Part II of the Interview with Graham Priest

The following is the second part of the interview with Philosopher Graham Priest. Part I can be found here.



Q: What is so special about Australia in that it produces so many fine Philosophers!?

Well, I think that it is true that Australia (and more generally, Australasia) has produced many fine philosophers in the last 60 years. This is surprising for a country with a current population of about 20 million (less than that of Texas) – especially in the light of what I said about this being a rather anti-intellectual country.  I have heard the matter discussed a number of times, always somewhat inconclusively.  Such things are, of course, partly a matter of accident. A good philosopher happens to arise; they produce good students; and the tradition perpetuates itself. But there has to be more to it than that.   I think perhaps there are things about Australian culture that is conducive to the philosophical flourishing.  First, Australia is an open-minded place – at least, its philosophical community is. We are not bound by centuries of tradition, as European countries are, or by the influence of religion, in the way that the US is. People are not put off by the fact that an idea is novel or unorthodox.  Secondly, however, the culture is very much a no-nonsense culture. If you have ideas, you are expected to make them clear, and justify them. Australian philosophy conferences are known for their pretty fierce (but friendly) discussions. This produces a climate where new ideas can emerge, bad ones die, and good ones are strengthened.

The following are questions that are more philosophical.

Q: It seems that, in ordinary discourse, whenever one asserts p and another wishes to express disagreement, the latter asserts not-p. To the dialetheist, however, the latter has not expressed disagreement since p and not-p are in principle logically compatible, and thus to assert p does not entail that one cannot also assert not-p; indeed, the dialetheist may accept p and also accept not-p, in which case he would agree with his interlocutor. Prima facie, this seems to present a difficulty for the dialetheist, for it seems that he faces certain expressive limitations. In nuce, it does not seem that he can express disagreement. How might a dialetheist respond?

And so to philosophy: One must distinguish between the illocutory acts of assertion and denial. The former indicates the acceptance of something; the latter its rejection. And Frege notwithstanding, denial is not the same as the assertion of a negation. It is clear that no one who accepts either truth-value gaps or gluts can accept Frege’s position; but it is unacceptable for quite straightforward reasons anyway.  We all find ourselves confused sometimes, endorsing contradictory views that are not acceptable to us.  We find ourselves asserting p and ~p. But we do not deny p.  It’s the fact that we accept both p and ~p that is the problem.  Now, an utterance of, e.g., ‘It is not raining’ can be an assertion of the proposition that it is not raining, or a denial of the proposition that it is raining. How does one tell the difference? By recognizing the speaker’s intentions. In the same way, one can recognize an utterance of ‘The door is open’ as an assertion, a question, and a command.  And – to get around the question finally – a disagreement is registered when one party asserts something, and one denies it.

Q: Let us grant that the dialetheist can express disagreement by employing a predicate which reads ‘false and not also true’. The dialetheist, then, if he wishes to express disagreement with p, asserts p is ‘false and not true.’ However, this leads to an extended paradox

(L) This statement is false and not true

If it is true, then it is false and not true. If it is false and not true, then it is true. In either case it is true and false and not true.

As you have pointed out before, to deny a sentence is to assert that it is not true, while to assert the negation of a sentence is to assert that the sentence is false. Of course, the two are not equivalent because according to dialetheism to assert the negation of a sentence does not entail that one cannot also assert the sentence (it may be true and false) and to deny a sentence is simply to deny that the sentence is true (it may be simply false). If this is correct, then the worry exists that extended paradoxes like (L) vitiate the distinction between denying a sentence and asserting the negation of a sentence. In other words, the simply false predicate cannot secure consistency when employed and the danger arises that the distinction between denying and asserting the negation becomes vacuous, which is ironic considering the distinction was made in order to show how a dialetheist can express disagreement and exclude dialetheia. What say you, Dr Priest?

First, as I explain in answer to my last question. To deny p is not to assert anything. A fortiori, it is not to assert that p is (false and) not true.  You can construct the extended liar paradox just as you have done, and you show correctly that it is both true and not true. That is a true contradiction. But the aim of a dialetheic account of the semantic paradoxes was not to avoid contradiction, but to tame it. (And of course, the fact that some things are true and not true does not entail that all things are, so that the distinction collapses extensionally.)  Some things are both true and not true. By contrast, I don’t think one can assert and deny the same thing (at the same time, to the same hearer, etc.)

