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 Transconsistent and 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.
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 all contradictions are true, or that someone can believe that 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.
