Abstract
This work examines a number of arguments to the effect that quantification requires identity of the objects that are quantified over; the arguments concern the domain of quantification, the range of quantifiers, the collapse of the existential and the universal quantifiers, and the intelligibility of quantification. The central role of identity in quantification is identified in each case. Also considered is quantification in non-classical contexts, and it is argued that even in logics and set theories that supposedly do not demand identity for quantification, identity is still presupposed. Along the way, some recent challenges to this overall approach are considered.
For Décio Krause,
who inspires all of us
to look deeper and further.
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Acknowledgements
It is a pleasure to dedicate this paper to Décio Krause, who for years has patiently heard and carefully responded to my concerns about identity and quantification while we collaborated on a number of related projects. He has been throughout a model of intellectual honesty, curiosity and insight, insisting on the importance of questioning deeply held assumptions and not taking anything for granted. His work is endlessly stimulating. On so many occasions, I randomly opened a page of Identity in Physics (which he wrote with Steven French) and after reading just a few paragraphs had to stop to reflect on and engage with the abundance of fresh and perceptive ideas that his work is invariably so full of. A great friend and wonderful philosophical interlocutor, he inspired me and generations of philosophers and logicians to do better and go further—and I very much look forward to our many discussions, collaborations and exchanges ahead.
For particularly helpful conversations on the issues examined in this paper, my thanks go to Ali Abasnezhad, Jonas Arenhart, Jody Azzouni, Newton da Costa, Steven French, Norbert Gratzl, Andreas Kapsner, Décio Krause, Chris Menzel, Lavinia Picollo, and David Ripley.
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Bueno, O. (2023). Identity and Quantification. In: Arenhart, J.R.B., Arroyo, R.W. (eds) Non-Reflexive Logics, Non-Individuals, and the Philosophy of Quantum Mechanics. Synthese Library, vol 476. Springer, Cham. https://doi.org/10.1007/978-3-031-31840-5_9
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