Epistemic logic without closure

Synthese (forthcoming)

Authors
Martin Smith
University of Edinburgh
Stephan Leuenberger
University of Glasgow
Abstract
All standard epistemic logics legitimate something akin to the principle of closure, according to which knowledge is closed under competent deductive inference. And yet the principle of closure, particularly in its multiple premise guise, has a somewhat ambivalent status within epistemology. One might think that serious concerns about closure point us away from epistemic logic altogether—away from the very idea that the knowledge relation could be fruitfully treated as a kind of modal operator. This, however, need not be so. The abandonment of closure may yet leave in place plenty of formal structure amenable to systematic logical treatment. In this paper we describe a family of weak epistemic logics in which closure fails, and describe two alternative semantic frameworks in which these logics can be modelled. One of these—which we term plurality semantics—is relatively unfamiliar. We explore under what conditions plurality frames validate certain much-discussed principles of epistemic logic. It turns out that plurality frames can be interpreted in a very natural way in light of one motivation for rejecting closure, adding to the significance of our technical work. The second framework that we employ—neighbourhood semantics—is much better known. But we show that it too can be interpreted in a way that comports with a certain motivation for rejecting closure.
Keywords epistemic logic  closure  compartmentalisation  fragmentation  risk minimisation  plurality semantics  neighbourhood semantics
Categories (categorize this paper)
DOI 10.1007/s11229-019-02368-6
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 43,728
External links

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

Elusive Knowledge.David K. Lewis - 1996 - Australasian Journal of Philosophy 74 (4):549 – 567.
Knowledge and its Limits.Timothy Williamson - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.
Knowledge and Lotteries.John Hawthorne - 2004 - Studia Logica 84 (1):161-163.
Philosophical Explanations.R. Nozick - 1981 - British Journal for the Philosophy of Science 35 (1):83-85.
Basic Knowledge and the Problem of Easy Knowledge.Stewart Cohen - 2002 - Philosophy and Phenomenological Research 65 (2):309-329.

View all 30 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Epistemic closure.Peter Baumann - 2011 - In Duncan Pritchard & Sven Bernecker (eds.), The Routledge Companion to Epistemology. Routledge. pp. 597--608.
Living Without Closure.Krista Lawlor - 2005 - Grazer Philosophische Studien 69 (1):25-50.
Epistemic Logic and Epistemology.Wesley H. Holliday - forthcoming - In Sven Ove Hansson Vincent F. Hendricks (ed.), Handbook of Formal Philosophy. Springer.
When Does Epistemic Closure Fail?M. Yan - 2013 - Analysis 73 (2):260-264.
A Note on Gettier Cases in Epistemic Logic.Timothy Williamson - 2015 - Philosophical Studies 172 (1):129-140.
Response to Egré and Xu.Wesley H. Holliday - 2013 - In Johan van Benthem Fenrong Liu (ed.), Logic Across the University: Foundations and Applications. College Publications. pp. 39-46.
Ryan on Epistemic Closure Principles.John M. Collins - 2002 - Philosophia 29 (1-4):371-376.
What We Can Learn From the Skeptical Puzzle.Tim Black - 2009 - Iris. European Journal of Philosophy and Public Debate 1 (2):439-447.

Analytics

Added to PP index
2019-09-03

Total views
26 ( #331,293 of 2,264,671 )

Recent downloads (6 months)
26 ( #30,347 of 2,264,671 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature