# Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism

@article{Holliday2015EpistemicCA, title={Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism}, author={W. Holliday}, journal={Journal of Philosophical Logic}, year={2015}, volume={44}, pages={1-62} }

Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be… Expand

#### 43 Citations

Epistemic closure, assumptions and topics of inquiry

- Philosophy, Computer Science
- Synthese
- 2014

It is argued that knowledge is best understood as a topic-restricted notion, and that such a conception is a natural one given the authors' limited cognitive resources. Expand

Roles, Rigidity, and Quantification in Epistemic Logic

- Mathematics, Computer Science
- Johan van Benthem on Logic and Information Dynamics
- 2014

This paper lays out a philosophical approach to epistemic predicate logic implemented formally in Melvin Fitting’s First-Order Intensional Logic, that it is argued solves conceptual problems not faced in the case of alethic modal predicate logic. Expand

Epistemic Logic with Evidence and Relevant Alternatives

- Philosophy
- 2018

Starting with Jaakko Hintikka’s seminal work, epistemic logic has now grown up to a huge academic industry. When we look back to its history, however, there is a practical paradox. While Hintikka’s… Expand

Epistemic Logic and the Problem of Epistemic Closure

- Mathematics
- 2016

This paper argues that propositional modal logics based on Kripke-structures cannot be accepted by epistemologists as a minimal framework to describe propositional knowledge. In fact, many authors… Expand

Epistemic Logic and Epistemology

- Philosophy
- 2018

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics… Expand

The Case Against Closure of A Priori Knowability under Modus Ponens

- 2015

The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori… Expand

Information dynamics and uniform substitution

- Computer Science
- Synthese
- 2013

The decidability of this schematic validity problem for public announcement logic (PAL and PAL-RC) over models for finitely many fully introspective agents, as well as models for infinitely many arbitrary agents is proved. Expand

Closure of A Priori Knowability Under A Priori Knowable Material Implication

- Mathematics
- 2015

The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori… Expand

Fallibilism and Multiple Paths to Knowledge

- Philosophy
- 2015

Being a fallibilist isn’t easy. A fallibilist about empirical knowledge, in Lewis’s (1996) sense, holds that an agent can know a contingent empirical proposition P , even if she has not ruled out… Expand

A Computational Learning Semantics for Inductive Empirical Knowledge

- Mathematics, Computer Science
- Johan van Benthem on Logic and Information Dynamics
- 2014

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs… Expand

#### References

SHOWING 1-10 OF 117 REFERENCES

Erratum to: Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism

- Mathematics, Computer Science
- J. Philos. Log.
- 2015

This paper introduces models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology, and gives an exact characterization of the closure properties of knowledge according to these theories, as formalized. Expand

Epistemic Logic, Relevant Alternatives, and the Dynamics of Context

- Mathematics, Computer Science
- ESSLLI Student Sessions
- 2011

This article proposes formalizations of two versions of the Relevant Alternatives Theory of knowledge, focusing more on the second, especially on logical issues associated with developing a dynamic epistemic logic of context change over models for the RA theory. Expand

The problem of logical omniscience, I

- Philosophy
- Synthese
- 2004

From their beginning, I epistemic and doxastic logics-the logics of knowledge and belief have been modeled on modal logic-the logic of necessity and possibility. Knowledge and belief, in such logics,… Expand

Roles, Rigidity, and Quantification in Epistemic Logic

- Mathematics, Computer Science
- Johan van Benthem on Logic and Information Dynamics
- 2014

This paper lays out a philosophical approach to epistemic predicate logic implemented formally in Melvin Fitting’s First-Order Intensional Logic, that it is argued solves conceptual problems not faced in the case of alethic modal predicate logic. Expand

When epistemic closure does and does not fail: a lesson from the history of epistemology

- Philosophy
- 2004

Does the failure of a necessary condition for knowledge to be closed under known entailment imply that knowledge itself is not closed under known entailment? More generally, does the failure of a… Expand

A strategy for assessing closure

- Mathematics
- 2006

This paper looks at an argument strategy for assessing the epistemic closure principle. This is the principle that says knowledge is closed under known entailment; or (roughly) if S knows p and S… Expand

Probability and Danger

- Philosophy
- 2009

What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that… Expand

Modal and Anti-Luck Epistemology

- Philosophy
- 2010

The influence of Edmund Gettier's ―Is Justified True Belief Knowledge?‖ seems to extend to every corner of epistemology. Gettier's counterexamples to the tripartite account of knowledge, according to… Expand

Knowledge and assumptions

- Philosophy
- 2011

When epistemologists talk about knowledge, the discussions traditionally include only a small class of other epistemic notions: belief, justification, probability, truth. In this paper, we propose… Expand

Why Safety Doesn't save Closure

- 2012

Knowledge closure is, roughly, the following claim: For every agent S and propositions P and Q, if S knows P, knows that P implies Q, and believes Q because it is so implied, then S knows Q. Almost… Expand