Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this article, I (...) address two criticisms that have been raised in Tatton-Brown against our approach: that it leads to a form of relativism according to which validity is equated with social agreement and that it implies an antiformalizability thesis according to which it is not the case that all rigorous mathematical proofs can be formalized. I reject both criticisms and suggest that our previous case studies provide insight into the plausibility of two related but quite different theses. (shrink)

Problems of logical theory choice are current being widely dis- cussed in the context of anti-exceptionalist views on logic. According to those views, logic is not a special science among others, so, in particular, the methodology for theory choice should be the same in logic as for other scientific disciplines. Richard Routley advanced one such methodology which meshes well with anti-exceptionalism, and argued that it leads one to choosing one single logic, which is a kind of ultralogic. We argue that (...) the choice for only one correct system of logic may be rejected on the basis of the methodology proposed by Routley and, furthermore, that taking anti-exceptionalism about logic seriously recommends that a pluralist view of logic should be accepted. We call this view “full-blooded anti-exceptionalism”, and the resulting view on logic, lacking a proper name, “local pluralism”. (shrink)

Logical pluralism is the view that there is more than one correct logic. In this article, I explore what logical pluralism is, and what it entails, by: (i) distinguishing clearly between relativism about a particular domain and pluralism about that domain; (ii) distinguishing between a number of forms logical pluralism might take; (iii) attempting to distinguish between those versions of pluralism that are clearly true and those that are might be controversial; and (iv) surveying three prominent attempts to argue for (...) logical pluralism and evaluating them along the criteria provided by (ii) and (iii). (shrink)

Telic monism in logic is the thesis that there is one single philosophically primary goal to logic. A different way to put it is that there is only one canonical application to logic. This thesis is widely present—implicitly or more explicitly—in the literature on the philosophy of logic, yet has not been examined nor argued for extensively. In this paper I will present and critically examine telic monism. One prominent candidate for the canonical application of logic, namely the formal codification (...) of logical consequence in natural language, will be challenged directly. The critique will then be generalized by appealing to a practice-based philosophy of logic. The general argument I put forth here claims that we have no principled reason to assume there to be just one primary goal to logic. Rather, I claim that it is more plausible that there actually is a variety of goals, purposes and applications to logic, without one of them enjoying primacy over the others. If this argument succeeds, at least one of the consequences is that it allows for a kind of logical pluralism that has previously been deemed insignificant, namely logical instrumentalism. (shrink)

In this paper I articulate and defend a view that I call phenomenal dogmatism about intuitive justification. It is dogmatic because it includes the thesis: if it intuitively seems to you that p, then you thereby have some prima facie justification for believing that p. It is phenomenalist because it includes the thesis: intuitions justify us in believing their contents in virtue of their phenomenology—and in particular their presentational phenomenology. I explore the nature of presentational phenomenology as it occurs perception, (...) and I make a case for thinking that it is present in a wide variety of logical, mathematical, and philosophical intuitions. (shrink)

According to the most popular non-skeptical views about intuition, intuitions justify beliefs because they are based on understanding. More precisely: if intuiting that p justifies you in believing that p it does so because your intuition is based on your understanding of the proposition that p. The aim of this paper is to raise some challenges for accounts of intuitive justification along these lines. I pursue this project from a non-skeptical perspective. I argue that there are cases in which intuiting (...) that p justifies you in believing that p, but such that there is no compelling reason to think this is because your intuition is based on your understanding of the proposition that p. (shrink)

Radical empiricism is the view that experience is the only source of knowledge. Hence, radical empiricism denies the existence of a priori knowledge. Its most famous proponents are John Stuart Mill and W. V. Quine. Although both reject a priori knowledge, they offer different empiricist accounts of the knowledge alleged by their opponents to be a priori. My primary concern in this paper is not with the cogency of their positive accounts. My focus is their arguments against a priori knowledge. (...) My goal is to establish that although they offer very different arguments against the existence of a priori knowledge, each of their arguments suffers from a common defect. They both fail to appreciate the phenomenon of epistemic overdetermination and its role in the theory of knowledge. (shrink)

