Gillian Russell: Logical Nihilism | Who Shaves the Barber? #53

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Gillian Russell

In recent years, philosophers have debated the question of logical pluralism: the view that there is more than one correct logic (see my interview with Greg Restall on this very issue). The idea, roughly, is that which putative logical laws hold depends on what sorts of “cases” we take logic to be about; different kinds of cases yield different (but equally legitimate) logics. A common logical monist objection is to say that a form of argument is only a logical law if it applies in all cases. If this is true, it raises the question: what argument forms do hold in all cases? At this point in the debate, a third position becomes viable, defined by the answer: none.

Gillian Russell, a philosopher of language and logic, argues both that applying in all cases is necessary for qualifying as a logical law; and that no argument form applies in all cases. As such, she believes there are no logical laws. Much of our discussion surrounds her claim that no argument form applies to all cases. Is this really true even of the law of non-contradiction, the “law” that says that ‘A and not-A’ can never be true? Of conjunction elimination (‘A and B’ entails ‘A’)? Of identity (‘A’ entails ‘A’)? Russell runs through purported counterexamples to these laws; what’s more, she illustrates a method for conjuring counterexamples to any proposed “law”.

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Dialetheism: From Language to Reality

A physical contradiction?

I recently published a post in defense of dialetheism. I argued that in the case of statements about “man-made” states of affairs, it is obvious that some contradictions are true. For example, the law can easily contradict itself in such a way that a statement about what is legally mandated be a true contradiction. I invented “Timmy the Square Circle” to show that, similarly, there can be true contradictions about fictional characters. If this doesn’t seem intuitively obvious, read that post before this one.

The concluding paragraph included this teaser:

It is perhaps now tempting to draw a sharp line: the world of man-made ideas allows for true contradictions, reality doesn’t. However, this line is not so sharp.

If we grant that there are true contradictions about what is made up, does this tell us anything about whether there are true contradictions about objective reality? To say there are is a stronger, and intuitively harder to swallow, version of dialetheism. As we’ll see, however, there is no way to say anything about anything without talking, in part, about the man-made. This inescapable fact leaves open the possibility of true contradiction in claims about the physical world, even if it’s the case that the physical world itself, independent of our descriptions of it, cannot be contradictory.

Conceptual reality: Liar and Sorites paradoxes

We first need to establish that there are different “levels” of objective reality, and accepting a contradiction in one level may be much more counterintuitive than in another level.…

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The Easy Case for Dialetheism: Timmy the Square Circle and Divaltopian Law

Dialetheism is the view that some contradictions are true. Put another way, dialetheists claim that there are propositions that are both true and false at the same time and in the same respect.

For many people, this is plain crazy. Others find it extremely counterintuitive but will grant it because they’ve heard quantum mechanics proves it. Others still may suspect it is a desperate response to certain logical paradoxes, such as the Liar.

I wish to argue that all of this is quite beside the point. I don’t understand quantum mechanics (at all), but I would be surprised if there were really no way to account for experimental data without recourse to true contradictions. I’m (somewhat) better versed in debates about logic. I can tell you with confidence: the paradoxes have plenty of coherent solutions. Philosophers disagree primarily on the relative costs and benefits of these solutions. If dialetheism were truly incoherent and demonstrably impossible, we wouldn’t be backed into it: cheaper options than insanity are for sale.

There is a much simpler reason to be a dialetheist: despite initial appearances, it is intuitively compelling and even quite obviously true. We need no special training in physics or logic to see this.

Before getting on with the argument, a quick clarification about a misinterpretation of dialetheism that I encounter alarmingly often: dialetheism is the view that there is at least one true contradiction. It is not the view that all contradictions are true. That view is actually nuts. For example, that my name is William Nava is only true, it is not also false.…

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