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In Hamkins (Rev Symb Log 5(3):416–449, 2012) set theorist Joel David Hamkins uses considerations about forcing arguments, together with an analogy between set theory and geometry to motivate his set-theoretic multiverse program. I’ll argue that Hamkins develops the latter (familiar) analogy in an unusual way, that promises to motivate multiverse theory in particular (rather than merely some form of pluralism). He suggests what I’ll call a leveling up approach to mathematical pluralism which motivates distinctive features of his multiverse theory. However, I’ll question whether Hamkins’ multiverse proposal ultimately delivers leveling up. Then I’ll sketch a counterpossible counterfactual-based twist on Hamkins multiverse which does provide relevant leveling up.

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Hamkins’ Analogy Between Set Theory and Geometry: Pluralism by Leveling Up?

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    2025年

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  • Sharon Berry

摘要

In Hamkins (Rev Symb Log 5(3):416–449, 2012) set theorist Joel David Hamkins uses considerations about forcing arguments, together with an analogy between set theory and geometry to motivate his set-theoretic multiverse program. I’ll argue that Hamkins develops the latter (familiar) analogy in an unusual way, that promises to motivate multiverse theory in particular (rather than merely some form of pluralism). He suggests what I’ll call a leveling up approach to mathematical pluralism which motivates distinctive features of his multiverse theory. However, I’ll question whether Hamkins’ multiverse proposal ultimately delivers leveling up. Then I’ll sketch a counterpossible counterfactual-based twist on Hamkins multiverse which does provide relevant leveling up.