With respect to the metaphysics of infinity, the tendency of standard debates is to either endorse or to deny the reality of ‘the infinite’. But how should we understand the notion of ‘reality’ employed in stating these options? Wittgenstein’s critical strategy shows that the notion is grounded in a confusion: talk of infinity naturally takes hold of one’s imagination due to the sway of verbal pictures and analogies suggested by our words. This is the source of various philosophical pictures that (...) in turn give rise to the standard metaphysical debates: that the mathematics of infinity corresponds to a special realm of infinite objects, that the infinite is profoundly huge or vast, or that the ability to think about infinity reveals mysterious powers in human beings. First, I explain Wittgenstein’s general strategy for undermining philosophical pictures of ‘the infinite’ – as he describes it in Zettel; and then show how that critical strategy is applied to Cantor’s diagonalization proof in Remarks on the Foundations of Mathematics II. (shrink)

This is a work in the philosophy of language and metasemantics. Its purpose is to help answer the question about how words acquire their meanings. The work is divided into two parts. The purpose of Part One is to defend the claim that, despite numerous attempts, the so-called Kripkenstein’s sceptical challenge, and especially the problem of finitude, has not been offered a successful straight solution. The purpose of Part Two is to critically examine Robert Brandom’s philosophy, which can be treated (...) as an answer to the sceptical challenge in my interpretation. My main claim is that although Brandom’s so-called normativist approach does provide a principled solution to the sceptical challenge, the proposal faces a host of other problems in the light of which I reject it. -/- What is Kripkenstein’s sceptical challenge? The name 'Kripkenstein' is an abbreviation used in the literature for Saul Kripke’s reading of Ludwig Wittgenstein’s later works, published in 1982. In the long essay, Kripke presents (that Wittgenstein presented) a sceptical challenge that demands an explanation of how any word can have a determinate meaning. The challenge is usually thought to consist of three interrelated problems: (1) the problem of finitude, (2) the problem of error, and (3) the problem of normativity. Following Martin Kusch, I view the problem of finitude as the most important one. According to the problem, briefly, since any actual subject is a finite being, i.e. capable of exhibiting only finite expressions of linguistic signs, it will always be possible to ask whether, in a given context, she is following a rule S1 or rule S2 that corresponds to the meaning of the sign. For example, supposing that the sign in question is '+', it can be asked whether the subject in a given context has followed the addition rule or an alternative quaddition rule, according to which any addition problem exceeding certain arbitrary cardinality results in five. According to the hypothesis, the actual use of '+' by any speaker is compatible with both rules. Since any speaker has only finite dispositions to the mathematical conduct, there will always be some limit after which there is no fact of the matter, according to the sceptic, which rule the subject will have turned out to have followed. Hence, it is indeterminate whether any actual subject has ever calculated according to the addition rule or the quaddition rule. -/- From my view, despite the work of Kripke and Kusch, the problem of finitude has not been taken as seriously as it ought to have been. This in turn has significant consequences for the metasemantic theory concerning the origin and nature of meaning. In particular, I claim that the way how the meaning of words is determined must be understood as temporal in nature. Moreover, I claim that Kripke’s causal-historical account of reference can work as a non-straight solution to the challenge that explains how at least the meanings of some words can be temporally determined. -/- One central aim of Brandom’s philosophy is to give a straight answer to the problem of finitude by providing an answer to the problem of normativity. However, I claim that Brandom’s version of the 'normativity of meaning' hypothesis cannot work as he intends. The key issues are difficult to summarise, but to put it succinctly, the crucial problem concerns Brandom’s ambition to give an answer to a version of Agrippa’s trilemma, or how a chain of justifications can end in anything else than (i) premises that have already been used, (ii) a primitive premise, or an (iii) infinitude of premises. My claim is that Brandom’s resolution to the trilemma is not sound. (shrink)

Rumfitt has given two arguments that in unilateralist verificationist theories of meaning, truth collapses into correct assertibility. In the present paper I give similar arguments that show that in unilateral falsificationist theories of meaning, falsehood collapses into correct deniability. According to bilateralism, meanings are determined by assertion and denial conditions, so the question arises whether it succumbs to similar arguments. I show that this is not the case. The final section considers the question whether a principle central to Rumfitt's first (...) argument, ‘It is assertible that if and only if it is assertible that it is assertible that ’, is one that bilateralists can reject, and concludes that they cannot. It follows that the logic of assertibility and deniability, according to a result by Williamson, is the little known modal logic K4 studied by Sobociński. The paper ends with a plaidoyer for bilateralists to adopt this logic. (shrink)

