A Logical Modeling of Severe Ignorance

Journal of Philosophical Logic 52 (4):1053-1080 (2023)
  Copy   BIBTEX

Abstract

In the logical context, ignorance is traditionally defined recurring to epistemic logic. In particular, ignorance is essentially interpreted as “lack of knowledge”. This received view has - as we point out - some problems, in particular we will highlight how it does not allow to express a type of content-theoretic ignorance, i.e. an ignorance of φ that stems from an unfamiliarity with its meaning. Contrarily to this trend, in this paper, we introduce and investigate a modal logic having a primitive epistemic operator I, modeling ignorance. Our modal logic is essentially constructed on the modal logics based on weak Kleene three-valued logic introduced by Segerberg (Theoria, 33(1):53–71, 1997). Such non-classical propositional basis allows to define a Kripke-style semantics with the following, very intuitive, interpretation: a formula φ is ignored by an agent if φ is neither true nor false in every world accessible to the agent. As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditional approach. We dub it severe ignorance. We axiomatize, prove completeness and decidability for the logic of reflexive (three-valued) Kripke frames, which we find the most suitable candidate for our novel proposal and, finally, compare our approach with the most traditional one.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

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

A Logic for Disjunctive Ignorance.Jie Fan - 2021 - Journal of Philosophical Logic 50 (6):1293-1312.
Logical ignorance and logical learning.Richard Pettigrew - 2021 - Synthese 198 (10):9991-10020.
Following logical realism where it leads.Michaela Markham McSweeney - 2019 - Philosophical Studies 176 (1):117-139.
Inexpressible Ignorance.Shamik Dasgupta - 2015 - Philosophical Review 124 (4):441-480.
Lucky Ignorance, Modality and Lack of Knowledge.Oscar A. Piedrahita - 2021 - Pacific Philosophical Quarterly (3).
Inan on Objectual and Propositional Ignorance.Erhan Demircioglu - 2016 - Croatian Journal of Philosophy 16 (3):305-311.
Culpable ignorance in a collective setting.Säde Hormio - 2018 - Acta Philosophica Fennica 94:7-34.
A Logic-Based Approach to Pluralistic Ignorance.Jens Ulrik Hansen - 2012 - In Jonas De Vuyst & Lorenz Demey (eds.), Future Directions for Logic: Proceedings of PhDs in Logic II. College Publications. pp. 67-80.
Awareness of ignorance.İlhan İnan - 2020 - SATS 20 (2):141-173.

Analytics

Added to PP
2022-04-03

Downloads
34 (#448,660)

6 months
6 (#448,852)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Stefano Bonzio
University of Turin
Pierluigi Graziani
Università degli Studi di Urbino
Vincenzo Fano
Università degli Studi di Urbino

Citations of this work

Axiomatizing Rumsfeld Ignorance.Jie Fan - 2023 - Journal of Philosophical Logic 53 (1):79-97.

Add more citations

References found in this work

Knowledge and belief.Jaakko Hintikka - 1962 - Ithaca, N.Y.,: Cornell University Press.
Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
The Logic of Nonsense.Sören Halldén - 1949 - Uppsala, Sweden: Upsala Universitets Arsskrift.

View all 33 references / Add more references