Hyperlogic: A System for Talking about Logics

Proceedings for the 22nd Amsterdam Colloquium (2019)
  Copy   BIBTEX


Sentences about logic are often used to show that certain embedding expressions, including attitude verbs, conditionals, and epistemic modals, are hyperintensional. Yet it not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. This paper does two things. First, it argues against a standard account of logic talk, viz., the impossible worlds semantics. It is shown that this semantics does not easily extend to a language with propositional quantifiers, which are necessary for regimenting some logic talk. Second, it develops an alternative framework based on logical expressivism, which explains logic talk using shifting conventions. When combined with the standard S5π+ semantics for propositional quantifiers, this framework results in a well-behaved system that does not face the problems of the impossible worlds semantics. It can also be naturally extended with hybrid operators to regiment a broader range of logic talk, e.g., claims about what laws hold according to other logics. The resulting system, called hyperlogic, is therefore a better framework for modeling logic talk than previous accounts.



External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Propositional Quantification in Bimodal S5.Peter Fritz - 2020 - Erkenntnis 85 (2):455-465.
Semantics for Counterpossibles.Yale Weiss - 2017 - Australasian Journal of Logic 14 (4):383-407.
A classically-based theory of impossible worlds.Edward N. Zalta - 1997 - Notre Dame Journal of Formal Logic 38 (4):640-660.
Impossible Worlds.Franz Berto & Mark Jago - 2013 - Oxford: Oxford University Press.
Systems of modal logic for impossible worlds.Charles G. Morgan - 1973 - Inquiry: An Interdisciplinary Journal of Philosophy 16 (1-4):280 – 289.
Impossible Worlds.David Vander Laan - 1999 - Dissertation, University of Notre Dame
Counteressential Conditionals.Kenneth L. Pearce - 2016 - Thought: A Journal of Philosophy 5 (1):73-81.
A Note on Algebraic Semantics for S5 with Propositional Quantifiers.Wesley H. Holliday - 2019 - Notre Dame Journal of Formal Logic 60 (2):311-332.
Logically Impossible Worlds.Koji Tanaka - 2018 - Australasian Journal of Logic 15 (2):489.
Validity Measurement in Some Propositional Logics.Branislav Boričić - 1997 - Mathematical Logic Quarterly 43 (4):550-558.
Provability logics with quantifiers on proofs.Rostislav E. Yavorsky - 2001 - Annals of Pure and Applied Logic 113 (1-3):373-387.


Added to PP

344 (#59,556)

6 months
91 (#52,188)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Alexander W. Kocurek
Cornell University

Citations of this work

Logic talk.Alexander W. Kocurek - 2021 - Synthese 199 (5-6):13661-13688.

Add more citations

References found in this work

Propositional quantifiers in modal logic.Kit Fine - 1970 - Theoria 36 (3):336-346.
On What Cannot Be.Daniel Cohen - 1990 - In J. Dunn & A. Gupta (eds.), Truth or Consequences: Essays in Honor of Nuel Belnap. Boston, MA, USA: Kluwer Academic Publishers. pp. 123--132.

Add more references