Logically speaking

Graham Priest interviewed by Richard Marshall.

Graham Priest is one of the giants of philosophical logic. He has written many books about this, including Doubt Truth to be a Liar, Towards Non-Being: the Logic and Metaphysics of Intentionality, Beyond the Limits of Thought, In Contradiction: A Study of the Transconsistentand Introduction to Non-Classical Logic. He can be found in Melbourne and New York, and sometimes in St. Andrews. His big theme is paraconsistency and dialetheism. He is also interested in Buddhism. He is very, very smart.

3:AM: You’re famous for denying that propositions have to be either true or false (and not both or neither) but before we get to that, can you start by saying how you became a philosopher? Were you always someone who had these questions about how we thought and how the world was, or was it something completely different that you got you into the rather strange world of philosophy?

Graham Priest: Well, I was trained as a mathematician. I wrote my doctorate on (classical) mathematical logic. So my introduction into philosophy was via logic and the philosophy of mathematics. But I suppose that I’ve always had an interest in philosophical matters. I was brought up as a Christian (not that I am one now). And even before I went to university I was interested in the philosophy of religion – though I had no idea that that was what it was called. Anyway, by the time I had finished my doctorate, I knew that philosophy was more fun than mathematics, and I was very fortunate to get a job in a philosophy department (at the University of St Andrews), teaching – of all things – the philosophy of science. In those days, I knew virtually nothing about philosophy and its history. So I have spent most of my academic life educating myself – usually by teaching things I knew nothing about; it’s a good way to learn! Knowing very little about the subject has, I think, been an advantage, though. I have been able to explore without many preconceptions. And I have felt free to engage with anything in philosophy that struck me as interesting.

3:AM: Now, you’re interested in the very basis of how we think. You are saying that assuming that every proposition has to be true or false (and not both or neither) is a mistake. So you are asking questions that are deeper than the ones about which is the best way of getting truth. But nevertheless, truth and rationality are targets of your arguments. Is that right? Could you say something about this?

GP: Well, first a clarification. I’m not interested in the way that people actually think (at least not professionally); that’s a matter for cognitive psychologists. Next, dialetheism (the view that some contradictions are true) does not imply any kind of relativism. I believe just as much as you do that when we ask questions there are true answers (in cases where there is a fact of the matter), and that there are some ways of trying to figure out what these are that are better than others. In that sense, neither truth nor rationality are targets of my work. As I argued in Doubt Truth to be a Liar, dialetheism is quite compatible with very orthodox views about truth and rationality. What my work does target is a certain mistaken claim about truth. Contrary to orthodoxy in Western philosophy, some claims are true and false, that is, they have a true negation. Nor is this irrational. Indeed it is arrived at in the most rational of ways: by seeing where the evidence and arguments about paradox, motion, the limits of thought, and so on, take us.

3:AM: So paraconsistent logic is a logic that tries to work out how we might formally understand treating some propositions as being both true and false at the same time. You argue that Aristotle’s the guy who defends the ‘law of non-contradiction’ and that his defence is suspect in various ways. So can you say what’s so wrong with thinking that a proposition, such as that expressed in a sentence like ‘the cat is on the mat,’ is either true or false and not both or neither. Can you give examples of how this works?

GP: The only significant and extended defence of the Principle of Non-Contradiction (PNC) in the history of western philosophy (that I am aware of, anyway) was by Aristotle in Metaphysics, Gamma; and indeed it is badly flawed. There is one major argument, and scholars cannot even agree on how it is suppose to work, let alone that it works. The other arguments are mostly beside the point, targeting the view that allcontradictions are true, or that someone can believethat all contradictions are true.

Now, in the standard logic of our day, any contradiction entails everything. Thus, from ‘it is and it isn’t raining’, it follows (quite counter-intuitively) that you are frog. A paraconsistent logic is one where this principle of inference fails. A paraconsistent logic is clearly necessary if one wishes to handle inconsistent information in any sensible way. Dialetheism is the view that some claims are both true and false; that is, that for some sentences, A, both A and ~A are true (‘~’ is a logician’s way of writing ‘it’s not the case that’). Any dialetheist must subscribe to a paraconsistent logic; otherwise they would be committed to the claim that everything is true, which, presumably, it isn’t. Dialetheism is in no way committed to the claim that every claim is both true and false. (One should note that many contemporary logicians think that a paraconsistent logic gives the correct account of validity, but for reasons that have nothing whatever to do with dialetheism. Indeed, Aristotle’s logic, syllogistic, was paraconsistent, though he was no dialetheist.) On a standard dialetheist semantic picture, there are but two truth values, true and false; a sentence may have just one of these, or both. (And on some accounts, one might add ‘or neither’ as well.) Paradoxical sentences like ‘This sentence is false’ have both. But run-of-the-mill sentences such as ‘the cat is on the mat’ (for a particular cat and a particular mat) have only one truth value.

