In discussions of Fitch’s paradox, it is usually assumed without further argument that knowledge is factive, that if a subject knows that p, then p is true. It is argued that this common assumption is not as well-founded as it should be, and that there in fact are certain reasons to be suspicious of the unrestricted version of the factiveness claim. There are two kinds of reason for this suspicion. One is that unrestricted factiveness leads to paradoxes and unexpected results, (...) the other is that the usual arguments for factiveness are not as compelling as is commonly thought. There may in fact be some kinds of contexts, where factiveness doesn’t hold for knowledge—the usual arguments for factiveness don’t suffice to support the claim that knowledge is unrestrictedly factive. Perhaps all that can be shown is that knowledge is at times factive, or that it is default factive, as it were: this doesn’t show that there can’t be counterexamples, however. Certain aspects of knowledge without unrestricted factiveness are examined briefly. (shrink)

Augment the propositional language with two modal operators: □ and ■. Define ⧫ to be the dual of ■, i.e. ⧫=¬■¬. Whenever (X) is of the form φ → ψ, let (X⧫) be φ→⧫ψ . (X⧫) can be thought of as the modally qualified counterpart of (X)—for instance, under the metaphysical interpretation of ⧫, where (X) says φ implies ψ, (X⧫) says φ implies possibly ψ. This paper shows that for various interesting instances of (X), fairly weak assumptions suffice for (...) (X⧫) to imply (X)—so, the modally qualified principle is as strong as its unqualified counterpart. These results have surprising and interesting implications for issues spanning many areas of philosophy. (shrink)

An analysis of Moore's paradox is given in doxastic logic. Logics arising from formalizations of various introspective principles are compared; one logic, K5c, emerges as privileged in the sense that it is the weakest to avoid Moorean belief. Moreover it has other attractive properties, one of which is that it can be justified solely in terms of avoiding false belief. Introspection is therefore revealed as less relevant to the Moorean problem than first appears.

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

Knows-knows principles in epistemology say that if you know some proposition, then you are in a position to know that you know it. This paper examines the viability of analogous principles in ethics, which I call ought-ought principles. Several epistemologists have recently offered new defences of KK principles and of other related principles, and there has recently been an increased interest in examining analogies between ethics and epistemology, and so it seems natural to examine whether defences of KK and related (...) principles carry over to OO principles. In this paper, I introduce two OO principles, and I show how some arguments in favour of KK carry over to them. Then I show how these OO principles can be used to shed light on a much-discussed case in ethics, that of Professor Procrastinate. (shrink)

In this note, I consider various precisifications of the slogan ‘evidence of evidence is evidence’. I provide counter-examples to each of these precisifications (assuming an epistemic probabilistic relevance notion of ‘evidential support’).

The Fitch paradox poses a serious challenge for anti-realism. This paper investigates the option for an anti-realist to answer the challenge by restricting the knowability principle. Based on a critical discussion of Dummett's and Tennant's suggestions for a restriction desiderata for a principled solution are developed. In the second part of the paper a different restriction is proposed. The proposal uses the notion of uniform formulas and diagnoses the problem arising in the case of Moore sentences in the different status (...) propositional letters receive. The new proposal is able to avoid some of the criticism on its predecessors. (shrink)

Fitch’s argument purports to show that for any unknown truth, p , there is an unknowable truth, namely, that p is true and unknown; for a contradiction follows from the assumption that it is possible to know that p is true and unknown. In earlier work I argued that there is a sense in which it is possible to know that p is true and unknown, from a counterfactual perspective; that is, there can be possible, non-actual knowledge, of the actual (...) situation, that in that situation, p is true and unknown. Here I further elaborate that claim and respond to objections by Williamson, who argued that there cannot be non-trivial knowledge of this kind. I give conditions which suffice for such non-trivial counterfactual knowledge. (shrink)

Some propositions are structurally unknowable for certain agents. Let me call them ‘Moorean propositions’. The structural unknowability of Moorean propositions is normally taken to pave the way towards proving a familiar paradox from epistemic logic—the so-called ‘Knowability Paradox’, or ‘Fitch’s Paradox’—which purports to show that if all truths are knowable, then all truths are in fact known. The present paper explores how to translate Moorean statements into a probabilistic language. A successful translation should enable us to derive a version of (...) Fitch’s Paradox in a probabilistic setting. I offer a suitable schematic form for probabilistic Moorean propositions, as well as a concomitant proof of a probabilistic Knowability Paradox. Moreover, I argue that traditional candidates to play the role of probabilistic Moorean propositions will not do. In particular, we can show that violations of the so-called ‘Reflection Principle’ in probability need not yield structurally unknowable propositions. Among other things, this should lead us to question whether violating the Reflection Principle actually amounts to a clear case of epistemic irrationality, as it is often assumed. This result challenges the importance of the principle as a tool to assess both synchronic and diachronic rationality—a topic which is largely independent of Fitch’s Paradox—from a somewhat unexpected source. (shrink)

One diagnosis of Fitch’s paradox of knowability is that it hinges on the factivity of knowledge: that which is known is true. Yet the apparent role of factivity and non-factive analogues in related paradoxes of justified belief can be shown to depend on familiar consistency and positive introspection principles. Rejecting arguments that the paradox hangs on an implausible consistency principle, this paper argues instead that the Fitch phenomenon is generated both in epistemic logic and logics of justification by the interaction (...) of analogues of the knowability principle and positive introspection theses that are characteristic of, even if not entailed by, epistemic internalism. (shrink)

It is widely believed that for all p, or at least for all entertainable p, it is knowable a priori that (p iff actually p). It is even more widely believed that for all such p, it is knowable that (p iff actually p). There is a simple argument against these claims from four antecedently plausible premises.

