Tag Archives: Oslo

Forcing is simply the iterative conception undertaken with multivalued logic, ForcingFest, Oslo, June 2024

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I shall be speaking at the ForcingFest meeting at the University of Oslo, 21 June 2024.

Abstract. I will explain how the forcing construction can be seen as a direct implementation of the iterative conception, giving rise to the cumulative hierarchy, but undertaken in the context of multivalued logic. The shape of the logic that is available in effect enables a certain constructive interference of the truth values in such a way that can affect the truth judgements. The core utility of forcing arises from the fact that we can often control these consequences by making a careful choice of the logic to be used, thereby controlling the truth values even of natural set-theoretic statements such as the continuum hypothesis.

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The continuum hypothesis could have been a fundamental axiom, CFORS Grad Conference, Oslo, June 2024

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I shall be giving a keynote lecture for the CFORS Grad Conference at the University of Oslo, 19-20 June 2024.

Abstract. I shall describe a simple historical thought experiment showing how our attitude toward the continuum hypothesis could easily have been very different than it is. If our mathematical history had been just a little different, I claim, if certain mathematical discoveries had been made in a slightly different order, then we would naturally view the continuum hypothesis as a fundamental axiom of set theory, one furthermore necessary for mathematics and indeed, indispensable for calculus.

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The paper is now available at How the continuum hypothesis could have been a fundamental axiom.

Varieties of potentialism, Oslo, April 2023

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This will be an online talk for the Infinity & Intentionality project of Øystein Linnebo in Oslo, 25 April 2023. Zoom link available from the organizers.

Abstract: I shall survey the surprisingly enormous variety of potentialist conceptions, even in the case of arithmetic potentialism, spanning a spectrum from linear inevitabilism and other convergent potentialist conceptions to more radical nonamalgamable branching-possibility potentialist conceptions. Underlying the universe-fragment framework for potentialism, one finds a natural modal vocabulary capable of expressing fine distinctions between the various potentialist ideas, as well as sweeping potentialist principles. Similarly diverse conceptions of ultrafinitism grow out of the analysis. Ultimately, the various convergent potentialist conceptions, I shall argue, are implicitly actualist, reducing to and interpreting actualism via the potentialist translation, whereas the radical-branching nonamalgamable potentialist conception admits no such reduction. 

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Infinite draughts and the logic of infinitary games, Oslo, November 2021

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This will be a talk 11 November 2021 for the Oslo Seminar in Mathematical Logic, meeting online via Zoom at 10:15am CET (9:15am GMT) at Zoom: 671 7500 0197

Abstract. I shall give an introduction to the logic of infinite games, including the theory of transfinite game values, using the case of infinite draughts as a principal illustrative instance. Infinite draughts, also known as infinite checkers, is played like the finite game, but on an infinite checkerboard stretching without end in all four directions. In recent joint work with Davide Leonessi, we proved that every countable ordinal arises as the game value of a position in infinite draughts. Thus, there are positions from which Red has a winning strategy enabling her to win always in finitely many moves, but the length of play can be completely controlled by Black in a manner as though counting down from a given countable ordinal. This result is optimal for games having countably many options at each move—in short, the omega one of infinite draughts is true omega one.

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