For Kant, philosophical investigations are inherently analytic. The proper method of philosophy is analysis, and the object of analysis are concepts. Hence, Kant’s short description of philosophy as “rational cognition […] from concepts” (KrV, A 837/B 865) can be substituted by “philosophy is conceptual analysis”. The article shows that Kant follows a representationalism about concepts and a combination of intensional and extensional feature semantics. Against the claim that Kant is a proponent of the concept-judgement-inversion, it is argued that concepts are (...) being articulated in form of singular terms, propositions, and sets of propositions alike. Kant interlinks different kinds of concepts with different kinds of definitions, as the reconstruction of his theory of definitions reveals. Philosophy foremost deals with what Kant calls “given” empirical and pure concepts. Such concepts are object of analysis, i.e., explication and exposition. The article ends with answers to five possible objections. Is philosophy all about analysis? (shrink)

Paying attention to the inner workings of mathematicians has led to a proliferation of new themes in the philosophy of mathematics. Several of these have to do with epistemology. Philosophers of mathematical practice, however, have not (yet) systematically engaged with general (analytic) epistemology. To be sure, there are some exceptions, but they are few and far between. In this chapter, I offer an explanation of why this might be the case and show how the situation could be remedied. I contend (...) that it is only by conceiving the knowing subject(s) as embodied, fallible, and embedded in a specific context (along the lines of what has been done within social and feminist epistemology) that we can pursue an epistemology of mathematics sensitive to actual mathematical practice. I further suggest that this reconception of the knowing subject(s) does not force us to abandon the traditional framework of epistemology in which knowledge requires justified true belief. It does, however, lead to a fallible conception of mathematical justification that, among other things, makes Gettier cases possible. This shows that topics considered to be far removed from the interests of philosophers of mathematical practice might reveal to be relevant to them. (shrink)

In the current dialogue between two authors with different views on analysis, philosophy, and the use of labels, the leading question is: How should one understand the expression ‘analytic philosophy’? Lewin argues that as there are no generally agreed tenets and methods of what is being called ‘analytic philosophy’, the name is to be replaced by a more specific one or abandoned. Williamson defends the use of this phrase, claiming that it is quite serviceable, as it relates to a broad (...) tradition of influence, while it is not even required to adhere to the method of analysis in any distinctive sense. Lewin counters that, in this case, ‘analytic philosophy’ is too empty. One could heal this by conceptual analysis of ‘analytic philosophy’ — but then Kant, for whom philosophy is inherently analytic, would be a proponent of analytic philosophy. Another option is to follow Ryle’s ideal of a label-free, coherent and honest thinking. As Lewin argues, Williamson’s views seem at least partially to agree with Kant’s conception of the difference between philosophy and history of philosophy as well as empirical analysis and the underlying empirical realism. Williamson replies that he uses ‘analytic philosophy’ in its current meaning, which is not composed of the meanings of ‘analytic’ and ‘philosophy’. The current use is different from the earlier ones and not applicable to Kant. He argues against the transcendental idealism and the coarse-grained distinction between analytic and synthetic and a priori and a posteriori that requires an update. (shrink)

Social metaphysics is a source of important philosophical and moral insight. Furthermore, much social metaphysics appears to be substantive. However, some have recently argued that standard views of metaphysics cannot accommodate substantive social metaphysics. In this paper I offer a new diagnosis of this problem and defend a new solution, showing that this problem is an illuminating lens through which to examine the nature and boundaries of metaphysics. This case instantiates a broad, common pattern generated by attempts to align distinctions (...) between realism and anti-realism, mind-independence and mind-dependence, and legitimate and non-legitimate inquiry. I show that the best response is to abandon the association between substantive metaphysics and mind-independence, and I sketch a new definition of substantivity, given in terms of explanatory power, that makes room for substantive social metaphysics while also offering an attractive basis for general metaphysics. (shrink)

This paper argues for the diversification of university-level philosophy curricula. I defend the ideal of expansionist pluralism and connect it to metaphilosophical myopia – problematically limited or constrained visions of the range of forms taken by philosophy. Expansively pluralist curricula work to challenge metaphilosophical myopia and one of its costs, namely, a specific kind of hermeneutical injustice, perpetrated against the communities and traditions shaped by the occluded forms of philosophy.