This paper scrutinizes the debate over logical pluralism. I hope to make this debate more tractable by addressing the question of motivating data: what would count as strong evidence in favor of logical pluralism? Any research program should be able to answer this question, but when faced with this task, many logical pluralists fall back on brute intuitions. This sets logical pluralism on a weak foundation and makes it seem as if nothing pressing is at stake in the debate. The (...) present paper aims to improve this situation by looking at a promising case study and drawing general lessons about the kind of evidence that would support logical pluralism. I argue that the best motivation for logical pluralism will ultimately be rooted in certain kinds of performative data. (shrink)

Anti-exceptionalism about logic is the thesis that logic is not special. In this paper, I consider, and reject, a challenge to this thesis. According to this challenge, there are basic logical principles, and part of what makes such principles basic is that they are epistemically exceptional. Thus, according to this challenge, the existence of basic logical principles provides reason to reject anti-exceptionalism about logic. I argue that this challenge fails, and that the exceptionalist positions motivated by it are thus unfounded. (...) I make this case by disambiguating two senses of ‘basic’ and showing that, once this disambiguation is taken into account, the best reason we have for thinking that there are basic principles actually implies that those principles do not require a special epistemology. Consequently, the existence of basic logical principles provides reason to accept, rather than reject, anti-exceptionalism concerning the epistemology of logic. I conclude by explaining how an abductivist, anti-exceptionalist approach to the epistemology of logic can accommodate the notion of basic logical principles. (shrink)

The paper develops a conception of epistemic warrant as applied to perceptual belief, called "entitlement", that does not require the warranted individual to be capable of understanding the warrant. The conception is situated within an account of animal perception and unsophisticated perceptual belief. It characterizes entitlement as fulfillment of an epistemic norm that is apriori associated with a certain representational function that can be known apriori to be a function of perception. The paper connects anti-individualism, a thesis about the nature (...) of mental states, and perceptual entitlement. It presents an argument that explains the objectivity and validity of perceptual entitlement partly in terms of the nature of perceptual states–hence the nature of perceptual beliefs, which are constitutively associated with perceptual states. The paper discusses ways that an individual can be entitled to perceptual belief through its connection to perception, and ways that entitlement to perceptual belief can be undermined. (shrink)

The paper develops a conception of epistemic warrant as applied to perceptual belief, called “entitlement”, that does not require the warranted individual to be capable of understanding the warrant. The conception is situated within an account of animal perception and unsophisticated perceptual belief. It characterizes entitlement as fulfillment of an epistemic norm that is apriori associated with a certain representational function that can be known apriori to be a function of perception. The paper connects anti‐individualism, a thesis about the nature (...) of mental states, and perceptual entitlement. It presents an argument that explains the objectivity and validity of perceptual entitlement partly in terms of the nature of perceptual states–hence the nature of perceptual beliefs, which are constitutively associated with perceptual states. The paper discusses ways that an individual can be entitled to perceptual belief through its connection to perception, and ways that entitlement to perceptual belief can be undermined. (shrink)

Tyler Burge presents an original study of the most primitive ways in which individuals represent the physical world. By reflecting on the science of perception and related psychological and biological sciences, he gives an account of constitutive conditions for perceiving the physical world, and thus aims to locate origins of representational mind.

The view that logic is true independently of a subject matter is criticized—enlarging on Quine's criticisms and adding further ones. It is then argued apriori that full reflective understanding of logic and deductive reasoning requires substantial commitment to mathematical entities. It is emphasized that the objectively apriori connections between deductive reasoning and commitment to mathematics need not be accepted by or even comprehensible to a given deductive reasoner. The relevant connections emerged only slowly in the history of logic. But they (...) can be recognized retrospectively as implicit in logic and deductive reasoning. The paper concludes with discussion of the relevance of its main argument to Kant's question—how is apriori knowledge of a subject matter possible? (shrink)

The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of 'blind but blameless' reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible.