3:AM: So paraconsistent logic contrasts with the assumptions of classical logical. Now this logic, developed in the modern era by people like Frege and Russell seemed to suggest that what it was doing was giving a very abstract description of how we really think. It was almost like they were giving the abstract formula for a kind of biological reflex. We were creatures that had evolved to have these features of cognition that the classical logicians were codifying. But you take a very different view. You place the development of classical logic in a historical framework and basically say that it is just a cultural artifact, stylized and context specific as, say, the development of noir in film or Romanticism in literature. You are working in Australia and it seems Australia finds you views amenable. Europe is comfortable with the deviant logic of Hegelian, Marxian dialectics and so on. The Anglo-American tradition is rooted in classical logic, although in the UK there’s Dummet and his intuitionist logic. So how far do you think that logic is linked to place or culture and how much of disputes between philosophers might be explained by different assumptions at this base level? What is the story we should have about the status of logic according to you?

GP: Well, for a start, I don’t think that logic has anything to do with the way that people actually reason. Standard work in cognitive psychology (e.g., the Wason Card Test) shows that people often reason invalidly in systematic ways. Logic is about the norms of correct inference. But the word ‘logic’ is ambiguous. It can mean our theories of inference, or it can mean the subject of these. Compare ‘dynamics’. Sometimes this means a theory of how things move (as in ‘Newtonian dynamics’). Sometimes it means how things actually move (as in ‘the dynamics of the earth’).

So for ‘logic’. In the sense that ‘logic’ refers to our theories of the norms of correct reasoning, it is clear that these are, like all theories, constructed at particular places and times, and bear the historical traces of these. You don’t need to know much about the history of logic in this sense to know how much it has evolved in Western philosophy over the last 2,500 years (and continues to evolve). And of course, there can be rival and competing theories in logic – there always have been. As for whether logic the subject of the theories, the norms themselves, change, that is not so obvious. Can claims of the form ‘this follows from that’ actually change their truth value? This is a hard question. I am inclined to think not; but to justify this view would take a lot more space than is appropriate here.

3:AM: Now what may puzzle someone who hears the arguments for having true contradictions is what then happens to rational thought. So one way I might wish to expose your faulty thinking is to lead you to a point where your argument implies a contradiction. So theists often find themselves faced with accusations that their belief about God implies God is both interventionist and non-interventionist, or immanent and non-immanent. When you get to the idea of the Christian trinity, where God is one person and three people simultaneously, you kind of think that this is decisively problematic. But you seem to be saying that there is no problem. So how can any argument be defeated on your view?

GP: A quick answer is that a view can be defeated if it can be shown to lead to something rationally unacceptable. For example, if my views could be shown to entail that I am a frog, I would give them up. Why is that consequence unacceptable? Well, because there is no evidence for it, and good evidence against it.

But more should be said. Some contradictions are true; it does not follow that all are. Some contradictions are rationally acceptable; it does not follow that all are. There is a lot more to rational acceptability than mere logical possibility. That you are a frog is a logical possibility, but to believe it would be ground for certifiable insanity. A rational person, as Hume put it, apportions their beliefs according to the evidence. So what happens if I have some set of beliefs which entails A, and you demonstrate to me that ~A? Logically, it is possible to accept A and ~A, but absent special considerations, this would seem to be ad hoc and rationally unappealing. True contradictions would seem to be, after all, unusual. Is there any rational reason to suppose that this is one of them?

Take some concrete examples. You mention God. If there were a God of the Abrahamic kind, then God would no doubt be a most unusual object. Maybe God can be three and one. But a standard version of the problem of evil argues that if there were a God of this kind, there could be no gratuitous suffering in the world. Suppose the argument sound. Anyone who thinks that there is no gratuitous suffering in the world does not appear to be living in the same world as I am. Could I accept that there is and is not gratuitous suffering in the world? That would seem to be crazy – just as much as supposing that the local supermarket has and has not milk on its shelf. This is not a claim about some strange object like God, but about a perfectly mundane situation. Moreover, if it really is true that there is no gratuitous suffering in the world, this makes a nonsense of much of standard morality. I should not be compassionate to those who appear to be suffering this way, for example: they are not. This contradiction hardly seems acceptable.