In his work, On Law and Justice, Alf Ross sought to explain law in scientific/empirical terms, in terms that would require no recourse to what he called “metaphysics” or “idealism.” The result is a sort of translation of legal rules and official actions into propositions of behavior, predictions of behavior, and shared ideology. The present work raises questions about the tensions within Ross's work(s), and discusses the places where Ross's analysis seems to fall short of its ambitions. In the course (...) of the discussion, the article considers issues relating to legal mistake, explanations of judicial behavior, and different types of normativity. (shrink)

This paper discusses the relation between Crispin Wright’s alethic pluralism and my global expressivism. I argue that on many topics Wright’s own view counts as expressivism in my sense, but that truth itself is a striking exception. Unlike me, Wright never seems to countenance an expressivist account of truth, though the materials needed are available to him in his approaches to other topics.

I consider two attempts to combine realism with pluralism about the units of selection: Sober and Wilson’s combination of “model” and “unit” pluralism, and Sterelny and Griffiths’ “local pluralism”. I argue that both of these attempts fail to show that realism and pluralism are compatible. Sober and Wilson’s pluralism turns out, on closer inspection, to be a kind of monism in disguise, while Sterelny and Griffiths’ local pluralism involves a combination of realism and anti-realism about interactors, and the units of (...) selection, that is fundamentally unstable. My conclusion is that one must choose whether to be a realist or a pluralist in this area: one cannot be both. The question of which we should choose is a further question that I do not take a stand on. (shrink)

This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions. -/- Underlying this argument is the following philosophical view. Mathematical belief springs from certain intuitions, each of which can be either accepted or doubted in its entirety, but not half-accepted. Therefore, our beliefs about reality, bivalence, choice and consistency should all be aligned.

Editorial NoteThis lecture was given by Per Martin-Löf at Leiden University on August 25, 2001 at the invitation by Göran Sundholm to address the topic mentioned in the title and to reflect on Dummett’s earlier effort of almost a decade before. The lecture was part of a three-day conference on Gottlob Frege. Sundholm arranged for the lecture to be recorded and commissioned Bjørn Jespersen to make a transcript. The information in footnote 1, which Sundholm provided, has been independently confirmed by (...) Thomas Ricketts in an email to the author. The present version has been edited by Ansten Klev. Following the displayed text there is a lacuna in the original transcript corresponding to a pause in the recording when the tape was changed. The continuous text of the present version is the result of a few additions to the original transcript suggested by Klev and agreed to by the author. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. I provide a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Defenders of the enhanced indispensability argument argue that the most effective route to platonism is via the explanatory role of mathematical posits in science. Various compelling cases of mathematical explanation in science have been proposed, but a satisfactory general philosophical account of such explanations is lacking. In this paper, I lay out the framework for such an account based on the notion of “the mathematical stance.” This is developed by analogy with Dennett’s well-known concept of “the intentional stance.” Roughly, adopting (...) the mathematical stance towards a particular physical phenomenon involves treating it as an abstract mathematical structure for the purposes of prediction and explanation. Interestingly, Dennett himself frequently draws analogies between his intentional stance towards beliefs and desires and scientists’ stance towards centers of gravity. I explore the theoretical role played by centers of gravity within science and discuss how an indispensabilist platonist ought to categorize the ontological status of this type of posit. I conclude with some thoughts on how an approach based on the mathematical stance might be developed into a more general philosophical account of the application of mathematics in science. (shrink)

Husserl endorses ideal verificationism, the claim that there is a necessary correlation between truth and the ideal possibility of experience. This puts him in the company of semantic anti-realists like Dummett, Tennant, and Wright who endorse the knowability thesis that all truths are knowable. Unfortunately, there is a simple, seductive, and troubling argument due to Alonzo Church and Frederic Fitch that the knowability thesis collapses into the omniscience thesis that all truths are known. Phenomenologists should be worried. I assess the (...) damage by surveying responses that may be open to Husserl. In particular, I explore whether Husserl ought to have adopted intuitionistic logic and motivate a restriction of ideal verificationism on phenomenological grounds. (shrink)

