Three Essays in Intuitionistic Epistemology
type: CreativeWork
description: We present three papers studying knowledge and its logic from an intuitionistic viewpoint. An Arithmetic Interpretation of Intuitionistic Verification Intuitionistic epistemic logic introduces an epistemic operator to intuitionistic logic which reflects the intended BHK semantics of intuitionism. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the product of verification. The BHK interpretation of intuitionistic logic has a precise formulation in the Logic of Proofs and its arithmetical semantics. We show here that this interpretation can be extended to the notion of verification upon which intuitionistic knowledge is based. This provides the systems of intuitionistic epistemic logic extended by an epistemic operator based on verification with an arithmetical semantics too. This confirms the conception of verification incorporated in these systems reflects the BHK interpretation. Intuitionistic Verification and Modal Logics of Verification The systems of intuitionistic epistemic logic, IEL, can be regarded as logics of intuitionistic verification. The intuitionistic language, however, has expressive limitations. The classical modal language is more expressive, enabling us to formulate various classical principles which make explicit the relationship between intuitionistic verification and intuitionistic truth, implicit in the intuitionistic epistemic language. Within the framework of the arithmetic semantics for IEL we argue that attempting to base a general verificationism on the properties of intuitionistic verification, as characterised by IEL, yields a view of verification stronger than is warranted by its BHK reading. Intuitionistic Knowledge and Fallibilism Fallibilism is the view that knowledge need not guarantee the truth of the proposition known. In the context of a classical conception of truth fallibilism is incompatible with the truth condition on knowledge, i.e. that false propositions cannot be known. We argue th…
abstract: We present three papers studying knowledge and its logic from an intuitionistic viewpoint. An Arithmetic Interpretation of Intuitionistic Verification Intuitionistic epistemic logic introduces an epistemic operator to intuitionistic logic which reflects the intended BHK semantics of intuitionism. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the product of verification. The BHK interpretation of intuitionistic logic has a precise formulation in the Logic of Proofs and its arithmetical semantics. We show here that this interpretation can be extended to the notion of verification upon which intuitionistic knowledge is based. This provides the systems of intuitionistic epistemic logic extended by an epistemic operator based on verification with an arithmetical semantics too. This confirms the conception of verification incorporated in these systems reflects the BHK interpretation. Intuitionistic Verification and Modal Logics of Verification The systems of intuitionistic epistemic logic, IEL, can be regarded as logics of intuitionistic verification. The intuitionistic language, however, has expressive limitations. The classical modal language is more expressive, enabling us to formulate various classical principles which make explicit the relationship between intuitionistic verification and intuitionistic truth, implicit in the intuitionistic epistemic language. Within the framework of the arithmetic semantics for IEL we argue that attempting to base a general verificationism on the properties of intuitionistic verification, as characterised by IEL, yields a view of verification stronger than is warranted by its BHK reading. Intuitionistic Knowledge and Fallibilism Fallibilism is the view that knowledge need not guarantee the truth of the proposition known. In the context of a classical conception of truth fallibilism is incompatible with the truth condition on knowledge, i.e. that false propositions cannot be known. We argue th…
author: Protopopescu, Tudor
keywords: Epistemology, Logic and Foundations of Mathematics, Philosophy, Intuitionistic Epistemic Logic, Verification, BHK Semantics, Fallibilism, Intuitionistic Knowledge, Arithmetic Semantics
date published: 2016-09-30T07:00:00Z
date modified: 2026-07-24T01:59:05Z
provider: City University of New York - Graduate Center
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: The Graduate School and University Center of The City University of New York