Q: When formalizing the predicate ‘false and not true,’ is there not a danger that the dialetheist must employ a consistent negation? If not, if the predicate does not require a consistent negation, then of what use is the predicate at all?

I think that the substantive reply to this is contained in my previous answers. Denial is not a sentential operator. It is an illocutory force operator.  It cannot be defined in terms of sentential operators like negation at all. What use is a truth predicate – well, truth is a rather useful notion. What use is a falsity predicate: to say that the negation of a sentence is true. (Indeed, that can be taken to be its definition.)

Q: In, A Consistent Reading of Sylvan’s Box, Daniel Nolan suggests a reading of Sylvan’s Box that supposedly threatens your claim that the story is essentially inconsistent.  Nolan’s suggests reading the story as you, within the story, merely believing that you have come across an impossible box and disposing of it in an inconsistent manner.  Nolan goes on to claim such a reading is not incompatible with your experiences that take place in the story.  Moreover, given that you, in real life and in the story, accept that there are true contradictions, you are primed to believe that you have found an impossible object, more so than someone who does not hold your views.  Do you think that such a reading could be deemed a bad reading given that, within the story, your evidence for believing that you have found an impossible object is strong and seemingly justifies your conclusion?  Furthermore, since it seems that any agent, e.g. Nick, who shared those experiences, would come to the same conclusion, doesn’t this offer substantial support for your intended reading?  Also, even if someone were to take Nolan’s suggestion, do you think that some points that count against explosion might be retained since the story becomes one about an explicit belief in a contradiction but also one in which you and Nick continue to act rationally?

First, I do not deny the possibility of the reading of the story that Daniel gives. It seems to me that that is beside the point, however. Works of fiction can be interpreted in numerous different ways. Just think how many ways that Hamlet has been interpreted!  Doubtless Sylvan’s Box could be given a Freudian reading, a metafictional reading (in fact, Maureen Eckert just done this), and lots of others.  The important point is that there is one legitimate, though perhaps rather flat footed, interpretation, where it is a straight and veridical narrative. (For what it is worth, though this means little, it is also the one I had in mind.)  Moreover, anyone can read it and understand it in that sense.  In virtue of this, all the points I made, as well as the ones you mention about belief and rationality, still hold.

Q: (1) When it comes to giving similar paradoxes “uniform solution,” you’ve endorsed five different claims that seem to be in tension with each other:

(a) The Principle Of Uniform solution dictates that all paradoxes of the same “type” be solved in a uniform fashion, &
(b) That the Inclosure Schema delineates a “type,” and indeed
(c) That, if someone were to embrace one of the standard consistent solutions to the Liar Paradox but get around Russell’s Paradox by an appeal to mathematical nominalism, then the POUS would be violated. Moreover, you’ve granted that:
(d) The Barber Paradox can be seen to fall under the Inclosure Schema. (It would be surprising if this were not so, given that it was invented to illustrate the structure of Russell’s Paradox, which is in turn one of your favorite IS paradoxes!) Despite this, you’ve argued that:
(e) The POUS does not dictate that we solve Barber in the same way as we solve the main IS paradoxes.

You have justified (e) by saying that it is not enough that a proposed paradox structurally conform to the IS, but also that we have good reason to think that all of its premises are true. (You very reasonably deny that we have any good reason to believe in the existence of a barber who succeeds in shaving everyone in the town in which he lives who does not shave himself.) Why, however, couldn’t the mathematical nominalist say precisely the same thing about the Russell Set (since the nominalist denies the existence of sets in general!), use the various standard arguments for nominalism–Benacerraf, etc.–to deny the Existence component of Russell’s Paradox in a non-question-begging matter, and thus be perfectly entitled by your own standards to solve the Liar Paradox in a different way, without thus violating the POUS?

I have not said that the Barber paradox falls under the Inclosure Schema. In fact, I denied this. It fits the form, but more than that is required – viz that there is prima facie ground for thinking that the premises are true (or a priori true).  (Beyond the Limits of Thought, 17.2).  Of course someone can deny that the premises are true. (In fact, anyone except a dialetheist had better do this, since the conditions entail a contradiction!)  But it remains the case that they are prima facie true. If they weren’t, we would not find the paradoxes paradoxical.

