Abolishing Platonism in Multiverse Theories

Axiomathes 32 (2):321-343 (2020)
  Copy   BIBTEX

Abstract

A debated issue in the mathematical foundations in at least the last two decades is whether one can plausibly argue for the merits of treating undecidable questions of mathematics, e.g., the Continuum Hypothesis, by relying on the existence of a plurality of set-theoretical universes except for a single one, i.e., the well-known set-theoretical universe V associated with the cumulative hierarchy of sets. The multiverse approach has some varying versions of the general concept of multiverse yet my intention is to primarily address ontological multiversism as advocated, for instance, by Hamkins or Väätänen, precisely for the reason that they proclaim, to the one or the other extent, ontological preoccupations for the introduction of respective multiverse theories. Taking also into account Woodin’s and Steel’s multiverse versions, I take up an argumentation against multiversism, and in a certain sense against platonism in mathematical foundations, mainly on subjectively founded grounds, while keeping an eye on Clarke-Doane’s concern with Benacerraf’s challenge. I note that even though the paper is rather technically constructed in arguing against multiversism, the non-negligible philosophical part is influenced to a certain extent by a phenomenologically motivated view of the matter.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,088

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On Predictions and Explanations in Multiverse Scenarios.Keizo Matsubara - 2018 - In Antonio Piccolomini D’Aragona, Martin Carrier, Roger Deulofeu, Axel Gelfert, Jens Harbecke, Paul Hoyningen-Huene, Lara Huber, Peter Hucklenbroich, Ludger Jansen, Elizaveta Kostrova, Keizo Matsubara, Anne Sophie Meincke, Andrea Reichenberger, Kian Salimkhani & Javier Suárez (eds.), Philosophy of Science: Between the Natural Sciences, the Social Sciences, and the Humanities. Cham: Springer Verlag. pp. 43-54.
Beyond Falsifiability: Normal Science in a Multiverse.Sean M. Carroll - 2019 - In Dawid Richard, Dardashti Radin & Thebault Karim (eds.), Epistemology of Fundamental Physics: Why Trust a Theory? Cambridge University Press.
Multiverse Assumptions and Philosophy.James R. Johnson - 2018 - Filosofiâ I Kosmologiâ 20:8-17.
Does God So Love the Multiverse?Don N. Page - 2010 - In Melville Y. Stewart (ed.), Science and Religion in Dialogue. Oxford, UK: Wiley-Blackwell. pp. 380--395.
A naturalistic justification of the generic multiverse with a core.Matteo de Ceglie - 2018 - Contributions of the Austrian Ludwig Wittgenstein Society 26:34-36.
Platonism and anti‐Platonism: Why worry?Mary Leng - 2005 - International Studies in the Philosophy of Science 19 (1):65 – 84.
The Set-theoretic Multiverse as a Mathematical Plenitudinous Platonism Viewpoint.Sakaé Fuchino - 2012 - Annals of the Japan Association for Philosophy of Science 20:49-54.
The Level I Multiverse Is Not the Same as the Level III Multiverse.Alan McKenzie - 2017 - NSPIRE-HEP, High Energy Physics (HEP) Database, CERN Online Publications, EUROPE.
Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.

Analytics

Added to PP
2020-11-14

Downloads
17 (#765,400)

6 months
6 (#252,172)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Stathis Livadas
University of Patras (Alumnus)

Citations of this work

Against the countable transitive model approach to forcing.Matteo de Ceglie - 2021 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020. College Publications.

Add more citations

References found in this work

Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
The set-theoretic multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.

View all 26 references / Add more references