I recently published a post in defense of dialetheism. I argued that in the case of statements about “man-made” states of affairs, it is obvious that some contradictions are true. For example, the law can easily contradict itself in such a way that a statement about what is legally mandated be a true contradiction. I invented “Timmy the Square Circle” to show that, similarly, there can be true contradictions about fictional characters. If this doesn’t seem intuitively obvious, read that post before this one.
The concluding paragraph included this teaser:
It is perhaps now tempting to draw a sharp line: the world of man-made ideas allows for true contradictions, reality doesn’t. However, this line is not so sharp.
If we grant that there are true contradictions about what is made up, does this tell us anything about whether there are true contradictions about objective reality? To say there are is a stronger, and intuitively harder to swallow, version of dialetheism. As we’ll see, however, there is no way to say anything about anything without talking, in part, about the man-made. This inescapable fact leaves open the possibility of true contradiction in claims about the physical world, even if it’s the case that the physical world itself, independent of our descriptions of it, cannot be contradictory.
Conceptual reality: Liar and Sorites paradoxes
We first need to establish that there are different “levels” of objective reality, and accepting a contradiction in one level may be much more counterintuitive than in another level. This is best seen with examples.
Let’s start with the famous Liar sentence: “This sentence is false”. Is it about fiction or reality? Well, it’s about itself. And what is that? The standard account says it is (or seems to be) a proposition, but that only pushes the question back: what sort of things are propositions? They’re not quite fictions. Meaning is real enough. They’re certainly not physically real. Maybe they’re a part of conceptual or abstract reality? What would that mean?
However we answer, this much seems safe to say: the cost of accepting the Liar as a true contradiction is higher than the cost of a fictional character with contradictory properties but lower than the cost of a contradiction about physical reality. At worst, a dialetheic solution to the Liar suggests there are contradictions implicit in our network of basic concepts (at least in the corner of the semantic web where negation, reference, truth, and circularity hang out). Now, I’m not terribly confident about which solution to the Liar is best. But if the worst the dialetheic solution has going against it is that it stomachs a conceptual contradiction, then it’s a damn attractive view. As I’ll argue below, it shouldn’t be all that surprising to find contradictions in our concepts.
What about the Sorites paradox? At first glance, the Sorites seems to involve perfectly concrete objects, such as red patches, heaps of sand, and drunk people. But it’s clear that the source of the contradiction is conceptual. What would it mean to accept that I could be both drunk and sober? Only that meaning emerges in such a way that the application conditions of “drunk” and “sober” create an overlap. This may be a bit weird, and it is about objective reality, insofar as meanings are not made up by fiat, but are naturally occurring phenomena over which we typically have no direct control. But we’re still quite far from a physical contradiction. Dialetheic solutions to the Sorites, as to the Liar, suggest only that our concepts may have contradictions built in.
[As an aside: though I think true contradictions about vague statements are plausible, I don’t subscribe to dialetheic solutions to the Sorites, because they don’t avoid precise cutoffs. If we’re going to accept precise cutoffs anyway, epistemicism is the simplest, most intuitive way to go.]
Physical reality: Quantum mechanics
Okay, so maybe true contradictions are possible, even when they’re plausibly about “objective” reality, so long as they’re quarantined to the conceptual realm. Can we at least say true contradictions are impossible about physical reality?
Let’s propose a Consistent Physicality Principle (CPP): Whatever the physical state of affairs is, it cannot also not be the physical state of affairs.
I think something like CPP is true, though not quite. Before I explain the qualification, let’s look at the two most prominent candidates for violations. The first is quantum mechanics.
A disclaimer: I’m hilariously ignorant on the subject. Rather than pretend to know more than I do, or expect you to know more than perhaps you do, let’s just assume that experimental results in quantum mechanics point to particles with literally contradictory properties. The following seems safe to say:
1 – There are many interpretations of quantum mechanics, only some of which stomach contradictory facts. If accepting contradictory particles means violating CPP and violating CPP is really unacceptable, we have other ways of dealing with the problematic data.
