Nikolaj Jang Lee Linding Pedersen

The neo-Fregean account of arithmetical knowledge is centered around the abstraction principle known as Hume’s Principle: for any concepts X and Y , the number of X ’s is the same as the number of Y ’s just in case there is a 1–1 correspondence between X and Y . The Caesar Problem, originally raised by Frege in §56 of Die Grundlagen der Arithmetik , emerges in the context of the neo-Fregean programme, because, though Hume’s Principle provides a criterion of identity for objects falling under the concept of Number–namely, 1–1 correspondence—the principle fails to deliver a criterion of application. That is, it fails to deliver a criterion that will tell us which objects fall under the concept Number, and so, leaves unanswered the question whether Caesar could be a number. Hale and Wright have recently offered a neo-Fregean solution to this problem. The solution appeals to the notion of a categorical sortal. This paper offers a reconstruction of their solution, which has the advantage over Hale and Wright’s original proposal of making clear what the structure of the background ontology is. In addition, it is shown that the Caesar Problem can be solved in a framework more minimal than that of Hale and Wright, viz . one that dispenses with categorical sortals. The paper ends by discussing an objection to the proposed neo-Fregean solutions, based on the idea that Leibniz’s Law gives a universal criterion of identity. This is an idea that Hale and Wright reject. However, it is shown that a solution very much in keeping with their own proposal is available, even if it is granted that Leibniz’s Law provides a universal criterion of identity.

Traditional theories of truth – such as the correspondence theory – are monist in character. All propositions, regardless of subject-matter, are true in the same way (if true). Recently, this view has been called into question by alethic pluralists (most notably Crispin Wright and Michael Lynch). According to the pluralist, the nature of truth varies across domains. Pluralists try to motivate their position by appealing to the following principle: for any domains D1 and D2, if the metaphysical constitutions of respectively D1 and D2 differ, then D1-propositions and D2-propositions are true in different ways (if true). The aim of the paper isto present a monist challenge to this principle. The gist of the challenge is this: even if metaphysical pluralism (i.e. the antecedent) is granted, truth can be given a uniform account within a correspondence framework. The basic argument is this: every domain that the alethic pluralist is interested in is truth-apt. But any domain that deals in truth-apt propositions likewise deals in facts – after all, it seems a mere platitude that facts are what makes propositions true (if true). Once facts are admitted, the monist can argue as follows: a proposition is true if, and only if, it corresponds to reality. Now, a proposition corresponds to reality if, and only if, it represents reality correctly – and a proposition represents reality correctly if, and only if, what is says is a fact, or is the case. However, since the notion of fact is available for any truth-apt domain, a proposition – whatever its (truth-apt) domain – can be taken to be true if, and only if, it corresponds to reality. Thus, metaphysical pluralism does not imply alethic pluralism.

Our main aim in this paper is to contribute towards a better understanding of the epistemology of absence-based inferences. Many absence-based inferences are classified as fallacies. There are exceptions, however. We investigate what features make absence-based inferences epistemically good or reliable. In Section 2 we present Sanford Goldberg’s account of the reliability of absence-based inference, introducing the central notion of epistemic coverage. In Section 3 we approach the idea of epistemic coverage through a comparison of alethic and evidential principles. The Equivalence Schema–a well-known alethic principle–says that it is true that $p$ if and only if $p$ . We take epistemic coverage to underwrite a suitably qualified evidential analogue of the Equivalence Schema: for a high proportion of values of $p$ , subject $S$ has evidence that $p$ due to her reliance on source $S^{*}$ if and only if $p$ . We show how this evidential version of the Equivalence Schema suffices for the reliability of certain absence-based inferences. Section 4 is dedicated to exploring consequences of the Evidential Equivalence Schema. The slogan ‘absence of evidence is evidence of absence’ has received a lot of bad press. More elaborately, what has received a lot of bad press is something like the following idea: absence of evidence sufficiently good to justify belief in $p$ is evidence sufficiently good to justify belief in $\sim p$ . A striking consequence of the Evidential Equivalence Schema is that absence of evidence sufficiently good to justify belief in p is evidence sufficiently good to justify belief in $\sim p$ . We establish this claim in Section 4 and show how this supports the reliability of an additional type of absence-based inference. Section 4 immediately raises the following question: how can we make philosophically good sense of the idea that absence of evidence is evidence of absence? We address this question in Section 5. Section 6 contains some summary remarks

