In philosophy, specifically in metaphysics, we often speak of what is “possible” or “contingent” and what is “necessary”. If something is necessarily true, then it cannot possibly to be false. An example of necessary truth might be mathematical theorems. If something is contingent, then it’s true but possibly could have been false. We often talk about things like the circumstances of one’s birth as being contingent. Possibility itself is the more difficult concept. In ordinary language, “possible” can mean different things. It can express mere uncertainty, i.e. that something could be true “for all I know”. Philosophically it means something more specific but still rather hard to pin down.

In this post I will address a fallacy that sometimes arises when thinking about possibility and necessity.

Possible worlds and modal logic

The standard way of dealing with possibility and necessity in philosophy is through “possible worlds”. A possible world is a maximal set of facts about the universe, in other words all the information to specify (as much as possible) the state of everything in the universe. This set of facts must be internally consistent, but other specific requirements are unknown (for example, it’s not known whether the laws of physics are possibly different). We call the set of facts about our own universe the “actual world”. Note that possible worlds are not generally thought of as “parallel universes” though this is one interpretation and some people do subscribe to it.

A proposition is possibly true if there exists a possible world in which it is true. A proposition is necessarily true if it is true in all possible worlds. Possibly false and necessarily false are defined similarly.

Just like we can do ordinary logic with true and false statements, we can use a modified version called modal logic with possibly or necessarily true and false statements. For example, here is a proof that if something is actually true then it must be possibly true:

1. If P is actually true, then it is true in the actual world. (Law of modal logic)
2. The actual world is a possible world. (Law of modal logic)
3. If P is true in a possible world, then P is possibly true. (Law of modal logic)
4. P is actually true. (Premise)
5. P is true in the actual world. (1, 4)
6. P is true in a possible world. (2, 5)
7. P is possibly true, QED. (3, 6)

A similar proof can be given that anything that is necessarily true is actually true. Other theorems can be proven in this logic as well, such as that possibly P implies not necessarily not P. (These are left as exercises for the reader.)

Possibility criteria

So we have a systematic way to reason about possibility and necessity, and certain necessary truths are easy to discern, but we haven’t addressed the difficult problem of identifying when something is possible. There is unfortunately no perfect solution. What many people go by, and what is perhaps the best criterion we have, is conceivability. Essentially, if you can consistently imagine something being true, then it is most likely (we think) possibly true. When talking about more or less ordinary situations, this makes sense. I can imagine a deer being in my living room, and most people would agree that it is possible for a deer to be in my living room. Deer are real animals and it is conceivable that someone could capture one and bring it virtually anywhere, and my living room exists and is large enough to contain a deer. Often when discussing specific examples like this we see that, while there is one proposition or fact that we’re focusing on, many facts about the world would have to be different. For example, to accommodate a deer being in my living room, a significant amount of air would need to be displaced. It is to be assumed that when someone says “a possible world where P is true” they mean that P and anything necessary to accommodate P are true. Additionally, when talking about possible worlds there are always “redundancies”, by which I mean many possible worlds that fit our description and which differ in ways that are trivial to us or our present discussion. For example, there is not much difference (to me) between a deer being in my living room and a deer with one fewer hairs being in my living room. I didn’t even specify male or female deer in my description, which makes it apply to a vast “class” of possible worlds. Depending on context, we may either assume that we pick a possible world arbitrarily that fits out description, or that we are referring to all possible worlds fitting the description.

Conceivability lines up with our intuitive notions about possibility, but it is not without controversy. It is not always clear whether conceivability must imply possibility and it may even be unclear what is conceivable. A classic example of this is the “philosophical zombie” or p-zombie thought experiment of which David Chalmers is a famous proponent. The basic idea is to imagine a world where humans are behaviorally identical to those in the actual world, but lack conscious experience. They are like robots (or, indeed, zombies) carrying out actions with no genuine perception or thought. The general conclusion is that, because p-zombies are conceivable, they are possible, and because they are possible, consciousness must not be purely physical. It’s an argument in favor of mind-body dualism.

Responses to the p-zombie argument often focus on the conceivability and/or possibility of p-zombies. Some argue that, while you think you are imagining humans acting identically but lacking consciousness, you are merely imagining normal humans and telling yourself they don’t have consciousness. In other words, the p-zombie might not actually be conceivable. Others argue that conceivability doesn’t imply possibility (in this case specifically). Conceivability might be the best approximation we have, but it lacks logical force. There is nothing about conceivability that strictly implies something must be possible. In fact, it could be the case that everything that is actually true is necessarily true, and there are no possible worlds other than the actual one, though few people believe that to be the case.

The fallacy

My concern is a different one. While conceivability may or may not imply possibility, possibility definitively does not imply conceivability. Let’s suppose for a moment that conceivability does imply possibility: then everything that is conceivable is possible, but this does not mean that everything that is possible is conceivable. To assume that something must be conceivable to be possible is the fallacy of affirming the consequent. “If P then Q” does not imply “if Q then P”.

So why even bring this up? To put it briefly, it’s a mistake I’ve seen people make. This is similar to my post Why do unlikely things happen? In both cases, a person may have unreasonable skepticism born from fallacious intuitive understandings of math and logic. It may seem strange for a skeptic like me to talk about “unreasonable skepticism”, but what it basically amounts to is closed-mindedness (as opposed to the suspension of judgment of classical skepticism). Usually I see it manifest like this: someone has a theory or hypothesis. They can’t imagine how they could be wrong, and so they conclude that they can’t possibly be wrong.

The problem is that, while the human imagination is an amazing thing, it is still severely limited by lived experience and simple biological necessity. We say that truth is stranger than fiction—fiction being things imagined. It is absurd for an individual human to think that they could imagine everything that is true, much less everything that is possibly true. Phrased like that it makes sense, but psychologically it can be difficult not to wholeheartedly believe that which you cannot imagine to be false.