2 – Quantum mechanical objects are posited objects. Though we’ve made observations that we think are best explained by these posited objects, we’re incapable of directly observing these objects. So it’s not like we’ve “seen” a quantum contradiction. This is especially important because:
3 – We don’t really know what the physical is. Our notion of “physical reality” – along with the intuition that it must be consistent – is borrowed from the everyday experience of physicality as concrete stuff. Physics now tells us that solid matter is mostly empty space. So is it really physical? The intuitive and scientific understandings of the physical have diverged tremendously. The intuitive one just doesn’t apply to what quantum mechanics is about. So, when we say that a particle posited by quantum mechanics exhibits contradictory properties, and from that infer a “physical” contradiction, what are we inferring, exactly? We’re not justified in inferring a contradiction about concrete stuff. It’s probably best to admit that we don’t yet understand what sort of thing this contradiction is supposed to be about.
So where does that leave CPP? Inconclusive. But if the intuitive pull of CPP is very strong (as it seems to be), and quantum reality so mysterious, then the epistemically justified position is skepticism that quantum mechanics really violates CPP. It’s just too easy to imagine that, for example, the inconsistency enters unseen via the definitions of these posited objects, and not via reality itself. In such a case, a quantum mechanical contradiction might well be true, but only in virtue of the descriptive framework, so that we’re still dealing with a conceptual contradiction, not a “physical” one.
Physical reality: Zeno’s Arrow
There’s no easy or agreed upon solution to Zeno’s Arrow (I don’t think the Achilles is solved either, but I’m in the minority there, so I won’t press it now). Quickly, the paradox: consider an arrow moving along a trajectory. At any given instant (duration = 0), the arrow is in only one place. Therefore, in an instant, the arrow makes zero progress. But if the arrow’s trajectory consists entirely of instants, then how does it ever make any progress at all?
Hegel argued for a dialetheic solution: at any given instant, the arrow is both in place and already ahead of its place.
This solves the problem. It also means the arrow is in two places at once. This isn’t about fictional characters or weird sentences. It’s not about the concept “arrow”. For this solution to work, the stuff of the arrow needs to literally be in two places at the same time. There seems to be no way around it here: mustn’t this solution violate CPP?
Not necessarily. Obviously, our understanding of Zeno’s Arrow is contingent on concepts, such as arrow, instant, time, motion, place, object, and predication. Just as we speculated that the concepts involved in the Liar might turn out to be contradictory, or that vague predicates are, or that stipulated definitions of quantum particles are, so we may speculate that our concepts of arrows, instants, etc., might be inconsistent, without that meaning anything about the purported referents themselves.
Plantinga’s evolutionary argument against naturalism
Alvin Plantinga‘s famous evolutionary argument against naturalism, though crafted toward different aims, suggests why our everyday concepts might turn out to be inconsistent. Doing the argument justice would take us too far afield, so here’s the broad gist: we have little reason to think evolution selects for discovering and believing the truth. Evolution, if we understand it correctly, selects for survival and procreation. To whatever extent knowing the truth optimizes our chances for survival and procreation, we should expect to have a good grasp of the truth. In whatever contexts knowing the precise truth does not correlate perfectly with optimal evolutionary strategy, however, we should expect not to be all that great at discovering the truth.
The same argument goes for developing a consistent network of concepts to describe and reason about reality. Having a generally consistent network of concepts is probably useful for survival. But is having a perfectly consistent network of concepts optimal evolutionary strategy? Probably not. It’s likely that a less-than-perfectly consistent network of concepts might be more evolutionarily useful in some contexts.
If this is true, then there could be true contradictions about arrows and instants because of our network of beliefs and assumptions about arrows and instants; in other words, because of how we implicitly “define” these terms when we use them. This could be the case even if the real objects we try to refer to when we use the words “arrow” and “instant” are, when considered independently of the assumptions baked into our descriptions of them, perfectly consistent.
Note that the more relevant a concept is to our survival prospects, the more likely it is that it developed consistently. Though there’s the possibility of inconsistency in any of our concepts, it seems more likely for rather abstract concepts, like “truth”, and less likely for a concept like “arrow”. To me, this makes a dialetheic solution to the Liar more palatable than a dialetheic solution to Zeno’s Arrow. But even for the Arrow, inconsistency is quite plausible. “Instant”, after all, is a pretty abstract concept.