A mathematical theory T is categorical if, and only if, any two models of T are isomorphic. If T is categorical, it can be shown to be semantically complete: for every sentence ϕ in the language of T, either ϕ follows semantically from T or ¬ϕ does. For this reason some authors maintain that categoricity theorems are philosophically significant: they support the realist thesis that mathematical statements have determinate truth-values. Second-order arithmetic (PA2) is a case in hand: it can be shown to be categorical and semantically complete. The status of second-order logic is a controversial issue, however. Worries about the purported set-theoretic nature and ontological commitments of second-order logic have been influential in the debate.

In this paper we explore the potential bearing of the extended mind thesis—the thesis that the mind extends into the world—on epistemology. We do three things. First, we argue that the combination of the extended mind thesis and reliabilism about knowledge entails that ordinary subjects can easily come to enjoy various forms of restricted omniscience. Second, we discuss the conceptual foundations of the extended mind and knowledge debate. We suggest that the theses of extended mind and extended knowledge lead to a bifurcation with respect to the concepts of belief and knowledge. We suggest that this conceptual bifurcation supports a form of pluralism about these concepts. Third, we discuss whether something similar can be said at the metaphysical level

While historically prominent theories of truth such as the correspondence theory, coherentism, pragmatism, verificationism, and instrumentalism diverge in many ways, they converge in at least one fundamental respect. They are all monist theories of truth. They incorporate the thesis that there is one property—and one property only—in virtue of which propositions can be true. The truth pluralist, on the other hand, rejects this idea. There are several properties in virtue of which propositions can be true. This article offers a survey of recent work on alethic pluralism—presenting various incarnations of the view, objections leveled against them, and various lines of response available to pluralists

Crispin Wright has recently introduced a non-evidential notion of warrant – entitlement of cognitive project – as a promising response to certain sceptical arguments, which have been subject to extensive discussion within mainstream epistemology. The central idea is that, for a given class of cognitive projects, there are certain basic propositions – entitlements – which one is warranted in trusting provided there is no sufficient reason to think them false. (See Wrigh [2].) The aim of this paper is to provide an account of the notion of entitlement of cognitive project and briefly discuss the question whether there is any work for the notion of entitlement to do within the philosophy of mathematics. Bearing in mind its applications in mainstream epistemology, it will be suggested that the notion can be used to formulate a response to certain kinds of scepticism which call into question the warrantability of (acceptances of) propositions that appear integral to mathematical theorizing in a given mathematical theory T – in particular, that T is consistent and that T ’s background logic is sound.

The relative merits and demerits of historically prominent views such as the correspondence theory, coherentism, pragmatism, verificationism, and instrumentalism have been subject to much attention in the truth literature and have fueled the long-lived debate over which of these views is the most plausible one. While diverging in their specific philosophical commitments, adherents of these historically prominent views agree in at least one fundamental respect. They are all alethic monists. They all endorse the thesis that there is only one property in virtue of which propositions can be true, and so, in this sense, take truth to be one. The truth pluralist, on the other hand, rejects this idea. There are several properties in virtue of which propositions can be true. The literature on truth pluralism has been growing steadily for the past twenty years. This volume, however, is the first of its kind—the first collection of papers focused specifically on pluralism about truth. Part I is dedicated to the development, investigation, and critical discussion of different forms of pluralism. An additional reason to look at truth pluralism with interest is the significant connections it bears to other debates in the truth literature—the debates concerning traditional theories of truth and the deflationism/inflationism divide being cases in hand. Parts II and III of the volume connect truth pluralism to these two debates.