Q: On the same subject–Let’s assume that the IS does delineate which paradoxes are “of a type” and thus must be given uniform solution. You’ve argued (quite plausibly) that “evading the Schema” isn’t sufficiently fine-grained to satisfy the requirement of uniform solution, while your own dialetheist solution does. On the other hand, on the level of abstraction at which the Schema operates, wouldn’t someone who denied the Existence component of Russell’s Paradox for nominalist reasons, the Existence component of the Liar Paradox on the basis of considerations derived from their favored views about the philosophy of language and so on be just as “unified” as the dialetheist, who, after wading through various arguments about the particulars of each case, embraced all three Schema components (Existence, Closure and Transcendence) in every case?

Yes, that would certainly be a uniform solution.  (I do not claim that the solution I propose is the only one such. Just that the orthodox views concerning the set-theoretic paradoxes and semantic paradoxes are not uniform.) The question, then, becomes how adequate a solution this would be. Simply to deny the existence of Omega in all cases is highly unorthodox, since it requires a denial of the existence of even some countable sets (in the case, e.g., of Berry’s paradox). If one denies the existence of all sets on nominalist grounds then one has to face the usual challenges of nominalism, and specifically the question of how to make sense of mathematics. I don’t know of any very satisfactory answer to that question.  (I’m not sure what is meant by the thought that a philosophy of language might provide ground for denying the existence of Omega in the case of the Liar paradox. However, if one is already committed to nominalism for other reasons, one hardly needs another reason.) There also remains the fact that various of the paradoxes can survive without the existence of Omega. The liar paradox is an example of such.

Q: You have argued in various places that Disjunctive Syllogism is not universally truth-preserving, because it has counter-examples–cases where P is both true and false, making (P v Q) and ~P true, but in which Q fails to be true. Given the importance of rejecting rules like Disjunctive Syllogism to your overall case for dialetheism (after all, a dialetheist who thought Disjunctive Syllogism *was* universally truth-preserving would be a trivialist!), it might seem to be a problem for your view that (a) the argument just sketched out relies on a distinction between false claims that are also true and false claims that are just false, but (b) as you are, of course, aware, many critics have pointed out that any phrase that one devises to express this distinction can be recycled in fresh paradoxes (e.g. “this sentence is just false and fails to be true”, etc.) Some dialetheists, like JC Beall, lean heavily on the vocabulary of acceptance and rejection to get around these sorts of problems. (For example, in “Spandrels of Truth,” he constantly uses the language of rejection to distinguish dialetheias from ordinary falsehoods.) This move is, however, not available to you, given your argument in “Doubt Truth To Be A Liar” that dialetheists should accept that the grounds for rational rejection and rational acceptance might sometimes overlap. One might think this concession deprives you of your last available tool for expressing the distinction needed for your argument against the validity of Disjunctive Syllogism. Do you see this as a problem?

This question needs to be spelled out in more detail. Why might one think that? Without knowing this, it is hard to address the question.  But here are some (maybe) relevant points.  The DS is invalid. This can be shown in the semantics given in IC by giving a simple counter-model, as is done there, and does not need the notion of rejection at all.  The machinery of being true only (true and not false) does indeed deliver paradoxes, but the machinery was never intended to be consistent. This does not invalidate the argument for the invalidity of IC. No less than JC, I have always employed the notion of rejection. (See IC, ch. 7.) And I still maintain that one cannot accept and reject something. (Go on, try it!)   The argument of DTBL ch. 6 does not show otherwise.  It shows that one can sometimes be in a situation where one ought to accept and reject. Normative dilemmas are a fact of life. And if one thinks that this one is not an acceptable dilemma, DTBL, p. 110 shows how to get out of it by taking certain normative claims to be defeasible.

Editor’s Note, the following was clarification for the previous question.

The worry is that, at least intuitively, the counter-model relies on a distinction between false statements that are also true and those that are not. (Indeed, in general the semantics of IC seem to rely on this distinction, but particularly crucially in this case.) If, in some case, one cannot express that a particular Q is ‘just’ untrue, then, having expressed that the relevant (P v Q) is true, that the P is both true and false and that the Q is false, one has left open the question of whether DS preserves truth in this instance. It is only a counter-example if one has ruled out Q’s truth.

