Is the notion of “possible” vacuous?

Question

We use the term possible to often refer to events that don’t violate a certain model of reality and impossible to refer to events that do. A human being having ten fingers vs. a human being with five heads.

But the series of events in the world clearly seem to be a single chain. And in this chain, events happen or don’t happen. Of course, there are other universes and worlds postulated, but those haven’t been demonstrated. And even if they did exist, events may be single chains in those universes as well (although I believe there is a certain interpretation in QM where all possible events happen).

So what does it mean to say that an event X is possible if X either happens or doesn’t happen? Shouldn’t we instead use the phrases “has happened”, “can’t happen”, or “will happen”? Using the word possible, especially when referring to events in the past, seems to imply the world could have turned out a different way from the current status quo. But despite whatever you believe in, there is clearly no way to rewind the past, so I fail to see how you can possibly have evidence for this.

Is this yet another term, that despise its supposed usefulness, does not have any basis in reality?

Answer 1

You already said it yourself in your first sentence:

We use the term possible to often refer to events that don’t violate a certain model of reality and impossible to refer to events that do.

Note the word model. Sure, events might form a chain, but since we have an incomplete model and thus don't know with certainty how the chain looks like in the future (and in fact it looks like there can exist no model at all that can get rid of all uncertainty), we say:

According to our model of reality, it is possible that the chain will look like X in the future.

In reality, only one event will be actually happening. But when we talk about "possible", "probable", etc., it is because we need to deal with our uncertainty regarding the actual future.

Model =/= reality.

Answer 2

By using words like "can't" or "imaginable," you seem to commit yourself to the generic sense of the word "possible" (for "can" and "-able"). However, you then seem to focus on an Aristotelian sense of the word, where something never happening is equivalent to something being impossible.

So overall, your question seems to have a trivial answer ("No"), but I will add that Immanuel Kant himself does go so far as to complain one time that:

Possibility, existence, and necessity nobody has ever yet been able to explain without being guilty of manifest tautology, when the definition has been drawn entirely from the pure understanding. For the substitution of the logical possibility of the conception—the condition of which is that it be not self-contradictory, for the transcendental possibility of things—the condition of which is that there be an object corresponding to the conception, is a trick which can only deceive the inexperienced.

Granted, he does offer his own substantive doctrine of modality, where demonstrating that something is possible is conditioned strongly by demonstrating that such a thing fits in to the single chain of experience he postulates (though c.f. the more strongly subjectivist/person-by-person relativist description of time, in the A-edition of the first Critique). And he also believed in a fairly strong account of free will, with genuine (if inexplicable) metaphysical possibilities involved.

More broadly, if possibility is not given in abstracto, neither is necessity, seeing as the two can be interdefined ("not possibly not" = "necessarily", or "not necessarily not" = "possibly"). If we deny those two modalities, why not deny actuality as well? "But that's obviously absurd," so perhaps it's (relatively) obviously absurd to deny the other modalities. But also, if we could accept actuality as a useful concept, without an ambient commitment to the potential(!) usefulness of the other modal concepts, we would land ourselves in the position of saying that there is e.g. a single chain of time, or a single world, or a single whatever, but this would not be necessary, would it? Granted, we would neither say that it is possible for there to be other times or worlds; but now you would be denying exclusive disjunction, which is another commitment you seem to have (when you say that any event either happens or doesn't happen).

Answer 3

Using the word possible, especially when referring to events in the past, seems to imply the world could have turned out a different way from the current status quo.

There are three distinct situations where people might say that.

1. A past event was conditioned on a strong random source, like measuring atomic decay. In this case (based on our current understanding of physics), it genuinely could have happened differently, and that is what people mean when they say "possible".

2. A past event was conditioned on a weak random source, like the roll of a die. That roll was entirely deterministic for all intents and purposes, but someone lacking a physics education might believe otherwise and think they're dealing with (1), so they also mean it could have happened differently, but they're wrong.

3. They're talking about a non-random past event about which we have incomplete knowledge. When they say it's "possible" that it happened a certain way, they don't mean that it could have happened differently. They mean that we don't know exactly what happened, and that possibility is at least consistent with what we do know. They do not mean that our lack of knowledge implies that it didn't need to happen the way it did, and certainly don't mean that the reality wasn't definitely one way or the other. (At least, most people who say that don't mean it that way. It's possible some do.)

Answer 4

The notion of possibility makes sense in environment with imperfect knowledge. If you know exactly the entirety of the state of some object, and the state of everything that will enteract at all times you wish to describe, then it is indeed useless: things either happen or not. Do note however, that the cases where the entirety of state is known are far more rare than where not. It is also impossible to know yourself and something that is not you but interacts with you: that would imply that your knowledge contains both you and that something, which violates axioms of the set theory, which means that it is impossible to know with certainty the future of something that contains yourself; same goes for any structure that one or other way(including compressed methods which use laws and initial parameters) describes a subset of a universe. What this means is that the notion of possability always make sense when describing the external universe.