David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Erkenntnis (S2):1-21 (2013)
The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were neutralized by the possibility of studying all these alternative logics within an agreed metalogical framework, typically that of first-order logic with set theory. In effect, metalogic is given the role of neutral arbiter. The paper will consider a variety of examples in which deep logical disputes re-emerge at the meta-level. One case is quantified modal logic, where some varieties of actualism require a modal meta-language (as opposed to the usual non-modal language of possible worlds model theory) in order not to make their denial of the Barcan formula self-defeating. Similarly, on some views the intended model theory for second-order logic can only be given in a second-order metalanguage—this may be needed to avoid versions of Russell’s paradox when the first-order quantifiers are read as absolutely unrestricted. It can be shown that the phenomenon of higher-order vagueness eventually forces fuzzy logical treatments of vagueness to use a fuzzy metalanguage, with consequent repercussions for what first-order principles are validated. The difficulty of proving the completeness of first-order intuitionistic logic on its intended interpretation by intuitionistically rather than just classically valid means is a more familiar example. These case studies will be discussed in some detail to reveal a variety of ways in which even metalogic is metaphysically contested, substantial and non-neutral
|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
Timothy Williamson (2007). The Philosophy of Philosophy. Blackwell Pub..
Timothy Williamson (1994). Vagueness. Routledge.
Timothy Williamson (2013). Modal Logic as Metaphysics. Oxford University Press.
Hartry H. Field (2008). Saving Truth From Paradox. Oxford University Press.
W. V. Quine (1986). Philosophy of Logic. Harvard University Press.
Citations of this work BETA
Timothy Williamson (2013). Response to Cohen, Comesaña, Goodman, Nagel, and Weatherson on Gettier Cases in Epistemic Logic. Inquiry 56 (1):77-96.
David Liggins (2016). Grounding and the Indispensability Argument. Synthese 193 (2):531-548.
Jeremy Goodman (2013). Inexact Knowledge Without Improbable Knowing. Inquiry 56 (1):30-53.
Similar books and articles
Andrew Bacon (2013). Non-Classical Metatheory for Non-Classical Logics. Journal of Philosophical Logic 42 (2):335-355.
Minghui Ma (2010). Toward Model-Theoretic Modal Logics. Frontiers of Philosophy in China 5 (2):294-311.
Alexander Paseau (2010). Pure Second-Order Logic with Second-Order Identity. Notre Dame Journal of Formal Logic 51 (3):351-360.
Vilém Novák (1987). First-Order Fuzzy Logic. Studia Logica 46 (1):87 - 109.
Giangiacomo Gerla & Virginia Vaccaro (1984). Modal Logic and Model Theory. Studia Logica 43 (3):203 - 216.
Peter Fritz (2013). Modal Ontology and Generalized Quantifiers. Journal of Philosophical Logic 42 (4):643-678.
Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity. Part I: Nineteenth-Century Axiomatics to Twentieth-Century Metalogic. History and Philosophy of Logic 23 (1):1-30.
Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-First-Century Semantics. History and Philosophy of Logic 23 (2):77-94.
G. Aldo Antonelli & Richmond H. Thomason (2002). Representability in Second-Order Propositional Poly-Modal Logic. Journal of Symbolic Logic 67 (3):1039-1054.
Kosta Došen (1992). Modal Logic as Metalogic. Journal of Logic, Language and Information 1 (3):173-201.
Roman Kontchakov, Agi Kurucz & Michael Zakharyaschev (2005). Undecidability of First-Order Intuitionistic and Modal Logics with Two Variables. Bulletin of Symbolic Logic 11 (3):428-438.
Steve Awodey & Erich H. Reck, Completeness and Categoricity, Part I: 19th Century Axiomatics to 20th Century Metalogic.
Steve Awodey & Erich H. Reck, Completeness and Categoricty, Part II: 20th Century Metalogic to 21st Century Semantics.
Timothy Williamson (2010). Barcan Formulas in Second-Order Modal Logic. In Michael Frauchiger (ed.), Themes From Barcan Marcus. Ontos Verlag 51-74.
Added to index2010-12-22
Total downloads215 ( #13,780 of 1,911,732 )
Recent downloads (6 months)19 ( #33,819 of 1,911,732 )
How can I increase my downloads?