3:AM: Now you are an extreme case of paraconsistent logician. You are a dialetheist. You claim not only that logic can accommodate a proposition being both true and false, but you also say that you think true contradictions exist in the world. Now in this move you move from claims about logic and reasoning to metaphysics. This will strike some people as being strange. They may say its one thing to say that it’s best to think about the world using these rules of inferences, but quite another thing to say that the reality of the world is structured in the same way as our reasoning. If our minds have evolved in a haphazard way to merely get around our part of the biosphere then it would be surprising that this process actually tracked reality or truth. And experimental data suggests we are only weakly selected for cognitive truth or consistency. So are you like Plato and think that our thoughts do cut nature at the joints, and how do you respond to the naturalist philosophers?

GP: I don’t think that this question has much to do with dialetheism. It is a quite general question about the adequacy of our cognitive apparatus. Let us suppose that this has evolved with the rest of our biological apparatus. It seems to me that there are good evolutionary reasons to suppose this apparatus gets things right, at least in gross terms. To state the obvious, a cognitive system that told it’s bearer that there was no problem when a sabre-tooth tiger was advancing would not last long. (I’m not sure what recent evidence you are referring to.) Of course, the results of scientific investigation take us much further than our basic cognitive apparatus. But even here, there is reason to believe that we are doing a decent job of determining the truth. If we weren’t, we presumably wouldn’t have had the rather spectacular success in technology that we have had. (Not that I can take much credit for that personally!) One might think that metaphysics is different from physics, but I don’t really see a principled difference. We make theoretical investigations of the Way The World Is. If our investigation of the evidence leads us to believe that something is true, then we have good reason to believe that the World Is That Way.

3:AM: I wondered if any of the recent work by x phi has supported your views? So for example Eric Schwitzgebel seems to be finding experimental evidence has led to him endorsing the idea of ‘inbetween beliefs’ and adopting a paraconsistent logic. What is your attitude to this idea that outside of the armchair there’s supporting evidence for your views?

GP: Well, if you ask most analytic philosophers, they will tell you that it is clearly absurd to accept an explicit contradiction. In fact, the evidence of x-phi now turning up suggests that most people do not find it absurd at all. (There is some more evidence to this effect found by Dave Ripley.) I must say that this concurs with my own impressionistic evidence. Sometimes I meet people at parties, and am asked to explain what I do. When I talk about accepting contradictions, most people cannot see why this should be at all interesting. They think it’s pretty obvious that most people do this, and are perfectly reasonable in doing so. But do I take it that this supports my view? Not really. After all, at one time most people believed that the sun went round the earth. They were just wrong. Only serious theoretical investigation can sort these matters out. The results do provide a welcome reply to dogmatic philosophers who reject the possibility of any sane person happily believing a contradiction, though.

3:AM: Now as I indicated earlier, there are examples of the kind of dialetheic position you hold embedded in certain well known religious beliefs. Buddhism, for example, is pretty relaxed about contradiction. I once tried out an argument with a Buddhist and he was sanguine about having to hold contradictory propositions. Meinong is also known I think for holding to the idea of true contradictions existing. So can you say whether you find that your position underwrites a new way of looking at the world and our place in it? For instance, do you think that the position is inclined to be less judgmental, more understanding, say, in the realm of ethics and in the management of disputes? Would the world be better if we were all more paraconsistent, even dialatheistic? And wouldn’t science struggle?

GP: Lots of questions here. First, endorsing the PNC is certainly highly orthodox in Western philosophy. Even before the current dialetheic phase, however, there were dissenting voices. Heraklitus and Protagoras endorsed contradictions – at least according to Aristotle. Some medieval theologians, such as Nicholas of Cusa, held God to be a contradictory object. In modern philosophy, the clearest dialetheist is Hegel, who said in his Logic, for example, that for something to be in motion is not for it to be in one place and one time, and another at another, but at one and the same time to both be and not be at a place. The case of Meinong is less clear. He certainly says things that look as though he is violating the PNC, but there is room for exegetical evasion.

Turning to the Eastern philosophical traditions, the PNC is less orthodox, though it has certainly had plenty of defenders there too. Buddhist philosophy (or philosophies: there are as many different traditions in Buddhism as there are in Christianity) is a particularly interesting case. The canon is certainly rich with the assertion of contradictions, but it is not clear that these are not just rhetorical devices, or that the apparent contradiction cannot be defused in some other way. In fact, I hold that some of these contradictions are meant to be taken seriously, in at least some of these traditions; but the point is contentious. About 10 years ago, I gave a talk (with Jay Garfield) at the Tibetan University at Sarnath in India, advocating this view. The audience contained Buddhist monks and other Buddhist scholars. When we got to the claim about contradictions, half the audience were nodding sagely; half were holding their heads in their hands in horror.

