David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
In the …rst part of this paper, the origins of modal-structuralism are traced from Hilary Putnam’s seminal article, "Mathematics without Foundations" (1967) to its transformation and development into the author’s modal-structural approach. The addition of a logic of plurals is highlighted for its recovery (in combination with the resources of mereology) of full, second-order logic, essential for articulating a good theory of mathematical structures. The second part concentrates on the motivation of large trans…nite cardinal numbers, arising naturally from the second-order machinery combined with an extendability principle on structures for set theories due independently to Zermelo (1930) and Putnam (in the paper just cited). The power of this is enhanced by a novel modal re‡ection principle recently introduced by the author. This is illustrated in detail with the …rst axiom of in…nity: After reviewing some of the trouble this basic classical axiom has caused for previous foundational programs, we show how it is derived easily using the re‡ection principle and a weak form of extendability for …nite structures. We conclude with some comparative remarks on how this improves on the closest set-theoretic analogue to the present proposal.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Geoffrey Hellman (2006). What is Categorical Structuralism? In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer 151--161.
Geoffrey Hellman (1988). The Many Worlds Interpretation of Set Theory. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:445-455.
Hellman Geoffrey (1996). Structuralism Without Structures. Philosophia Mathematica 4 (2):100-123.
Gabriel Uzquiano (2014). Mereology and Modality. In Shieva Kleinschmidt (ed.), Mereology and Location. Oxford University Press 33-56.
Francis Jeffry Pelletier & Bernard Linsky (2009). Russell Vs. Frege on Definite Descriptions as Singular Terms. In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of "on Denoting". Routledge
Michael Glanzberg (2001). Supervenience and Infinitary Logic. Noûs 35 (3):419-439.
Robert Goldblatt (2001). Quasi-Modal Equivalence of Canonical Structures. Journal of Symbolic Logic 66 (2):497-508.
Johan van Benthem, Giovanna D'Agostino, Angelo Montanari & Alberto Policriti (1998). Modal Deduction in Second-Order Logic and Set Theory - II. Studia Logica 60 (3):387-420.
Christopher Menzel (2014). Wide Sets, ZFCU, and the Iterative Conception. Journal of Philosophy 111 (2):57-83.
Johan Van Benthem, Giovanna D'Agostino, Angelo Montanari & Alberto Policriti (1998). Modal Deduction in Second-Order Logic and Set Theory: II. Studia Logica 60 (3):387 - 420.
John Martin Fischer & Neal A. Tognazzini (2010). Blame and Avoidability: A Reply to Otsuka. Journal of Ethics 14 (1):43 - 51.
Added to index2012-09-05
Total downloads36 ( #121,389 of 1,937,360 )
Recent downloads (6 months)5 ( #123,599 of 1,937,360 )
How can I increase my downloads?