David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Bulletin of Symbolic Logic 12 (1):60-99 (2006)
In this paper, we investigate (1) what can be salvaged from the original project of "logicism" and (2) what is the best that can be done if we lower our sights a bit. Logicism is the view that "mathematics is reducible to logic alone", and there are a variety of reasons why it was a non-starter. We consider the various ways of weakening this claim so as to produce a "neologicism". Three ways are discussed: (1) expand the conception of logic used in the reduction, (2) allow the addition of analytic-sounding principles to logic so that the reduction is not to "logic alone" but to logic and truths knowable a priori, and (3) revise the conception of "reducible". We show how the current versions of neologicism fit into this classification scheme, and then focus on a kind of neologicism which we take to have the most potential for achieving the epistemological goals of the original logicist project. We argue that that the "weaker" the form of neologicism, the more likely it is to be a new form of logicism, and show how our preferred system, though mathematically weak, is metaphysically and epistemogically strong, and can "reduce" arbitrary mathematical theories to logic and analytic truths, if given a legitimate new sense of "reduction".
|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
Otávio Bueno, Christopher Menzel & Edward N. Zalta (2013). Worlds and Propositions Set Free. Erkenntnis (4):1-24.
Enrico Martino & Massimiliano Carrara (2010). To Be is to Be the Object of a Possible Act of Choice. Studia Logica 96 (2):289-313.
Similar books and articles
Otavio Bueno (2001). Logicism Revisited. Principia 5 (1-2):99-124.
Patricia A. Blanchette (1994). Frege's Reduction. History and Philosophy of Logic 15 (1):85-103.
Kevin C. Klement, Gottlob Frege. Internet Encyclopedia of Philosophy.
José Ferreiros (1997). Notes on Types, Sets, and Logicism, 1930-1950. Theoria 12 (1):91-124.
Alexander Bird (1997). The Logic in Logicism. Dialogue 36 (02):341--60.
Bird Alexander (1997). The Logic in Logicism. Dialogue 36:341–60.
Rafal Urbaniak (2010). Neologicist nominalism. Studia Logica 96 (2):149-173.
Øystein Linnebo (2003). Frege's Conception of Logic: From Kant to Grundgesetze. Manuscrito 26 (2):235-252.
Added to index2009-01-28
Total downloads35 ( #50,473 of 1,102,977 )
Recent downloads (6 months)9 ( #24,626 of 1,102,977 )
How can I increase my downloads?