Author Archives: Peter Smith

Postcard from Cornwall

A photo taken along the South West Coast Path, as it runs to St Anthony Head in Cornwall. It’s a particularly beautiful stretch of the path, and a quick ferry ride takes us across the bay from the apartment we rent this time of … Continue reading

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Gerhard Gentzen’s Shorthand Notes

Springer have just published an exceptional volume that should quite certainly be in any university library that has any kind of logic collection. From the blurb of Saved from The Cellar – Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics: “Attempts … Continue reading

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Maddy on sets, categories, and the multiverse

Here are three large-scale issues. First, in what good sense or senses, if any, does ZFC provide a foundation for mathematics. Second, can category theory provide an alternative(?), or better(?) foundation for some or all mathematics? Third, should set theory … Continue reading

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Empty domains #3 – from Vej Kse

The following was posted as a comment to Empty domains #1 by Vej Kse — but I think it is particularly interesting and worth highlighting as a stand-alone post.  There is an elegant and natural (from a user’s perspective) way to allow … Continue reading

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Empty domains #2

Here is a long quotation from Oliver and Smiley in their Plural Logic, motivating their adoption of a universally free logic (i.e. one allowing empty domains and empty terms). If empty singular terms are outlawed, we are deprived of logic as a tool … Continue reading

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Empty domains #1

From wild mathematical universes back to nothing much at all: the question of empty domains in first-order logic. Not that I have anything very insightful to say:  but I want to get my mind clearer before committing myself to a … Continue reading

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New foundations?

This I find intriguing: Can we actually use [homotopy] type theory as the foundation for mathematics? That is, must we consider the objects of mathematics to “really” be built out of sets, with “types” just a convenient fiction for talking … Continue reading

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Nerdy annoyance

Lost a number of hours, too many, on a mysterious LaTeX problem. It turns out that fitch.sty (useful for setting Fitch-style proofs) loads a package mdwtab.sty which isn’t fully compatible with the standard tabular environment (useful for setting truth-tables). So when … Continue reading

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As good as it gets

We have been to some excellent local concerts over the last few months which I haven’t mentioned here (from the likes of Igor Levit, Rachel Podger and the English Concert, Cuarteto Casals, and a particularly on-form Academy of Ancient Music … Continue reading

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David Makinson’s Sets, Logic and Maths

As I go through chapters of my Introduction to Formal Logic, heavily rewriting them for the second edition (only scattered paragraphs are surviving unaltered from the first edition, and I’m adding wholy new chapters too), I’m occasionally pulling other introductory books … Continue reading

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