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The next Proof Society Seminar will take place on Monday 17 November 2025 at 14:00 CET. Our speaker will be Juliette Kennedy (https://www.mv.helsinki.fi/home/jkennedy/), from the University of Helsinki. Details can be found below.

How first order is first order logic?
Juliette Kennedy, University of Helsinki

Fundamental to the practice of logic is the dogma regarding the first order/second order logic distinction, namely that it is ironclad. Was it always so? The emergence of the set theoretic paradigm is an interesting test case. Early workers in foundations generally used higher order systems in the form of type theory; but then higher order systems were gradually abandoned in favour of first order set theory—a transition that was completed, more or less, by the 1930s.

In this talk I will look at first order logic from various points of view, arguing that the distinction between first order and higher order logics, such as second order logic, is somewhat context dependent. From the philosophical or foundational point of view this complicates the picture of first order logic as a canonical logic.

The Proof Society Seminar (https://www.proofsociety.org/proof-society-seminar/) is the official seminar of the Proof Society (https://www.proofsociety.org/), and it presents talks by leading researchers from all areas of proof theory. Everyone who is interested in the subject is warmly invited to attend! The talks take place online via Zoom, usually on Mondays, approximately once per month. They start at 13:00 UTC and may last up to 75 minutes plus questions.

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