The fallibility of deduction is the thesis that a thoughtful speaker-reasoner can wrongly believe that an inference is deductively valid. The author presents an argument to the effect that the fallibility of deduction is incompatible with the widespread view that deduction is epistemically unfruitful (the conclusion is contained in the premises, and the transition from premises to conclusion never extends knowledge). If the fallibility of deduction is a fact, the argument presented is a refutation of the doctrine of the unfruitfulness (...) of deduction. But its relevance goes further, because the argument reveals a connection between two different problems: a solution to the problem of fruitfulness (how can deductive inferences increase our knowledge?) is a starting point for a solution to the problem of fallibility (how can deductive inferences be wrong?). To solve the problem of fruitfulness, Michael Dummett proposed some general ideas concerning meaning and inference. Starting from these meaning-theoretical ideas, one can develop an explanation of the fallibility of deduction. The general explanatory strategy does not depend on the choice between a theory of meaning centered on truth, verification, inferential role, or on other key notions. (shrink)

Can it ever be rational to revise one's own logic by one's own lights? In this paper I argue that logic is never rationally revisable, even if one's own logic gives rise to paradoxes and allows one to derive any conclusion whatsoever. Instead of revising logic, we need to revise a certain widely held position in the philosophy of logic, one tied to the standard conception of validity and to the alleged monotonicity of deductive reasoning. I develop the alternative conception (...) of validity and of deductive reasoning, which explains why we are generally entitled to the conclusions of deductive reasoning, even though we rationally do not accept them in certain circumstances tied to paradoxes. (shrink)

Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the strategy used by Peirce to defend logical principles can be used to defend bivalence. Construing logic as the study of substitutions of equivalent representations, Peirce showed that some patterns of substitution get realized in the very act of questioning them. While I recognize that we can devise non-classical notations, I argue (...) that, when we make claims about those notations, we inevitably get saddled with bivalent commitments. I present several simple inferences to show this. The argument that results from those examples is ‘pragmatic’, because the inevitability of the principle is revealed in use (not mention); and it is ‘semiotic’, because this revelation happens in the use of signs. (shrink)

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order PA and Zermelo’s quasi-categoricity (...) theorem for second-order ZFC—these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic. (shrink)

This article aims to show that Wittgenstein’s remarks on religious belief and religious statements can be understood in modest philosophical terms, consistent with the thought that they are neither intended as serving to justify or undermine religious beliefs, nor as the expression of any theorizing about the nature of religious belief or the meaning of religious language. Instead, their philosophical significance is held to consist in their functioning to remind us of what we already know about the latter: such things (...) as in what circumstances one utters religious statements, what the consequences of accepting or rejecting religious beliefs are, and so on. His position is that all attempts to say something more than this are either a mark of philosophical arrogance or a manifestation of one’s own personal commitment to adopting a stance of religious belief or non-belief. As such, they do not furnish us with genuine philosophical insights. I argue that such an interpretation possess two principal merits. Firstly, it demonstrates that there is no tension between Wittgenstein’s remarks on the nature of philosophy and his remarks on religious belief and religious statements. Secondly, it shows that it is possible to philosophize about religion in a manner that does not assume that this has to consist either in presenting an apology for or critique of religion or in formulating philosophical theories regarding the nature of religious belief and the meaning of religious language. (shrink)

While it is common in social epistemology, philosophy of education and sociology to speak of theoretical knowledge, the concept of theoretical knowledge used in ordinary discourse has not been properly examined, and its relations to other types of knowledge remain unclear. This article argues that this ordinary language notion of theoretical knowledge has a distinct meaning different from the meanings of terms for other knowledge types, for example, knowledge‐that, and meta‐cognitive knowledge, and provides an analysis that characterizes theoretical knowledge as (...) distinguished by its indirectness. The article then discusses the implications of this view for the practical role of theoretical knowledge and suggests that a reappraisal of its epistemic significance is due. (shrink)

In this thesis, I elaborate and defend Donald Davidson's account of knowing one's own mental states that exhibit first-person authority. To that end, I place Davidson's account among others in the philosophical landscape concerning self-knowledge. Next, I examine his response to philosophical challenges that arise from mental content externalism and self-deception. Finally, I draw some insights froms Davidson's account to the broader aims of epsitemology.

