Who Shaves the Barber?

Gillian Russell: Logical Nihilism | WSB #53

May 22, 2019

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".

We conclude with a discussion of how we ought to respond to logical nihilism. We can throw up our hands and say "logic is dead!". We can call the problematic counterexamples illegitimate monsters and bar them from our vocabulary. Or — as Russell prefers — we can study under what conditions, or in what sorts of circumstances, certain logical regularities hold, even while knowing that none of them hold under all conditions.

For more on logical nihilism and Gillian Russell's other work, visit https://gillianrussell.net/research/

Visit http://williamnava.com for more info!

Special thanks to Jackie Blum for the podcast art and The Tin Box for the theme music.
Click here for the full list of episodes!

Topics discussed:

4:01 - "Social Spheres" and applying logic to social and political philosophy
11:38 - Intro: logic, nihilism, pluralism
30:22 - Reasoning, generality
45:06 - The "law" of non-contradiction
54:20 - Context-sensitive counterexamples
1:24:00 - Response: lemma incorporation
1:36:10 - Williamson's objection to non-classical logics