Before moving on, an obvious concern: yes, when we talk about an arrow, we unavoidably use our concept of an arrow. But the whole point of the concept is that it’s supposed to match the actual arrow. Thus, if there’s an inconsistency in the concept, there should be one in the thing itself, unless there’s a concept-thing mismatch. This is true. What I’m arguing depends on there being that kind of mismatch. For the same evolutionary reasons explained above, such a mismatch is to be expected. The existence of “natural kinds“, it should be said, is no objection to this. For even if natural kinds exist, we have no reason to think we have an infallible ability to grab on to them conceptually such that the concept-to-natural-kind match is perfect.
Another concern: some, including Plantinga himself, think this type of view leads to a self-defeating skepticism. I have my doubts about that, but it would be too long a digression to go into it here. I will address it in another post.
Let’s say my general picture is accurate. This implies that it’s possible for any kind of claim we make, even about the most concrete physical states of affairs, to be a true contradiction. Even so, under this account, the contradiction always enters at the level of description. So it seems like there’s still room for some version of CPP to be true.
Let’s propose a Strengthened Consistent Physicality Principle (SCPP): Whatever the description-independent “physical” state of affairs is, it cannot also not be the description-independent “physical” state of affairs.
Intuitively, SCPP seems right. Putting aside all that nonsense about descriptions, there can be no contradictions. Things can’t actually, in the physical world, be both as they are and also not as they are. This seems obvious.
The problem is that SCPP is, itself, a paradoxical claim. Whatever the “description-independent” state of affairs is, if it really is description-independent, then it cannot be referred to. SCPP wants to be about how things themselves must be, independent of how they’re described. But like any claim, SCPP involves description, and cannot actually be about something that can’t be described. The mention of “the description-independent ‘physical’ state of affairs” in SCPP seems to be a clear case of reference failure.
That’s not the end of the story, though. For suppose that there really is a world independent of our descriptions. Idealists aside, almost everyone believes this. Well, if there really is such a world, then I just referred to it. There is nothing more to reference than meeting reference criteria. So, if there is a world, and it is description-independent, then when I say “the description-independent world”, I’m referring to it. That is, after all, what it is: a description-independent world.
So we seem to both be able and not be able to refer to the description-independent state of affairs. (Note that this “ineffability paradox” is very similar to the Berry paradox; it is also related to a problem Kant faces in postulating noumena.)
I can see three ways out here. Option one is to deny the existence of a description-independent world. I’m not going there. It just seems so much more likely that there’s funky conceptual stuff going on than that full-blown idealism is true. Option two is to accept radical skepticism and deny the possibility of reference or meaning. This position is impossible to maintain. I’ve tried. You can’t actually do it.
Or option three: accept that we both can and cannot refer to description-independent reality. If we accept this, then SCPP is true (assuming you believe what it says about description-independent reality, which I do); and it is not true (because it fails to refer, and so has no truth value). In other words, SCPP is itself a true contradiction.
What sort of contradiction is it, a conceptual or physical one? Like any claim, what SCPP says is contingent on the meanings of the words it uses, so conceptual reality is involved. But, as we just established, it also succeeds in referring to physical reality itself. So it is a contradiction about physical reality.
As discussed above, however, Sorites contradictions are about physical things, but the source of the contradiction is always conceptual. This would seem to be the case with SCPP as well. Though SCPP refers to description-independent physical reality, its inconsistency arises from how the concept reference works, not from the way description-independent physical reality is.
Thus, we remain justified in trusting the intuition that SCPP must be true. SCPP isn’t its own counterexample. To whatever extent we can talk about description-independent reality at all, we haven’t found a reason to think it must be contradictory.
A final word: I’ve given no argument in favor of SCPP. I don’t have one to give, other than to say that it has a tremendous intuitive pull. All I have tried to do here is show that, to whatever extent problems like the Liar, Zeno’s Arrow, and quantum inconsistency call on us to accept true contradictions, they don’t require us to accept a physically inconsistent world. We can be dialetheists about all those problems and still contain our dialetheism to the realm of the conceptual.