ABSTRACT When a philosopher and a dog play Frisbee, do they cognize the same Frisbee? Is Fido subject to the “myth of the given”? The questions are not silly, for as Marjorie Grene quipped, “Epistemology is a branch of ethology.” What follows accepts what is usually called a “correspondence” theory of truth and a “realist” account of human knowledge. Nothing new, but what will be distinctive is that it seeks to exploit an unusual naturalism deriving from the American philosophical tradition. (...) It will particularly address the epistemic relation of sensing to knowing. A currently widespread view among those who object to realism can be traced to Wilfrid Sellars's 1956 critique of the “myth of the given.” Sellars argued that the normative “order of reasons” in which beliefs are adjudicated is discontinuous with the causal order of sensation or perception, so the former cannot be grounded in the latter. My claim will be that Sellars was half wrong, and the wrong half can be addressed by contemporary cognitive science and anthropology. The permission to employ the latter is granted by a special version of naturalism, “ordinal naturalism,” formed from the American philosophical tradition. (shrink)

According to the argument from moral disagreement, the existence of widespread or persistent moral disagreement is best explained by, and thus supports, the view that there are no objective moral truths. One of the most common charges against this argument is that it “overgeneralises”: it implausibly forces its proponents to also deny the existence of objective truths about certain matters of physics, history, philosophy, etc. (“companions in guilt” objections) or even about the argument’s own conclusion or its own soundness (“self-defeat” (...) objections). My aim in this article is to provide a detailed clarification and assessment of this overgeneralisation charge. Various (mostly empirical) issues relevant to assessing the above objections have so far not been sufficiently investigated. Nevertheless, there are good reasons to believe that realists have exaggerated the significance of their overgeneralisation charge. Both its companions in guilt and its self-defeat versions likely fail. (shrink)

A mental state is luminous if, whenever an agent is in that state, they are in a position to know that they are. Following Timothy Williamson’s Knowledge and Its Limits, a wave of recent work has explored whether there are any non-trivial luminous mental states. A version of Williamson’s anti-luminosity appeals to a safety- theoretic principle connecting knowledge and confidence: if an agent knows p, then p is true in any nearby scenario where she has a similar level of confidence (...) in p. However, the relevant notion of confidence is relatively underexplored. This paper develops a precise theory of confidence: an agent’s degree of confidence in p is the objective chance they will rely on p in practical reasoning. This theory of confidence is then used to critically evaluate the anti-luminosity argument, leading to the surprising conclusion that although there are strong reasons for thinking that luminosity does not obtain, they are quite different from those the existing literature has considered. In particular, we show that once the notion of confidence is properly understood, the failure of luminosity follows from the assumption that knowledge requires high confidence, and does not require any kind of safety principle as a premise. (shrink)

Tarski's analysis of the concept of truth gives rise to a hierarchy of languages. Does this fragment the concept all the way to philosophical unacceptability? I argue it doesn't, drawing on a modification of Kaplan's theory of indexicals.

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) problems. (shrink)

Semantic realism can be characterised as the idea that scientific theories are truth-bearers, and that they are true or false in virtue of the world. This notion is often assumed, but rarely discussed in the literature. I examine how it fares in the context of the semantic view of theories and in connection with the literature on scientific representation. Making sense of semantic realism requires specifying the conditions of application of theoretical models, even for models that are not actually used, (...) which leads to several difficulties. My conclusion is that semantic realism is far more demanding than one would expect. Finally, I briefly examine some pragmatist alternatives. (shrink)

Realism takes many forms. The aim of this paper is to show that the “Critique of pure Reason” is the founding document of realism and that to the present-day Kant’s discussion of realism has shaped the theoretical landscape of the debates over realism. Kant not only invents the now common philosophical term ‘realism’. He also lays out the theoretical topography of the forms of realism that still frames our understanding of philosophical questions concerning reality. The paper explores this by analysis (...) of Kant’s methodological procedure to distinguish between empirical and transcendental realism. This methodological procedure is still of great help in contemporary philosophy, although it has its limits. (shrink)

In this paper, I argue that the disjunction elimination rule presupposes the principle that a true disjunction contains at least one true disjunct. However, in some contexts such as supervaluationism or quantum logic, we have good reasons to reject this principle. Hence, disjunction elimination is restricted in at least one respect: it is not applicable to disjunctions for which this principle does not hold. The insight that disjunction elimination presupposes the principle that a true disjunction contains at least one true (...) disjunct is applied to two arguments which argue for this very principle. I show that these arguments are rule-circular since they rest on disjunction elimination. I claim that rule-circularity better explains why the arguments fail than the explanations provided by Rumfitt (2015), which, for instance, rely on controversial principles about truth. (shrink)

