Álvaro Rodríguez-González Barredo

Possibility is only definable in terms of there not being a conflict between certain combined concepts; thus the concept of possibility is the product of a comparison. But in every comparison the things which are to be compared must be available for comparison, and where nothing at all is given there is no room for either comparison or, corresponding to it, for the concept of possibility. This being the case, it follows that nothing can be conceived as possible unless whatever is real in every possible concept exists and indeed exists absolutely necessary.

New Elucidation, 1: 395

1

Last year, I came across a short argument by Philip Goff against physicalism, based on the mere possibility of philosophical zombies. There are loads of things that appear to be “possible”, short of sheer contradiction. It is possible that Michael Dukakis had become president of the United States in 1988, it is possible for humans to have developed six instead of five fingers, it is possible that Earth’s sky had been red instead of blue.

Of course, all of these get murky when they’re left to philosophers to ponder about. Possibility is a strange notion in that we categorically cannot find anything that doesn’t exhibit it (for obvious reasons), and that, when it is interesting to talk about it, it refers to things that don’t exist or events that didn’t take place. At the same time, it seems like there are things that are more possible than others. David Lewis’s contribution here is invaluable, though he paid the high price of accepting an ontology no-one would ever want to commit to in return of making sense of this. But let’s loan his locutions for a second regardless. It appears as though the world in which Dukakis beats Bush is much closer to ours than one in which we (most of us) have six fingers, and even closer than one in which the chemistry of our atmosphere is such as to render the sky red.

2

But let’s talk impossibility. Starting with the classics, it is impossible to have a four-sided triangle, it is impossible for a bachelor to be married, and so forth. Certain concepts are straightforwardly self-contradictory. A bachelor cannot be married because a bachelor is one who isn’t married. Showing that a triangle cannot have three and four sides at the same time may require a few more axioms, but the point is clear enough. In these cases we are just putting words together, the only way for “bachelor” to be something is if it isn’t married; the only way for a triangle to be something is if it isn’t a square or a line.

Maybe all it takes for something to be possible is that we can think of it. Now, “thinking” of something comes in many shades – we sort of can think of a four-sided triangle, thus the recurring example. But we cannot “see it with the eye of the mind”. Surely, though, that isn’t the criterion – many things that actually exist, and are thereby possible, we cannot “conceive” in the sense of representing them to ourselves. Think quarks, or ultraviolet radiation, or dark energy. So whatever the “conceivability” test for possibility is, “conceivable” must be here a term of art that leaves out logical horrors whilst respecting the humble cosmic horror.

Even if we grant that a seven-faced cube is harder to conceive than the Higgs field (what about the 4-d tesseract? is that even possible? in what sense?), there are even trickier cases. Back to freshers’ philosophy, can God write a version of the Transcendental Deduction so arid not even He can bear re-reading it? Aquinas seems to think that these paradoxes of omnipotence rely on concepts as faulty as the blatantly self-contradictory ones:

For a thing is said to be possible or impossible absolutely, according to the relation in which the very terms stand to one another, possible if the predicate is not incompatible with the subject, as that Socrates sits; and absolutely impossible when the predicate is altogether incompatible with the subject, as, for instance, that a man is a donkey.

Summa Theologiae, I q. 25 a. 3

So the rock so heavy God cannot lift it is simply another contradictio in adiecto, and, being charitable towards Aquinas, it is fairly easy to see why – no matter how heavy a rock is, or how convoluted a philosophical argument is, if we imagine ourselves “turning up” the dial on those measures, they will never be enough to thwart God’s power. But if we are less charitable, the notion of “compatibility” between a subject and a predicate may raise some eyebrows. Why is it that rocks are incompatible with being outside of the range of what God can do? It isn’t that everything is incompatible with God not having such a power – in the sentence “God cannot create a four-sided triangle”, our geometric foe is, apparently, friends with divine impotence. Something about what rocks are, and about their actually existing and having a weight makes their supreme growth internally inconsistent.

If we aren’t careful, though, we run an ancient and well-known risk. It is very easy for one to simply conclude that whatever is possible, exists; and whatever doesn’t exist, isn’t possible. Consider Dukakis’s bid for the presidency. On the one hand, it is part of who Dukakis actually is to not become president in 1988 – is he, as a subject, compatible with predicate “wins the 1988 election”? On the other hand, unless the tally came down to quantum indeterminacies (which may well have been), given the laws of nature and the state of things before the votes were cast, it may have been actually impossible for Dukakis to have won. It is “impossible” for my mug to start hovering in the air right now – since gravity holds -, but it is also “impossible” for it to fall right now to the floor in Madrid since I have it with me in Sheffield – since the current state of affairs isn’t the one that, together with the law of gravity, would result in its shattering in Spain. But if all things that happened had to happen, then almost everything is impossible.