Recently there has been a surge of interest in the intersection between epistemology and action theory, especially in principles linking rationality in thought and rationality in action. Recently there has also been a surge of interest in the epistemic significance of perceived peer disagreement: what, epistemically speaking, is the rational response in light of disagreement with someone whom one regards as an epistemic peer? The objective of this paper is to explore these two issues—separately, but also in connection with one another. I turn first to the idea that the normative standing of our actions depends on the normative standing of our beliefs. I endorse this idea. More precisely, I endorse a principle according to which sufficiently high credence in success conditions for a given goal-directed action is a necessary condition on rational execution of that action. I then turn to the debate concerning the epistemic significance of perceived peer disagreement. The basic issue is whether such disagreement is always epistemically significant in the sense of serving as a defeater of the initial credences of the disagreeing parties. Conformists argue that this is so while non-conformists deny it. I present a new argument against a brand of non-conformism that I call “strong non-conformism”. The key premise is the principle that sufficiently high credence in success conditions for a given goal-directed action is a necessary condition on rational execution of that action. I argue that, given this principle, strong non-conformism fails to yield the verdict that the epistemic requirement on rational action is violated in a case where, intuitively, it is violated. This is because strong non-conformism has it that disagreement with a perceived peer does not act as a defeater in the relevant case. Conformism fares better.

Pluralistic ignorance is a socio-psychological phenomenon that involves a systematic discrepancy between people’s private beliefs and public behavior in certain social contexts. Recently, pluralistic ignorance has gained increased attention in formal and social epistemology. But to get clear on what precisely a formal and social epistemological account of pluralistic ignorance should look like, we need answers to at least the following two questions: What exactly is the phenomenon of pluralistic ignorance? And can the phenomenon arise among perfectly rational agents? In this paper, we propose answers to both these questions. First, we characterize different versions of pluralistic ignorance and define the version that we claim most adequately captures the examples cited as paradigmatic cases of pluralistic ignorance in the literature. In doing so, we will stress certain key epistemic and social interactive aspects of the phenomenon. Second, given our characterization of pluralistic ignorance, we argue that the phenomenon can indeed arise in groups of perfectly rational agents. This, in turn, ensures that the tools of formal epistemology can be fully utilized to reason about pluralistic ignorance

Alethic pluralism is the view that the nature of truth is not uniform across domains. There are several ways of bang true $(T_1 ...\,T_n )$ A simple argument, the 'instability challenge', purports to show that this view is inherently unstable. One can simply say that something is uniformly true if and only if it is T₁ or ... or $\,T_n $ . Being uniformly true is a single truth property that applies across the board, and so the nature of truth is uniform across domains, contra pluralism. I defend pluralism against the instability challenge. I show that the challenge bifurcates: one Challenge is formulated in terms of predicates, and the other is formulated in terms of properties. Vie pluralist has the resources to defuse both of these. The sparse/abundant property distinction and considerations of explanatory asymmetry play a crucial role in my argument

In this paper I discuss two fundamental challenges concerning Crispin Wright's notion of entitlement of cognitive project: firstly, whether entitlement is an epistemic kind of warrant since, seemingly, it is not underwritten by epistemic reasons, and, secondly, whether, in the absence of such reasons, the kind of rationality associated with entitlement is epistemic in nature. The paper investigates three possible lines of response to these challenges. According to the first line of response, entitlement of cognitive project is underwritten by epistemic reasons – and thus supports epistemic rationality – because, when P is an entitlement, trust in P is a dominant strategy with respect to promotion of epistemic value. The second line of response replaces dominance with maximization of expected utility. I argue that both of these proposals are flawed and develop an alternative line of response.

Here is a well-known thought about truth: Truth consists in correspondence with reality. A sentence is true just in case what it says corresponds with how the world is. Theories of truth that incorporate this thought are naturally regarded as robust or “heavyweight”. Truth is to be understood in a realist fashion. The world decides what is true and what is not. A recent incarnation of the correspondence view is found in truth-maker theories, whose adherents maintain that truths are true in virtue of there being something – a truth-maker – in the world that makes them so.2.