Anyway, one can hardly say that dialetheism is a new way of looking at the world; it has a good history – though it may be new to contemporary analytic philosophers. Is it a more irenic position, though? I doubt it. Suppose one person maintains A, and one person maintains ~A. Someone who comes along and suggests that A&~A is likely to find both parties disagreeing with them. After all, the person who accepts A will characteristically reject ~A (and symmetrically for the person who accepts ~A). That is the real locus of disagreement. Ethical disagreements make the matter even worse. Suppose, for example, that one party holds that abortion ought be illegal, and another holds that it ought to be legally permissible. Even if it were to turn out to be both, there would still be an issue about what to do in practice. That is where the rubber would really hit the road.

And as to whether science would struggle: it would not. The corpus of science is inconsistent nearly all the time. Witness the inconsistency between quantum mechanics and general relativity. Even individual theories can be internally inconsistent, such as Bohr's theory of the atom. Scientists are quite used to living with contradiction. Perhaps, in the past, these contradictions have been resolved eventually. Being a dialetheist does not remove this option; it just adds others. The question is only: what is the best scientific theory to accept? If it turns out to be an inconsistent theory, so be it. Thus, for an hypothetical example, suppose that we had a theory of the micro-world according to which micro-objects really do behave in a contradictory fashion; however, all the actual observable predications of the theory were spectacularly verified, and none were refuted. Then it would be rational to accept this theory. Nor, while the situation remained thus, would there be any reason to revise it.

3:AM: Now what would you say to those who think that actually you’re kind of cheating, or at least that you’re guilty of false advertising. So, like physicists who make claims about vacuums and then we find that they are using the term in a way that allows for there to be something in the vacuum, so too with your contradictions. Once we get into the detail, what people thought was on offer is much more nuanced and not really as full blooded as might have been expected. So Roy Sorensen argues this when he defends his view of vagueness. He thinks that the contradictions that you endorse aren’t really the kind of contradictions that we need to worry about. What do you say to this kind of criticism?

GP: The view you mention goes back to a paper by Charles Chihara about 40 years ago. Views of the kind in question have been defended more recently by Roy Sorensen, Matti Eklund, and others. The view is to the effect that our language is inconsistent, in the sense that anyone who grasps the meaning of certain of its constructions (such as vague predicates or the truth predicate) is committed to endorsing or believing certain contradictions. These are not true, however. The cognitive states in question are just a by-product of language-mastery. This is certainly not my view. Dialetheias are true (spell out the details of truth in whatever way pleases – satisfying the T-schema, corresponding to reality, verified, or wot not), with all that this implies. There is no danger of the view collapsing into what seems to me to be this somewhat half-hearted view. Indeed, the danger is in the other direction. To be forced to endorse some contradictions but to deny their truth risks collapsing into bad faith of the worst kind.

3:AM: Another worry might be one that I think haunts some of my earlier questions. We want beliefs and so on to guide us. And when I’m disagreeing with someone, I kind of need to think that if I’m right and she disagrees then she’s wrong. And vice versa. So when rational peers disagree the problem is a genuine one of finding who got it wrong. I can imagine plutocrats and general hypocritical bastards all over thinking that this is a logic for them because the commitment to consistency is removed. They can say one thing and think another without sanction. Ricoeur’s ‘hermeneutics of suspicion,’ where philosophical programmes to unmask hypocrisies used to defend vested interests, including the arguments of Marx to unmask the upper classes and so on, seem to be programmes that wont thrive.

GP: Let’s start by fixing some terminology. To say that a claim is false is to say that its negation is true. To accept something is to believe it, to put it in one’s “belief box” as it were. To reject something is to refuse to put it in the box. Now let’s get some facts straight. Frege notwithstanding, to reject a claims is not to accept its negation. Most people sometimes find themselves in the situation of believing contradictions, things of the form A and ~A. When they do so, they may well revise their views. Perhaps this is usually the correct thing to do. However, in that state, they accept ~A but do not reject A. The same is true of dialetheists who wittingly and consciously endorse some statements of the form A and ~A. And those who take some sentence, A, to be neither true nor false reject A without accepting ~A.