Re: Rejection, the worry is not that you or any other dialetheist isn’t entitled to use rejection or hold (reasonably) that acceptance and rejection are, as a matter of individual psychology, mutually exclusive. The concern is rather that dialetheists like Beall (who, unlike you, seem to take ‘should be rejected’ and ‘should be accepted’ as necessarily mutually exclusive) sometimes seem to use rejection-talk as a something of a stand-in for the absent notion of ‘just false.’ Thus, for example, when Beall talks about ‘rejecting’ Curry sentences as a category (or, better yet, says they ‘are to be rejected’) presumably he isn’t making the fantastic claim that he has rejected all of them, but rather a normative claim about rationality.

All of this is, admittedly, pretty much a footnote to the question about your own views, but the point is this: Given your openness to rational dilemmas, you can’t use rejection language to distinguish statements that are both true and false from other kinds of false statements, and, for generally-agreed reasons, words like ‘just’ and ‘only’ won’t do either. Since you seem to need the distinction in order for DS to have counter-examples, is this a problem?

Editor’s Note, the following was the reply from Professor Priest.

The DS can be show to be invalid is the semantics of LP as follows. (The semantics has many presentations. Let us use the version in which evaluations are relations, R, between formulas and the values t and f.)

Consider the inference ~p, pvq / q. Take an interpretation where pRt, pRf, qRf, and it is not the case that qRt. By the truth and falsity conditions for negation and disjunction, (~p)Rt and (pvq)Rt. Hence there is an evaluation where the premises of the inference relate to t and the conclusion does not. Hence the inference is invalid.

Note that this argument does not invoke denial. Nor is it undercut if it turns out that there are formulas, A, such that ARt and it is not the case that ARt  - even if you could show by some argument (goodness knows what), that this held when A is the p in question. Deductive reasoning is, after all, monotonic. (Valid arguments are never made invalid by the addition of extra premises.)

Q: Your argument for the “classical re-capture” in “In Contradiction” relies on the notion that the statistical frequency of true contradictions is very low, and in particular that few statements that arise in ordinary contexts can reasonably be thought to be dialetheias. Elsewhere in the same book, however, you argue for a paraconsistent theory of change, whereby (a) as in standard tense logic, statements truth-values change over time, and more radically that (b) at any point where the subject of a statement is changing from being the way the statement asserts that it is to not being that way or vice versa, the statement is both true and false. (You formally express (b) as Zeno’s Principle.) Given that theory of change, and the fact that, as Heraclitus and Engels are quick to remind us, change is a constant, pervasive feature of practically all discernible reality, doesn’t it suddenly seem quite plausible that ordinary statements are dialetheic, not just in slightly contrived cases like contingent Liars or Kripke’s Nixon case, but in a wide variety of contexts? If I say “the cat is on the mat” while the cat is on the mat, won’t that statement be both true and false at the inevitable moment when the cat is in the process of departing from the mat? Won’t, indeed, a large, statistically significant number of ordinary statements be both true and false at any given time? (One might think that, given all this, the one domain of reliably contradiction-free statements would be the domain of statements about changeless things. Historically, perhaps, the most popular candidate for changeless truths would be the mathematical one, but of course, you postulate all sorts of contradictions there as well!) In light of all this, how can we be confident that the frequency of true contradictions is very low?

Interesting question, the issue of the statistical frequency of dialetheias is a sensitive one. Of course, we are not talking cardinality here. If there is one dialetheia, there is an infinite number. The question concerns, rather, their frequency in “ordinary arguments”. The account of change in IC does appear to put pressure on this. Note, though, that the contradictory statements in question are ones that describe an instantaneous state.  Thus, for example, when someone walks out of the room, the dialetheia occurs instantaneously. Normal arguments are not very often about instantaneous events.  The account of motion does not really change this matter. According to this, the contradictory states are, again, instantaneous (of the form: at time t, the object – or some point in it – is at point x).  Ordinary arguments, when they are about the world of change, tend to be about middle sized objects and their gross features, like whether Gaddafi is currently losing power in Libya: not an instantaneous matter at all. Actually, I think that a much more series challenge to the statistical claim is posed by the thought that when vague predicates are applied to borderline areas, the result is both true and false. Vague predicates are everywhere in ordinary reasoning.  IC does not raise this possibility at all, and I never used to bevery sympathetic to it. But I have become more so recently. Even here, though, most ordinary arguments would seem to be about definite cases. Gadaffi certainly is losing power in Libya at the moment, for example. Where reasoning about borderline cases is crucial, however – as in the discussion of sorites paradoxes – one may well want to suspend considerations of “the normal.”

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