Benedict Eastaugh

I realise editors need a shorthand for encouraging authors to polish their language but this can be done without using nativist language. Some of us who learned English later in life are bigger snobs about it than many native speakers. Let’s just encourage attention to clarity of expression.

A precise result here is: The statement that there exists an ultrafilter on every countable algebra of sets of natural numbers is Weihrauch equivalent to the jump of weak König's lemma.

I suppose I worry that readers might see the word 'theory' associated with ultrafilters and come away with the mistaken impression that these are things we can reason with, rather than objects which are in general non-computable.

Also unfortunate not to have any mention of computability-theoretic issues, although the axiom of choice is discussed. The existence of ultrafilters for Lindenbaum–Tarski algebras of countable languages doesn't require choice, and in fact is provable in a system conservative over PA.

I read the abstract and wondered why a journal was publishing results we'd known since the 1920s (ultrafilters) or the 1950s (ultraproducts), but then I realised it was in Philosophy Compass. Shame not to have anything on measurable cardinals, though!

Mangraviti also has a paper in the AJL on Plumwood's "liberation argument" against classical mathematics which you might find interesting. doi.org/10.26686/ajl...

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Forms of constructivism are also widespread amongst computer scientists. It's just that they usually don't bother to make the accompanying metaphysical or epistemological assertions, since their practice is by its nature restricted to computable functions.

That being said, the point about conservative reappropriation on page 2211 is well taken. A classic example might be Kreisel's unwinding programme, which aimed at mathematical goals (e.g. finding explicit bounds) through constructivising prima facie non-constructive mathematical proofs.

The Grundlagenstreit between Hilbert and Brouwer seems like such a natural case study that I'm a little surprised it wasn't addressed more fully. Hilbert was certainly very worried about the destabilising effect Brouwer seemed to be having.

It's not clear to me how much destabilisation is required in order for a math kind to become a critical math kind. Paraconsistent mathematics clearly doesn't qualify, since this is just a hobby of philosophers. Intuitionism might do.

Mangraviti's conception in the Erkenntnis paper of a critical math kind is a success term: "a math kind is a critical math kind relative to a given society if and only if its practitioners collectively destabilize one or more core elements of the dominant mathematics ideology in that society".

Mangraviti also has a paper in the AJL on Plumwood's "liberation argument" against classical mathematics which you might find interesting. doi.org/10.26686/ajl...

Newly revised: the SEP entry on Modularity of Mind, by me and Philip Robbins. It’s got a whole new section on the role of modularity in debates about the border between perception and cognition! #philsky #philosophy

YouTube video by MrAnagram9 Varzi on Holes

Varzi was interviewed by CNN at the time. Obviously they cut the more philosophically subtle and interesting parts of the interview, but it’s amusing nonetheless. youtu.be/2nu-7asEy0U?...

Along with many excellent colleagues, I signed this letter in support of Fiona Hill, in response to a letter from some unsurprising figures, attacking her. Text in screenshots for those who don't want to give the Guardian their money or data: www.theguardian.com/politics/202...

Does Schuringa engage at all with Reisch's 2005 book? His thesis (which I take it you allude to) that the Cold War "made [logical empiricism's social and cultural] agenda impossible and effectively forced the discipline to take [an] apolitical, highly abstract form" seems quite central here.

This is one for @lastpositivist.bsky.social really, but I was surprised by the limited discussion of the Vienna Circle, in which (modulo your point about the retroactive construction of analytic philosophy) a recognisably analytic style of philosophy was linked to sociopolitical issues.

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Higher-order metaphysics appears fashionable nowadays. Not sure if anyone's written on this but there seems to be an obvious tension between conceivability implying possibility, and higher-order metaphysics, since completeness fails for second-order logic.

I guess the counterpart in metaphysics would be the view that conceivability implies possibility, often traced back to Hume. There's quite a bit of contemporary work on this. One starting point might be Yablo's 1993 paper 'Is conceivability a guide to possibility?'. doi.org/10.2307/2108...

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Synthese has a cfp for a collection on Feminist Logic, edited by Sara Ayhan

link.springer.com/collections/...

Because justifying e.g. a precise set of rules in terms of capturing a consequence relation does in fact require some mathematical axioms: logic is, in this sense, mathematically entangled (or so I claim! But others disagree here). #PhilosophyMatters

All of these questions involve presuppositions in some sense. For example, it might seem that merely reasoning in accordance with (some) logic does not presuppose anything. But when we start inquiring about the nature and correctness of that logic, the picture starts to look different.

Then we also have questions like whether logic is normative or descriptive; whether there is a unique correct logic (monism) or if different rules should apply in different contexts (pluralism); and whether logic is just like any other science and to be justified as such (anti-exceptionalism).

Another (which I covered) is the mathematical presuppositions (axioms) necessary to show that a certain system of logic is adequate, in the sense that the deductive system is sound and complete relative to a (presupposed!) notion of logical consequence.

For example, one type of presupposition is the content supplied by a particular domain (physics, mathematics, literature, politics, etc.). On a widely-accepted understanding of logic, it has no special content (it is general or universal) and thus has no presuppositions in that sense.

I didn't imagine so! But there are so many kinds of presupposition potentially in play here that it's hard to say something useful without being more specific.

XV—On Consistency and Existence in Mathematics Abstract. This paper engages the question ‘Does the consistency of a set of axioms entail the existence of a model in which they are satisfied?’ within the

For more on this see Walter Dean's paper for the Aristotelian Society doi.org/10.1093/aris... and my Stanford Encyclopedia of Philosophy entry on reverse mathematics plato.stanford.edu/entries/reve... #PhilosophyMatters