This essay distinguishes between metaphysical and epistemological conceptions of analyticity. The former is the idea of a sentence that is ‘true purely in virtue of its meaning’ while the latter is the idea of a sentence that ‘can be justifiably believed merely on the basis of understanding its meaning’. It further argues that, while Quine may have been right to reject the metaphysical notion, the epistemological notion can be defended from his critique and put to work explaining a priori justification. (...) Along the way, a number of further distinctions relevant to the theory of analyticity and the theory of apriority are made and their significance is explained. (shrink)

Here we challenge the orthodoxy according to which abduction is an a posteriori mode of inference. We start by providing a case study illustrating how abduction can justify a philosophical claim not justifiable by empirical evidence alone. While many grant abduction's epistemic value, nearly all assume that abductive justification is a posteriori, on grounds that our belief in abduction's epistemic value depends on empirical evidence about how the world contingently is. Contra this assumption, we argue, first, that our belief in (...) abduction’s epistemic value is not and could not be justified a posteriori, and second, that attention to the roles experience plays in abductive justification supports taking abduction to be an a priori mode of inference. We close by highlighting how our strategy for establishing the a priority of abduction positively contrasts with strategies in Bonjour (1998), Swinburne (2001), and Peacocke (2004) aiming to establish the a priority of certain ampliative modes of inference or abductive principles. (shrink)

Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...) theoretically satisfying treatment of their favoured epistemic source. It is argued, first, that intuitions and perceptual experiences are at a certain level of abstraction the same type of mental state, presentations, which are distinct from beliefs, hunches, inclinations, attractions, and seemings. The notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states. Subsequently, it is argued that presentations, intuitive no less than sensory, are by their nature poised to play a distinctive epistemic role. Specifically, in the case of intuition, we encounter an intellectual state that is so structured as to provide justification without requiring justification in turn—something which may, thus, be thought of as ‘given’. (shrink)

The notion of a non-sensory mental state or event that plays a prominent role in coming to understand, an epistemic achievement distinct from mere knowledge, featured prominently in historical writings on philosophy, and philosophical methodology. It is, however, completely absent from contemporary discussions of the subject. This paper argues that intuition plays an epistemic role in understanding, including philosophical understanding, and offers an explanation of how intuition manages to play this role, if and when it does. It is argued, subsequently, (...) that this role is autonomous, in the sense that a source of understanding cannot be reduced to a source of justification, evidence, or reason. Finally, it is noted that such autonomy implies that popular forms of skepticism about intuition do not impugn intuition’s epistemic significance with respect to its status as a source of understanding. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

This book examines phenomenal conservatism, one of the most influential and promising internalist conceptions of non-inferential justification debated in current epistemology and philosophy of mind. It also explores the significance of the findings of this examination for the general debate on epistemic justification. According to phenomenal conservatism, non-inferential justification rests on seemings or appearances, conceived of as experiences provided with propositional content. Phenomenal conservatism states that if it appears to S that P, in the absence of defeaters, S thereby has (...) some justification for believing that P. This view provides the basis for foundationalism and many ordinary epistemic practices. This book sheds new light on phenomenal conservatism by assessing objections to it and examining epistemological merits and advantages attributed to it. In a nutshell, phenomenal conservatism is actually compatible with Bayesian reasoning, and it is unaffected by bootstrapping problems and challenges that appeal to the cognitive penetrability of perception. Nevertheless, appearance-based justification proves unstable or elusive and its antisceptical bite is more limited than expected. These difficulties could be surmounted if phenomenal conservatism were integrated with a theory of inferential justification. The book appeals to scholars and postgraduates in the field of epistemology and philosophy of mind who are interested in the rational roles of appearances. (shrink)

We are justified in employing the rule of inference Modus Ponens (or one much like it) as basic in our reasoning. By contrast, we are not justified in employing a rule of inference that permits inferring to some difficult mathematical theorem from the relevant axioms in a single step. Such an inferential step is intuitively “too large” to count as justified. What accounts for this difference? In this paper, I canvass several possible explanations. I argue that the most promising approach (...) is to appeal to features like usefulness or indispensability to important or required cognitive projects. On the resulting view, whether an inferential step counts as large or small depends on the importance of the relevant rule of inference in our thought. (shrink)