Now, a disagreement between two people occurs when, for some A, one accepts A and one rejects A. The question, then, is who is right. Dialetheism does not affect this matter. A dialetheist may accept something of the form A&~A. A non-dialethiest will reject A&~A. (They may accept ~(A&~A) as well; but that may not distinguish them from the dialetheist, who may do the same.) In any case, if one party holds that A (and only that A) and another holds that ~A (and only that ~A), someone who endorses A&~A is unlikely to resolve the dispute; both parties will probably disagree with them.

Now hypocrisy. One standard meaning of a hypocrite is someone who tells other people that they ought to do something, but does not do it themselves. Dialetheism has nothing to do with this. Another form of hypocrisy is stating that you have views that you do not have (to reap the benefit) – though this might better be called lying. Someone who believes A&~A but asserts only A is not in this camp. They do, after all, believe A. They might be lying in a different sense, though. There is a conversational maxim to the effect that one should assert the strongest relevant information in one’s possession. Thus, someone who asserts that A when they believe that A&~A might well mislead in virtue of the fact that they are not telling the whole truth. But dialetheist or not, someone who does not accept something, but asserts it to try to get people to believe that they do so, is simply lying. And someone who accepts that A is not going to make peace with someone who rejects A simply by adding ~A to their beliefs. Dialetheism provides no easy way out for a person who finds themself in a confrontation with someone who rejects their views.

3:AM: On the other hand, the dialectic position of Marx, based on his Hegelianism, is one where contradictions between thesis and antithesis lead to synthesis at the next level, in a process of never ending dialectic. This in some way seems close to your position. So then the hermeneutics of suspicion is supported by your approach, and not threatened at all. Your position seems to both threaten and endorse this kind of programme. This might be satisfying for a dialetheist paraconsistent philosopher. What do you say about all this?

GP: I don’t think it threatens it, as I have just explained. As for Hegel and Marx, I think, indeed, that they were dialetheists. They endorsed some contradictions. (Though they both had a tendency to call contradictions some things which are not contradictions in the logician’s sense; but some of the things they called so were.) This is a somewhat contentious view, but I have defended it elsewhere. ('Dialectic and Dialetheic', Science and Society53, 1990.) Dialecticians, then, are dialetheists. Dialetheists do not have to be dialecticians, however (though they may be). Dialectics tells a story about how development of a certain kind (in our concepts or in reality) is driven by contradictions which arise. This dynamic story is no part of dialetheism as such.

3:AM: You wrote Sylvan’s Box, about an empty box with something in it. It’s a great example of metaphysical literature. Can you say what made you write this and what you think readers have made of it? This leads us to thinking about imaginative literature and film and music. Your work is formidably technical but its implications seem to line up with some of the great imaginative literature and films which play with paradox and contradiction. Do you read metaphysical literature and science fiction, watch films and so on? Have any been of help/inspiration your thinking? And if you had to give us a list of your top 5 books for someone who was smart but not necessarily philosophically trained, what would you recommend?

GP: Gosh! I’m afraid that I’m not really one of the literati. I go to the movies when I get a chance, but I rarely read non-fiction. I listen to a lot of music, though. Especially opera. When I wrote Sylvan’s Box, I wanted to write something to the memory of my old friend, Richard Sylvan, who had died shortly before that. However, the main philosophical motivation was provided by the fact that someone had said to me that it was impossible to have a really inconsistent fiction: you have to reinterpret apparent contradictions somehow. I thought that was obviously untrue, so I wrote the story to show it. To interpret away the contradictions in the story is to misunderstand it (or at least to give it a highly non-standard interpretation). I think that most people who have read the story have taken that point. I believe it changed David Lewis’ mind about the matter, for example. Are there other philosophical lessons that one can take away from the story? Probably, but I’ll leave that matter to the creativity of the readers.

Since I don’t really read fiction, I don’t think I have been influenced by it in any way. On the odd occasions I do read, I like fiction that explores philosophical ideas. The novels of Sartre and Dostoievski are obvious examples. I also love the short stories of Borges. These are the closest thing to philosophy-fiction, if there is such a genre. The same general point goes for movies. Anyway, I would not dream of recommending any of these works to people (with or without philosophical interests) unless I were very sure of their tastes. What people like in these matters is so subjective (which is not to say that what is good is subjective). Opera is rarely philosophical in any sense (though it tends to move me more than any other form of art). Wagner’s operas, especially the Ring Cycle, do have philosophical under-girding, though. I recommend Bryan Magee’s The Tristan Chord: Wagner and Philosophy if anyone is interested in that matter.

ABOUT THE AUTHOR
Richard Marshallis still biding his time.