Graham Priest's Contradictions-in-the-World: Legal Inconsistencies and Zeno's Arrow

The following is a commentary on a interview (see video above) of the philosopher and logician Graham Priest conducted by Alex Malpass (who's a Research Fellow at the University of Bristol). The interview tackles such things as the logical paradoxes (specifically Zeno's arrow), quantum mechanics, Hegel and legal inconsistencies.

i) A Legal Contradiction or Inconsistency?

ii) Zero's Arrow, Other Paradoxes and Quantum Mechanics

iii) Priest's Fusion of Epistemology, Philosophy of Science and Logical Pluralism

A Legal Contradiction or Inconsistency?

It's very hard to accept Graham Priest's example (at 55 minutes and 14 seconds) of dialetheism-in-practice (as it were). He cites the the case of the Australian law on property owners being given the vote and aborginess being denied the vote.

So what happened when an aborigine gained property? He became an aborigine who could also vote. Thus Priest sees this as a dialetheic contradiction. Yes, it was certainly an inconsistency in the law. But was it also a contradiction-in-the-world?

Priest seems to dismiss this law-world distinction as just an example of different ways of viewing what "the world" is. He says:

"That really depends on what you mean by 'the world'.”

Priest admits, however, that this legal example is a "midway" case of dialetheism. But what does that mean?

Zeno's Arrow, Other Paradoxes and Quantum Mechanics

At 59:57 Priest offers us a very cogent and clear explanation of the "paradox of motion"; using Zeno's arrow and Hegel's position as examples. (See Graham Priest on Hegel's position on motion here.) The problem is that it's difficult to see how Priest ties all this to his dialetheism and he doesn't really say (at least not in this videoed interview). He simply explains and describes Zeno's arrow and leaves it (more or less) at that... That is, except for this statement:

“To be in motion is precisely to be in a contradictory state. It's to be here and not here at the same time.”

Who knows, perhaps Zeno's arrow is also a case of dialetheist contradiction and therefore not actually about the world. It may, instead, be about how we think about - or even perceive - the world. Here again we enter the world of epistemology – even if applied to a case which has clear logical implications.

One thing that can be said about Priest's dialetheism is that it's dependent on paradoxes That's ironic because Priest states that fellow dialetheists have concentrated too much on what he calls “self-referential paradoxes” - paradoxes which are very unlike Zeno's arrow. It's hardly a surprise, then, that a logic which “embraces contradictions” should rely on paradoxes to back it up (as it were).

Priest also relies (if to a lesser extent) on quantum mechanics to defend his dialetheism. That is, he mentions quantum mechanics a lot in his work. Yet, at the same time, Priest doesn't seem to believe that quantum mechanics does much work for (his) dialetheism. (At least he hints at that in the video above.) Though, again, why does Priest keep on bringing up aspects of quantum mechanics if it's (more ore less) beside the point when it comes to dialetheism?

If we return to paradoxes.

One can either take some kind of deflationary view of the paradoxes or say that they don't do much - or any - work for dialetheism. One thing is for sure, however, and this is that no one is going to solve (if that's the right word) the paradoxes any time soon – least of all a critic of dialetheism. So, again, it needs to be made clear what exactly the relation is between the paradoxes Priest cites and his own dialetheism.

Priest's Fusion of Epistemology, Philosophy of Science and Logical Pluralism

All Priest's examples of dialetheic contradictions are really about human perceptions of - or attitudes towards - the world, not the world itself. They also concern inconsistencies in scientific and legal theories about the world. This makes dialetheism both a position in epistemology and in the philosophy of science. If all that is the case, then surely dialetheism isn't a "robust ontology" which happily embraces contradictions-in-the world after all.

Of course Priest's next move may be to question this possibly bogus distinction between the world and our statements about - and knowledge of - the world. Actually, he does question this distinction and he even uses the term “social constructionism” . This is a (kind of) anti-realist (if not a social-constructionist) move. Still, most/all anti-realists don't accept that there are "true contradictions" in the world!

Priest also seems to endorse a position named “logical pluralism” in the video. This is almost parallel to Ludwig Wittgenstein's notion of language games. That is, Priest argues that different logics can be applied to different domains or problems. And that must also mean that certainly logics can be misapplied to certain domains or problems. (Though it may also be the case that the same logic can be applied to different domains without thereby creating any problems.) Priest himself says:

“You need one kind of logic to reason about one kind of thing and a different kind of logic to reason about something else.”

He then gives us some examples:

“You might want to use classical logic to reason about the physical world; intuitionist logic to reason about mathematical constructions; and paraconsistent logic to reason about truth.”

It must now be said that Priest is critical of what may be called naïve logical pluralism; just as he's critical of too-easy uses of quantum mechanics to back up (his) dialetheism. Nonetheless, Priest doesn't (completely) dismiss logical pluralism or the relevance of quantum mechanics to dialetheism. That is, he defends logical pluralism (in this video at least) and also frequently cites quantum mechanics (in his papers, books, seminars, etc.) to defend dialetheism.

So does Priest have a dialetheic position on the relevance of logical pluralism and quantum mechanics to dialetheism itself? That is:

Does Graham Priest believe that logical pluralism and quantum mechanics both are and are not relevant to dialetheism?

In a superficial sense, anyone can accept the position just stated. That is:

Logical pluralism and quantum mechanics are relevant to dialetheism in some respects (or ways) and they are not relevant to dialetheism in other respects (or ways).

But that isn't dialetheism! The dialetheic position must surely be this:

Logical pluralism and quantum mechanics are and are not relevant to dialetheism in exactly the same respects (or ways).

So to recap.

All in all it can be said that Priest fuses positions in epistemology, the philosophy of science and logical pluralism in order to back up (or defend) his dialetheism.