David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Analysis 69 (2):280-286 (2009)
In my paper , I noted that Fitch's argument, which purports to show that if all truths are knowable then all truths are known, can be blocked by typing knowledge. If there is not one knowledge predicate, ‘ K’, but infinitely many, ‘ K 1’, ‘ K 2’, … , then the type rules prevent application of the predicate ‘ K i’ to sentences containing ‘ K i’ such as ‘ p ∧¬ K i⌜ p⌝’. This provides a motivated response to Fitch's argument so long as knowledge typing is itself motivated. It was the burden of my paper to explore the case that knowledge typing is as motivated as truth typing by drawing on the parallels between epistemic paradoxes generated by sentences of the kind ‘this sentence is unknown’ and semantic paradoxes generated by sentences such as ‘this sentence is untrue’. Given that typing truth is one of the acknowledged options for solving semantic paradoxes, if the parity argument succeeds it follows that epistemic typing is as well-motivated as truth typing and that the typing response to Fitch's argument is correspondingly strong.Halbach presents an apparent problem for this argument. Let ‘ N’ and ‘ P’, respectively, denote the necessity and possibility predicates, ‘ K 1’ the knowledge predicate of first type, and let ‘γ’ be a K-free sentence such that γ ↔¬ P⌜ K 1⌜γ⌝⌝; we know such a ‘γ’ exists by a standard diagonalization argument. If we assume that γ is knowable at the next knowledge type, that is, at type 1, and that the possibility typing does not interfere with the knowledge typing, a contradiction quickly ensues. Formally: γ ↔¬ P⌜ …
|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
Volker Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (2):114 - 120.
Alexander Paseau (2008). Fitch's Argument and Typing Knowledge. Notre Dame Journal of Formal Logic 49 (2):153-176.
Volker Halbach, Hannes Leitgeb & Philip Welch (2003). Possible-Worlds Semantics for Modal Notions Conceived as Predicates. Journal of Philosophical Logic 32 (2):179-223.
Citations of this work BETA
Federico Pailos & Lucas Rosenblatt (2015). Solving Multimodal Paradoxes. Theoria 81 (3):192-210.
Similar books and articles
Volker Halbach (2009). Reducing Compositional to Disquotational Truth. Review of Symbolic Logic 2 (4):786-798.
Nick Chater (1997). What is the Type-1/Type-2 Distinction? Behavioral and Brain Sciences 20 (1):68-69.
Volker Halbach (2006). How Not to State T-Sentences. Analysis 66 (4):276–280.
Volker Halbach (2001). How Innocent is Deflationism? Synthese 126 (1-2):167 - 194.
Volker Halbach & Leon Horsten (2005). Computational Structuralism. Philosophia Mathematica 13 (2):174-186.
Volker Halbach, Axiomatic Theories of Truth. Stanford Encyclopedia of Philosophy.
Volker Halbach (1999). On Lehrer's Principle of Trustworthiness. Erkenntnis 50 (2/3):259 - 272.
Volker Halbach & Erik J. Olsson (1999). Editorial Overview. Erkenntnis 50 (2-3):149-153.
Bernd Buldt, Volker Halbach & Reinhard Kahle (2005). Reflections on Frege and Hilbert. Synthese 147 (1):1 - 2.
Added to index2009-04-11
Total downloads31 ( #102,719 of 1,726,249 )
Recent downloads (6 months)2 ( #289,836 of 1,726,249 )
How can I increase my downloads?