3

Some contemporary philosophers have rebelled against the apparent dilemma between a Stoic necessitarianism and a build-your-own-concept view of possibility; for instance, among the ranks of proponents of a powers ontology:

Some follow Hume, insisting that only deep or clear conceiving can tell us what is possible; others place no limits on the operations of the imagination, but restrict the role of conceiving to that of providing evidence for what is possible. Nonetheless, even with those conditions in place, the range of possibilities remains vast. Talking donkeys? Sure. Fire-breathing dragons? Why not. One-eyed, two-toed, three-armed, vengeful giants? But of course, this is a catholic approach to possibility! There is virtually no limit to the ways in which the constituents of the world could legitimately have been combined, or how they can be recombined, or how all these can or could have been arranged.

Williams, N. The powers metaphysic, 2019: 24

They, rather, think of possibility as a positive aspect of objects, which needs a metaphysical grounding. This stance was shared by the young(-ish) Kant, and this whole discussion may serve to illuminate what are some of his more obscure arguments.

Kant was convinced that the principle of non-contradiction cannot be all there is to distinguishing possibility from impossibility (Bew. 2: 78). We have already seen that it isn’t entirely straightforward what it means for a subject and a predicate to be, strictly speaking, self-contradictory in the way of the excluded third. Rather, Kant starts from the reasonable starting point that, among the things which don’t exist, some are possible and some aren’t. As for the impossible things, Kant contends, there must be something that impedes their existence (because they aren’t merely inexistent, but they couldn’t exist at any rate). This can be because the concept that attempts to refer to such a thing simply fails at being a concept, sure; but it doesn’t need to be that way. Kant takes Aquinas’s suggestion of the incompatibility between subject and predicate seriously:

[T]he impossible always contains the combination of something posited with something which also cancels it. I call this repugnancy the formal element in inconceivability or impossibility. The material element which is given here as standing in such a conflict is itself something and can be thought. A quadrangular triangle is absolutely impossible. Nonetheless, a triangle is something, and so is a quadrangle.

The only possible argument for the existence of God, 2: 77

Triangles and quadrangular things are real, and they are such that they are absolutely incompatible: a single object cannot be both at the same time. Yes, “four-sided triangle” fails to refer to any object insofar as there is no possibly existing object that would fall under such a description, but it fails because the two relata of this aborted predication behave in such a way as to deny one another. Similarly, a “green thought” is impossible, not because thought means “non-green substance”, but because green things and things that are thoughts are such that they stand in real opposition to one another. In this case, because everything that is green is, presumably, a perception of something external, etc.

Though many of these impossibilities may be easily traced back to our linguistic usages, we ostensibly learn about real oppositions between concepts that we didn’t necessarily know beforehand they stood in such a “repugnant” relation. To use yet another tired example, the same object cannot be made of CH4 and be water at the same time, the properties of water stand in real opposition to the chemical makeup of methane.

We can also look at this from a positive perspective. Let’s say unicorns (horses with horns) are possible. This may be so even if unicorns don’t exist. Moreover, unicorns might be possible even if horses and horns didn’t exist either. And we can keep deflating our expectations of actuality in order to ground possibility. Horses may be possible beings even if there were no animals in the world, or no living beings, or no beings made of carbon. But, Kant says, at some point this has to stop. If nothing about our possible concept relates back to something that actually exists, in what sense is it distinguishable from a purely void notion? This is the real, or material part of possibility; possibility is something positive, it presupposes that certain things actually obtain.

4

There’s much to be said about the problems with this account, and I haven’t even called things by their names – logical possibility vs. metaphysical possibility. I haven’t summoned the ghost of physical possibility either. The point, however, is fairly simple. We may, or we may not, be able to think of a philosophical zombie – I’m not sure what it means to conceive such a thing. But there is something that is clear. Not having an inner experience and outwardly behaving like a human are real things. As real things, it may be that they cannot co-exist in the same object. It isn’t always obvious whether we are putting words together or whether we are tracking something that could really be the case, and there’s no hard-and-fast logical test that is going to solve that for us. Thus, the physicalist cannot be defeated that easily. Possibility isn’t the default, we have to put in the work to find out what could be.