In this dissertation, I seek to explain G.W.F. Hegel’s view that human accessible conceptual content can provide knowledge about the nature or essence of things. I call this view “Conceptual Transparency.” It finds its historical antecedent in the views of eighteenth century German rationalists, which were strongly criticized by Immanuel Kant. I argue that Hegel explains Conceptual Transparency in such a way that preserves many implications of German rationalism, but in a form that is largely compatible with Kant’s criticisms of (...) the original rationalist version. After providing background on Hegel’s relationship to the traditional rationalist theory of concepts and Kant’s challenge to it, I claim that Hegel’s central task is to provide a theory of conceptual content that allows a relationship to the objective world without being dependent on the specifically sensory aspect of the world, which Kant’s theory of concepts required. Since many interpreters deny that Hegel’s use of the term “concept” is comparable to other historical philosophers (or our own), I first show that Hegel’s critique of standard conceptions of concepts presupposes an agreement of subject matter. I then show how Hegel’s account of the “formal concept” provides the skeleton for a view of conceptual content that relies on negative relations between terms, rather than a relation to sensibility, to provide content. Hegel’s account of conceptual content is completed when he shows how a universal term is further specified so that it can determine singular objects. This occurs in its adequate form in a teleological process. I argue that Hegel’s account of teleology in the Science of Logic is an attempt to explain how and where Conceptual Transparency obtains. A teleological process is one in which a concept constitutes an object, and this means that a concept is perfectly adequate to express that thing’s nature and not merely to represent it. However, in the final chapter, I show that Hegel’s concept of teleology is meant paradigmatically to illuminate how human purposive processes have constituted a social world that is conceptually accessible to us. In this way, the primary “province” of Hegel’s rationalism is the human constructed world. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...) so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

This essay presents a long, detailed, in many ways critical but also appreciative account, of David Bloor’s recent book The Enigma of the Aerofoil. I take that work as the crowning statement of ideas and principles developed over the past four decades by Bloor and other exponents of the ‘strong programme’ in the sociology of scientific knowledge. It therefore offers both a test-case of that approach and a welcome opportunity to review, clarify and extend some of the arguments brought against (...) it by critical realists. This purpose is particularly well served by Bloor’s having here assembled such a wealth of scientific, historical, political and socio-cultural data concerning one specific, very crucial period of research into theories of aerodynamic lift. His book thus provides an exceptionally useful point of engagement for anyone seeking to adjudicate these issues from a critically angled but engaged and constructive standpoint. (shrink)

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following, Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a (...) variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others. (shrink)

In this paper, we will discuss what is called the “Manifestation Challenge” to semantic realism, which was originally developed by Michael Dummett and has been further refined by Crispin Wright. According to this challenge, semantic realism has to meet the requirement that knowledge of meaning must be publically manifested in linguistic behaviour. In this regard, we will introduce and evaluate John McDowell’s response to this anti-realistic challenge, which was put forward to show that the challenge cannot undermine realism. According to (...) McDowell, knowledge of undecidable sentences’ truth-conditions can be properly manifested in our ordinary practice of asserting such sentences under certain circumstances, and any further requirement will be redundant. Wright’s further objection to McDowell’s response will be also discussed and it will be argued that this objection fails to raise any serious problem for McDowell’s response and that it is an implausible objection in general. (shrink)

Dummett’s notion of indefinite extensibility is influential but obscure. The notion figures centrally in an alternative Dummettian argument for intuitionistic logic and anti-realism, distinct from his more famous, meaning-theoretic arguments to the same effect. Drawing on ideas from Dummett, a precise analysis of indefinite extensibility is proposed. This analysis is used to reconstruct the poorly understood alternative argument. The plausibility of the resulting argument is assessed.

Intuitions about retractions have been used to motivate truth relativism about certain types of claims. Among these figure epistemic modals, knowledge attributions, or personal taste claims. On MacFarlane’s prominent relativist proposal, sentences like “the ice cream might be in the freezer” or “Pocoyo is funny” are only assigned a truth-value relative to contexts of utterance and contexts of assessment. Retractions play a crucial role in the argument for assessment-relativism. A retraction of a past assertion is supposed to be mandatory whenever (...) the asserted sentence is not true at the context of use and the context of assessment. If retractions were not obligatory in these conditions, there would be no normative difference between assessment-relativism and contextualism. The main goal of this paper is to undermine the claim that retractions reveal this normative difference. To this effect, the paper offers a review of three important objections to the obligatoriness of retractions. Taken together, these objections make a strong case against the alleged support that retractions give to assessment-relativism. The objections are moreover supported by recent experimental results that are also discussed. This will satisfy a further goal, which is to undermine the idea that there is a constitutive retraction rule. The paper also discusses two ways to understand what such a rule would be constitutive of, and concludes with a discussion of how to describe what retractions are. (shrink)

