We believe things can’t be both true and false, it can’t be both raining and not raining at the same time. Philosopher Graham Priest, however, thinks differently. In this interview, he argues true contradictions are an intrinsic part of reality.
Join Priest alongside other speakers such as Slavoj Zizek, Roger Penrose, and Phillipa Gregory at the HowTheLightGetsIn festival on September 21st-22nd debating topics from consciousness, to quantum mechanics, politics to beauty. Learn more here.
Most of us think in binaries: either it’s raining or it’s not, things are black or white, true or false. The philosophies of Frege and Russell in the 20th century formalised these binaries into the very logic of our thinking. Graham Priest pushes back against this. There is a huge variety of paradoxes which have puzzled philosophers throughout the ages, and that old view that contradictions are always false has yet to be justified. In this interview with the leading theorist of dialetheism we discover how it can be raining and not raining at the same time.
So, Graham what is the argument? Some commentators have argued that you seem to be saying that paradoxes are not just linguistic or conceptual issues, but that they exist in the world itself?
I don’t think I have ever said that. What I have said is that some contradictions are true (dialetheism, as it is now called). What makes a statement true is, in general, a combination of what words mean and how the world is. So ‘Australia is in the Southern Hemisphere’ is true partly in virtue of the meaning of ‘Southern Hemisphere’, and partly in virtue of some geographical facts. Many true contradictions are no exception to this general rule.
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What was your intellectual journey towards dialetheism? Was there a specific moment or experience that convinced you that true contradictions are a fundamental aspect of reality?
I was trained as a mathematician. My doctorate is in mathematical logic, and I was as classical a logician as anyone could be. Any logician must engage with some of the most profound mathematical results of the 20th century, such as Gödel’s Incompleteness Theorems. These are closely related to the paradoxes of self-reference. So I became interested in these. These paradoxes have been discussed by logicians for nearly two and a half thousand years, and there has been no success in solving them—at least if success is judged by consensus. These paradoxes are arguments for certain contradictions. Most have assumed that there must be something wrong with the arguments. I started to think ‘maybe this isn’t true: these arguments just establish their contradictory conclusions’. So I started to investigate this possibility, its ramifications and applications. After a period of time, I became persuaded that, despite being highly unorthodox, this is a very sensible view.
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How do you define a paradox? Are there criteria that distinguish a "true" paradox from one that merely appears paradoxical due to linguistic confusion or logical error?
A paradox is an argument which appears to be sound, but which ends in a contradiction. If the argument really is sound, the contradiction is true. If not, there is no reason to believe so. Of course, all the hard work has to go in determining whether the argument is sound. There is no magic bullet to determine this.
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The argument for Explosion presupposes that truth and falsity are exclusive. Hence an argument against true contradictions on the basis of Explosion begs the question.
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The Law of Non-Contradiction, that something has to be true or false, is a foundational principle of classical logic. How do you respond to those who argue that abandoning this law leads to an incoherent or meaningless view of reality?And how do you counter the explosion argument in favour of the law of Non-Contradiction, the idea that if we allow contradictions to be true we can reach any conclusion we want? Can you provide a concrete example of a true paradox in the world?
Well, what is called classical logic is a logic invented by logicians such as Frege and Russell at the turn of the 20th century—though it has some things (but only some things) in common with really classical logics. those of Ancient Greece, for instance.
If someone claims that abandoning the Principle of Non-Contradiction leads to an incoherent or meaningless view of reality (whatever that is supposed to mean), the onus is on them to make good this claim. I have never seen a successful argument for this.
The argument for Explosion presupposes that truth and falsity are exclusive. Hence an argument against true contradictions on the basis of Explosion begs the question. There are now many well understood formal logics which do not have this presupposition. They are called paraconsistent.
There are many possible examples of the kind you ask for (though of course they are all contentious). One is the sorites paradox. Take a long sequence of colour strips such that the colour of each is indistinguishable from that of the strips immediately adjacent to it, but such that the first strip is red and the last is not (say, blue). The strips in the middle of the sequence are symmetrically poised between being red and not being red. One may argue that they are both.
So, taking an example like "It's raining and it's not raining." How would you defend the claim that this could be a true paradox? What are the implications for our understanding of truth and reality?
This is a standard example taken from another sorites paradox, concerning a slow but continuous transition from a heavy downpour to the rain having stopped. Like the paradoxes of self-reference, there is no consensus about how this should be solved. A dialetheic solution is one of them, but of course there are others. One just has to engage in the discussion of which solution is best. For what it is worth, when ordinary people (not philosophers!) are interviewed about what to say of the such borderline cases, many are quite happy to say that it is raining and not raining.
What are the implications? That some contradictions are true, and that reality is such as to make them so.
You’ve argued against the transitivity of identity, the idea that everything has to be identical with itself. How do you address the criticism that rejecting this principle undermines the coherence of identity itself? Could you explain how this view aligns with, or contradicts, your commitment to realism?
