In Defense of Quantifier Generalism: Holism and Infinitary Resources
DOI:
https://doi.org/10.12775/LLP.2025.024Słowa kluczowe
quantifier generalism, algebraic generalism, individuals, holism, infinitary quantification, arithmetic, non-standard modelsAbstrakt
According to quantifier generalism, all facts about the world can be expressed in a language devoid of proper names, whose only referential expressions are variables bound by quantifiers. This paper considers and repels some of the recently raised objections against this position. The central part of the paper presents a critical analysis of the claim advanced by Ted Sider that quantifier generalism is inevitably holistic and therefore requires unusually strong expressive resources when applied to infinite domains. Using an example of arithmetic, it is shown that there is a simple generalistic description of natural numbers that does not resort to any infinitary conjunctions or quantifiers. Such generalistic accounts also exist in many cases involving continua (such as descriptions of matter distribution in a continuous space). Moreover, these accounts are arguably superior to their individualistic counterparts due to their parsimony. In addition to that, Sider’s argument alleging that generalism cannot account for the difference between non-isomorphic models of arithmetic is repelled.
Bibliografia
Belot, G. (1995), “New work for counterpart theorists: Determinism”, The British Journal for the Philosophy of Science, 46: 185–195.
Belot, G. (2018), “Fifty Million Elvis Fans can’t be wrong”, Noûs, 52: 946–981.
Boolos, G. S, and R. C. Jeffrey (1980), Computability and Logic, Second edition, Cambridge: Cambridge University Press.
Cowling, S. (2015), “Non-qualitative properties”, Erkenntnis, 80: 275–301.
Dasgupta, S. (2009), “Individuals: An essay in revisionary metaphysics”, Philosophical Studies, 145: 35–67.
Dasgupta, S. (2016), “Can we do without fundamental individuals? Yes”, pages 7–23 in E. Barnes (ed.), Current Controversies in Metaphysics, New York: Routledge.
Diehl, C. (2018), “A language for ontological Nnihilism”, Ergo, 5(37): 971–996.
Glick, D. (2016), “Minimal structural essentialism. Why physics doesn’t care which is which”, pages 207–225 in A. Guay and T. Pradeau (eds.), Individuals Across the Sciences, Oxford: Oxford University Press.
Glick, D. (2020), “Generalism and the metaphysics of ontic structural realism”, The British Journal for the Philosophy of Science, 71: 751–772.
Kment, B. (2012), “Haecceitism, chance and counterfactuals”, Philosophical Review, 121(4): 573–609.
Kuhn, S. T. (1983), “An axiomatization of predicate functor logic”, Notre Dame Journal of Formal Logic, 24(2): 233–241.
Plate, J. (2022), “Qualitative properties and relations”, Philosophical Studies , 179(4): 1297--1322. DOI: https://doi.org/10.1007/s11098-021-01708-y
Pooley, O. (2006), “Points, particles, and structural realism”, pages 83–120 in D. Rickles, S. French and J. Saatsi (eds.), The Structural Foundations of Quantum Gravity, Oxford: Oxford University Press.
Quine, W. v. O. (1960), “Variables explained away”, Proceedings of the American Philosophical Society, 104(3): 343–347.
Quine, W. v. O. (1976), “Algebraic logic and predicate functors”, pages 283–307 in The Ways of Paradox and Other Essays, Second Edition, Cambridge Mass.: Harvard University Press.
Sider, T. (2020), The Tools of Metaphysics and the Metaphysics of Science, Oxford: Clarendon Press.
Stachel, J. (2002), “ ‘The relations between things’ versus ‘the things between relations’: The Deeper meaning of the hole argument”, pages 231–266 in D. Malament (ed.), Reading Natural Philosophy. Essays in the History and Philosophy of Science and Mathematics, Chicago: Open Court.
Svenonius, L. (1960), Some Problems in Logical Model Theory, Library of Theoria, Lund.
Turner, J. (2011), “Ontological nihilism”, pages 3–52 in K. Bennett and D. W. Zimmerman (eds.), Oxford Studies in Metaphysics, Vol. 6, Oxford: Oxford University Press.
Turner, J. (2016), “Can we do without fundamental individuals? No”, pages 24-34 in E. Barnes (ed.), Current Controversies in Metaphysics, New York: Routledge.
van Fraassen, B. (1991), Quantum Mechanics: An Empiricist View, Oxford: Clarendon Press.
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Prawa autorskie (c) 2025 Tomasz Bigaj
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