According to the KK-principle, knowledge iterates freely. It has been argued, notably in Greco, that accounts of knowledge which involve essential appeal to normality are particularly conducive to defence of the KK-principle. The present article evaluates the prospects for employing normality in this role. First, it is argued that the defence of the KK-principle depends upon an implausible assumption about the logical principles governing iterated normality claims. Once this assumption is dropped, counter-instances to the principle can be expected to arise. (...) Second, it is argued that even if the assumption is maintained, there are other logical properties of normality which can be expected to lead to failures of KK. Such failures are noteworthy, since they do not depend on either a margins-for-error principle or safety condition of the kinds Williamson appeals to in motivating rejection KK. “Introduction: KK and Being in a Position to Know” Section formulates two versions of the KK-Principle; “Inexact Knowledge and Margins for Error” Section presents a version of Williamson’s margins-for-error argument against it; “Knowledge and Normality” and “Iterated Normality” Sections discuss the defence of the KK-Principle due to Greco and show that it is dependent upon the implausible assumption that the logic of normality ascriptions is at least as strong as K4; finally, “Knowledge in Abnormal Conditions” and “Higher-Order Ignorance Inside the Margins” Sections argue that a weakened version of Greco’s constraint on knowledge is plausible and demonstrate that this weakened constraint will, given uncontentious assumptions, systematically generate counter-instances to the KK-principle of a novel kind. (shrink)

N.B. Dr Bykvist is now based at the Faculty of Philosophy, University of Oxford. The full-text of this article is not currently available in ORA, but you may be able to access the article via the publisher copy link on this record page.

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it (...) relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of /stability/: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting /stable knowability principle/ and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience. (shrink)

Collects a variety of mathematics and logic puzzles, some based on the theorems of the mathematician Kurt Godel.

Inspired by Rudolf Carnap's Der Logische Aufbau Der Welt, David J. Chalmers argues that the world can be constructed from a few basic elements. He develops a scrutability thesis saying that all truths about the world can be derived from basic truths and ideal reasoning. This thesis leads to many philosophical consequences: a broadly Fregean approach to meaning, an internalist approach to the contents of thought, and a reply to W. V. Quine's arguments against the analytic and the a priori. (...) Chalmers also uses scrutability to analyze the unity of science, to defend a conceptual approach to metaphysics, and to mount a structuralist response to skepticism. Based on the 2010 John Locke lectures, Constructing the World opens up debate on central philosophical issues involving language, consciousness, knowledge, and reality. This major work by a leading philosopher will appeal to philosophers in all areas. This entry contains uncorrected proofs of front matter, chapter 1, and first excursus. (shrink)

The paradox of knowability poses real difficulities to our understanding of truth. It does so by claiming that if we assume a truth is knowable, we can demonstrate that it is known. This demonstration threatens our understanding of truth in two quite different ways, only one of which has been recognized to this point in the literature on the paradox. Jonathan Kvanvig first unearths the ways in which the paradox is threatening, and then delineates an approach to the paradox that (...) solves both of the problems raised by the paradox for our understanding of truth. His book will be of interest throughout philosophy, but especially to logicians and epistemologists. (shrink)

Sorensen here offers a unified solution to a large family of philosophical puzzles and paradoxes through a study of "blindspots": consistent propositions that cannot be rationally accepted by certain individuals even though they might by true.

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...) up-to-date and reliable guide essential for the student. (shrink)

This article shows that although Fitch’s paradox has been extremely widely studied, up to now no correct formalization of the problem has been proposed. The purpose of this article is to present the paradox front the viewpoint of combining logics. It is argued that the correct minimal logic to state the paradox is composed by a fusion of modal frames, and a fusion of modal languages and logics.

That truth provides the standard for believing appears to be a platitude, one which dovetails with the idea that in some sense belief aims only at the truth. In recent years, however, an increasing number of prominent philosophers have suggested that knowledge provides the standard for believing, and so that belief aims only at knowledge. In this paper, I examine the considerations which have been put forward in support of this suggestion, considerations relating to lottery beliefs, Moorean beliefs, the criticism (...) and defence of belief, and the value of knowledge. I argue that those considerations do not give us reason to give up the truth view in favour of the knowledge view and, moreover, that reflection on those considerations gives us some reason to reject the knowledge view. Thus, I conclude, we can continue to the take the apparent platitude at face value. (shrink)