On Logical Nihilism

I just encountered this great paper by Dr. Russell.

She's one of my favorite contemporary philosophers (along with a former classmate of mine Renée Jorgensen and Martha Nussbaum)! Fun fact: all taught here in the Midwest - apparently the Midwest United States is fast becoming one of the hottest spots to do philosophy ascending even against the influence of the East Coast!

A significant portion of her work is centered on the consequences of Skepticism about Logic, counter-examples to the (supposedly) logical validities, and the untenability of logic as a cognitive project. Turns out a lot of my interests align with those topics and considerations and I wanted to briefly discuss some fun intersections below! Note that she is not, as far as I understand it, a committed Logical Nihilist - she explores the tenability/correctness of that position.

Does Logical Pluralism Entail Logical Nihilism?

We can easily see how one might arrive at Logical Nihilism from the other (particularly if one accepts the traditional foundationalist conception of knowledge and justification):

1. Which logic is justified in Metalogical Proof? If we can't definitely rule on this, then logic seems like it's out of luck.
2. There's a genuine question about what decision procedure we might justifiably employ in each domain or area of inquiry (if we can at all) to determine the proper logic to use. (The cliche, "who decides?" actually seems to ring quite relevantly here.)
3. Since foundational concepts within the field of logic (and philosophy) rely on some implicit notion of deduction, we seem to have difficulty even getting to logic (foundationally-speaking) if those concerns are correct.

Hopefully, all is not doom and gloom!

Does Logical Skepticism Entail Logical Nihilism?

Recollect Crispin Wright's notion of warranted acceptance:

1. Wright argues that we're wrong in casting all Epistemic notions in Justification-talk, that people really deploy much weaker epistemic notions in real life and that philosophers have been talking passed this apparent fact.
2. This parallels Leibowitz and my concerns about God-talk in theology - e.g. - that philosophers are fixated on an irrelevant notion and/or conception of the Divine and so we needn't be fearful about the spectre of Skepticism.

Skeptical arguments appear to have schematic weaknesses:

3. They require very stringent notions surrounding certitude, deduction (which unfortunately since we're in the domain of logic we're saddled with - we can't easily retreat to Fallibilism in the philosophy of logic - this makes logic an attractive target for the Phyronnian), and Justification.
4. They must erect a specific conception to build up and then tear down (e.g. - infallibilism about justification coupled with foundationalism). If they are right, it's possible their arguments can still be dismissed as mere Straw Men or Red Herrings (that their arguments target an irrelevant concept anyway).

Why would logic be any different as human activity than say natural science (with respect to epistemic warrant)? That it's central to human inquiry doesn't necessarily entail that the standards of Justification are any higher.

More Forks in the Philosophical Road?

I wonder if there are alternatives to Logical Nihilism:

1. For instance, I'm a big fan of Gödel who famously predicted that reason will go in every direction. Logical Pluralism seems quite appropriate given those insights.
2. Per the above, some work of mine concerns how multiple logics interact - perhaps our conception about the "edifice" or hierarchy of logics (mostly inspired by Tarski's attempts to outmaneuver the Liar Paradox) our misguided. Perhaps, they are individually limited in some fashion but collectively resistant to certain skeptical worries.
3. What if logic is just shorn of its classical moorings at long last? (Eternalism, Universalism, A Priori, Two-Valued, etc.)
4. Is Restrictionism the natural answer to questions about the General Universality of logic? Most supposedly universal logical laws are really just ceteris parabis conditions, caveated, or qualified by some constraints? Euclid's axioms have folded into Hyperbolic Geometry, Quantum Theory into Special Relativity, and so on. Axioms and universal laws apply to certain regions of thought afterall. We see parallels in computer science (restricted logic gates) and the obvious insight that if Q is a tautology, so is P implies Q (where P can be a restriction statement). So, Q being a tautology entails that restricting Q is also a tautology. Therefore, if one believes that a logical validity or rule Q is just that (e.g. - it's analytic, a tautology, etc.), then it follows that one is committed to the restriction of that rule (which is just Restrictionism, the view). There are still universal generalizations on such a view, they are just conditioned (having a restriction clause).

Of course, even if these don't result in Logical Nihilism, each represents a radical break with the past. The end of the influence of Classical Antiquity over mathematics, perhaps? And we would be very Nietzschean here, going after the marble statutes with our mallets.