If someone claims that rejecting transitivity undermines the coherence of identity (whatever that means), the onus is on them to justify the claim. The transitivity of identity is certainly a standard assumption, but that is not good enough. One thing we have learned from the history of philosophy, logic, and science, is that standard assumptions are often false. Once such an assumption is challenged a case needs to be made for it.
Whether or not I’m a realist might depend on what you mean by ‘realism’. The word gets used to mean many different things. But in any case, I see no obvious connection between the transitivity of identity and realism—whatever that might mean.
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If one is not a dialetheist all inconsistent theories are off the table; but with dialetheism, some may well be. We still choose the best theory, but now this may be an inconsistent one.
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In embracing paradoxes as real, what are the ontological commitments that follow? How does this impact your view of metaphysics, particularly regarding concepts like objecthood and identity?
I’m not sure there is anything much more to say about this. Since I am a dialetheist, I think that some objects are contradictory. That says nothing about their objecthood per se. Dialetheism does not, in itself, imply that identity is non-transitive. It is quite compatible with a standard view of identity. However, in one of my books I applied it to give a non-transitive theory of identity.
So, what are the practical consequences of accepting that true paradoxes exist? How should this influence our everyday reasoning, decision-making, and scientific inquiry?
This is a big question, but the outline of an answer is as follows. Whenever we hold a view on some matter, it is usually embedded in some general theory or other—maybe a confused one. The rational thing to do is to accept whichever is the best theory, and so the answer it gives. If one is not a dialetheist all inconsistent theories are off the table; but with dialetheism, some may well be. We still choose the best theory, but now this may be an inconsistent one.
Mathematics and science are fields heavily reliant on consistency and non-contradiction. How do you see dialetheism affecting these domains? Are there areas where embracing paradoxes could lead to new insights or breakthroughs?
No, this is not true. First, we now know that there are coherent mathematical theories based on non-classical logics. Those based on a paraconsistent logic will be inconsistent. Moreover, inconsistent theories have been accepted by scientists. The most obvious example of this is classical dynamics. For about 200 years, this was based on the infinitesimal calculus, which was well known to be inconsistent. Scientists will accept whatever theory produces the right empirical results. If this is inconsistent, so be it. True, for the last 200 years scientists have not deliberately constructed inconsistent theories; but now that we have well-established non-classical mathematics, perhaps they will be.
If contradictions can be true, what does this mean for ethical reasoning and moral philosophy? Could there be true moral paradoxes, and if so, how should we navigate them?
Yes, there would appear to be normative dialetheias, where you ought to bring it about that something, and it is not the case that you ought to bring it about. If this is so, you just have to live with the contradiction, and take the consequences.
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Perhaps the other most common objection is: ‘I just don’t see how a contradiction can be true’. That says more about the speaker than the view itself. Many people found the Special Theory of Relativity hard to accept at first
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What are the most common objections you face regarding dialetheism, and how do you typically respond to them? For instance, how do you defend against the claim that accepting contradictions leads to logical and practical chaos?
The traditional arguments against dialetheism are those provided by Aristotle in his Metaphysics and they are pretty hopeless, as most modern commentators now agree. Probably the most common objection now is that dialetheism implies that everything is true. This depends on the principle of Explosion. The validity of Explosion presupposes that truth and falsity are exclusive, and so begs the question. There is no logical chaos in a paraconsistent logic. Such logics are as precise and mathematically articulated as any other contemporary system of formal logic.
Perhaps the other most common objection is: ‘I just don’t see how a contradiction can be true’. That says more about the speaker than the view itself. Many people found the Special Theory of Relativity hard to accept at first because they just ‘couldn’t see how time could run at different rates in different frames of reference’. In both cases, you just have to get used to the new theoretical framework.
Looking forward, what do you see as the future of dialetheism in philosophy? Do you believe that your views will gain wider acceptance, and if so, what shifts in philosophical thought or practice do you anticipate?
I certainly hope so, but of course the future of philosophy—as of so much else—is inherently unpredictable. Philosophical thinking (at least in the West) has been constrained by the dogmatism of consistency since Aristotle. Once these blinkers are off, who knows where philosophy could go?
How has your commitment to paradoxes and dialetheism influenced your personal worldview? Do you find that it has changed the way you approach life’s uncertainties and contradictions?
Not really. Perhaps the fact that I have had to come to reject something I took to be obvious has made me more suspicious of views which many people (including myself) are wont to take for granted.
What advice would you give to young philosophers who are grappling with the idea of true paradoxes? How should they approach the study of logic and metaphysics in light of your theories?
Approach things with an open mind. Don’t believe something simply because tradition says it is so. Don’t believe something simply because you read it in a book—mine included. Explore the ideas and look at the evidence for yourself; make your own mind up.
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