means "impossible given our past and our present", which further means that it does not take into account what could happen given other possible past and present circumstances. Future contingents deal with future possibilities, it does not concern past or present possibilities.

Fatalism is at odds with free will, for if nothing is contingent (i.e. if possibility is not real), then it is difficult to fathom how one might choose a different course of action. Which is to say: your will is an illusion under logic's cold gaze.

Aristotle takes a step backwards and offers the solution in the form of a disjunction:

Either (1) there will be a sea battle tomorrow
OR
(2) there will not be a sea battle tomorrow.

This dichotomy is now the necessary truth instead of the sea battle's occurance, according to Aristotle, because the logical operator denotes that one or the other is true. It is necessary that it will occur or not, an easy enough step back into a truth function of the amalgamated disjuncts, but a muddying of the law of the excluded middle. Muddying the law of the excluded middle means the principle of explosion can be invoked, rendering truth meaningless.

Later logicians and philosophers offered other solutions to the problem. Yet, Aristotle's prescient recognition of knots in skeins of logic, like the problem of future contingents, have remained remarkably tangled since antiquity.

Making it a problem for us, we future contingents.