In recent years an increasing number of psychologists have begun to explore the prevalence, causes and effects of ordinary people’s intuitions about moral realism. Many of these studies have lacked in construct validity, i.e., they have failed to measure moral realism. My aim in this paper accordingly is to motivate and guide methodological improvements. In analysis of prominent existing measures, I develop general recommendations for overcoming ten prima facie serious worries about research on folk moral realism. G1 and G2 require (...) studies’ answer choices to be as metaethically comprehensive as methodologically feasible. G3 and G4 prevent fallacious inferences from intuitions about related debates. G5 and G6 limit first-order moral and epistemic influences. G7 address studies’ instructions. And G8 and G9 suggest tests of important psychological presuppositions. (shrink)

A novel solution to the knowability paradox is proposed based on Kant’s transcendental epistemology. The ‘paradox’ refers to a simple argument from the moderate claim that all truths are knowable to the extreme claim that all truths are known. It is significant because anti-realists have wanted to maintain knowability but reject omniscience. The core of the proposed solution is to concede realism about epistemic statements while maintaining anti-realism about non-epistemic statements. Transcendental epistemology supports such a view by providing for a (...) sharp distinction between how we come to understand and apply epistemic versus non-epistemic concepts, the former through our capacity for a special kind of reflective self-knowledge Kant calls ‘transcendental apperception’. The proposal is a version of restriction strategy: it solves the paradox by restricting the anti-realist’s knowability principle. Restriction strategies have been a common response to the paradox but previous versions face serious difficulties: either they result in a knowability principle too weak to do the work anti-realists want it to, or they succumb to modified forms of the paradox, or they are ad hoc. It is argued that restricting knowability to non-epistemic statements by conceding realism about epistemic statements avoids all versions of the paradox, leaves enough for the anti-realist attack on classical logic, and, with the help of transcendental epistemology, is principled in a way that remains compatible with a thoroughly anti-realist outlook. (shrink)

The new theory of reference has won popularity. However, a number of noted philosophers have also attempted to reply to the critical arguments of Kripke and others, and aimed to vindicate the description theory of reference. Such responses are often based on ingenious novel kinds of descriptions, such as rigidified descriptions, causal descriptions, and metalinguistic descriptions. This prolonged debate raises the doubt whether different parties really have any shared understanding of what the central question of the philosophical theory of reference (...) is: what is the main question to which descriptivism and the causal-historical theory have presented competing answers. One aim of the paper is to clarify this issue. The most influential objections to the new theory of reference are critically reviewed. Special attention is also paid to certain important later advances in the new theory of reference, due to Devitt and others. (shrink)

According to a widespread interpretation, in the Investigations Wittgenstein adopted a deflationary or redundancy theory of truth. On this view, Wittgenstein’s pronouncements about truth should be understood in the light of his invocation of the equivalences ‘p’ is true = p and ‘p’ is false = not p. This paper shows that this interpretation does not do justice to Wittgenstein’s thoughts. I will be claiming that, in fact, in his second book Wittgenstein is returning to the pre-Tractarian notion of bipolarity, (...) and that his new development of this notion in the Investigations excludes the redundancy-deflationary reading. Wittgenstein’s thoughts about truth are instead compatible with another interpretative option: Wittgenstein remains faithful to his methodological pronouncements, and he merely presents us with platitudes about the notions of “true” and “false”. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of the propositions (...) which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)

Many work on flushing out what our consciousness means in cognitive and phenomenological terms, but no one has yet connected the dots on how consciousness and truth intersect, much less how our phenomenal consciousness can form the ground for most of our models of truth. Here, I connect those dots and argue that the basic structure of our phenomenal consciousness grounds the nature of truth as concordance, to harmonize in agreement, and that most extant theories on truth are well explained (...) in that grounding. Said another way, the unifying and bifurcating intentional structure of phenomenal consciousness is the non-epistemic ground of truth, such that most theories of truth can be explained as particular expressions of concordance based upon the differing aspects of that ground. (shrink)