For Kant, the human cognitive faculty has two sub-faculties: sensibility and the understanding. Each has pure forms which are necessary to us as humans: space and time for sensibility; the categories for the understanding. But Kant is careful to leave open the possibility of there being creatures like us, with both sensibility and understanding, who nevertheless have different pure forms of sensibility. They would be finite rational beings and discursive cognizers. But they would not be human. And this raises a (...) question about the pure forms of the understanding. Does Kant leave open the possibility of discursive cognizers who have different categories? Even if other discursive cognizers might not sense like us, must they at least think like us? We argue that textual and systematic considerations do not determine the answers to these questions and examine whether Kant thinks that the issue cannot be decided. Consideration of his wider views on the nature and limits of our knowledge of mind shows that Kant could indeed remain neutral on the issue but that the exact form his neutrality can take is subject to unexpected constraints. The result would be an important difference between what Kant says about discursive cognizers with other forms of sensibility and what he is in a position to say about discursive cognizers with other forms of understanding. Kantian humility here takes on a distinctive character. (shrink)

Against a view currently popular in the literature, it is argued that Kant was not a niıve realist about perceptual experience. Naive realism entails that perceptual experience is object-dependent in a very strong sense. In the first half of the paper, I explain what this claim amounts to and I undermine the evidence that has been marshalled in support of attributing it to Kant. In the second half of the paper, I explore in some detail Kant’s account of hallucination and (...) argue that no such account is available to someone who thinks that veridical perceptual experience is object-dependent in the naive realist sense. Kant’s theory provides for a remarkably sophisticated, bottom-up explanation of the phenomenal character of hallucinatory episodes and is crucial for gaining a proper understanding of his model of the mind and its place in nature. (shrink)

This essay considers Kant’s theory of modality in light of a debate in contemporary modal metaphysics and modal logic concerning the Barcan formulas. The comparison provides a new and fruitful perspective on Kant’s complex and sometimes confusing claims about possibility and necessity. Two central Kantian principles provide the starting point for the comparison: that the possible must be grounded in the actual and that existence is not a real predicate. Both are shown to be intimately connected to the Barcan formulas, (...) and Kant’s views on what he distinguishes as three different kinds of modality are then considered in light of this connection. (shrink)

This paper draws out and connects two neglected issues in Kant’s conception of a priori knowledge. Both concern topics that have been important to contemporary epistemology and to formal epistemology in particular: knowability and luminosity. Does Kant commit to some form of knowability principle according to which certain necessary truths are in principle knowable to beings like us? Does Kant commit to some form of luminosity principle according to which, if a subject knows a priori, then they can know that (...) they know a priori? I defend affirmative answers to both of these questions, and by considering the special kind of modality involved in Kant’s conceptions of possible experience and the essential completability of metaphysics, I argue that his combination of knowability and luminosity principles leads Kant into difficulty. (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)

In this paper I return to the question of whether intuition is object-dependent. Kant’s account of the imagination appears to suggest that intuition is not object-dependent. On a recent proposal, however, the imagination is a faculty of merely inner intuition, the inner objects of which exist and are present in the way demanded by object-dependence views, such as Lucy Allais’s relational account. I argue against this proposal on both textual and philosophical grounds. It is inconsistent with what Kant says about (...) how the imagination functions and is ultimately incompatible with the relational account it is supposed to support. Kant’s account of the imagination remains a serious obstacle for the view that intuition is object-dependent. (shrink)

This essay reassesses the relation between Kant and Kripke on the relation between necessity and the a priori. Kripke famously argues against what he takes to be the traditional view that a statement is necessary only if it is a priori, where, very roughly, what it means for a statement to be necessary is that it is true and could not have been false and what it means for a statement to be a priori is that it is knowable independently (...) of experience. Call such a view the Entailment Thesis. Along with many Kant scholars, Kripke thinks that Kant endorses the Entailment Thesis. Thus Kripke and many others take his arguments against the Entailment Thesis to tell against Kant and to mark an important point of disagreement with him. I will argue that this is a mistake. Kant does not endorse the Entailment Thesis that Kripke and many others attribute to him. He does endorse two quite different theses concerning the relation between necessity and the a priori, as he conceives them. One is a matter of definition and the other is a very substantial philosophical thesis indeed—to establish it is the aim of the entire Critique of Pure Reason. But Kripke’s arguments against the Entailment Thesis tell against neither of Kant’s theses, as they involve crucially different conceptions of necessity and the a priori. This superficial lack of disagreement masks deep disagreements, but these result from divergent views regarding matters such as realism, modal epistemology, and philosophical methodology; views which Kant does a lot, and Kripke very little, to argue for. (shrink)

The aim of the Analytic of Concepts is to derive and deduce a set of pure concepts of the understanding, the categories, which play a central role in Kant’s explanation of the possibility of synthetic a priori cognition and judgment. This chapter is structured around two questions. First, what is a pure concept of the understanding? Second, what is involved in a deduction of a pure concept of the understanding? In answering the first, we focus on how the categories differ (...) from the pure forms of sensibility and examine whether they are known only to be the pure forms of human thinking or rather the forms of discursive cognition as such. In answering the second, we draw a distinction between the application and the exemplification of the categories and use it to identify different ways of understanding Kant’s project in the Transcendental Deduction of the Categories. These questions connect because the answer to the first determines how we should understand the kind of entitlement which is to be established in the Deduction. (shrink)

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...) acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

In this paper I offer an interpretation of Kant’s theory of perceptual error based on his remarks in the Anthropology. Both hallucination and illusion, I argue, are for Kant species of experience and therefore require the standard co-operation of sensibility and understanding. I develop my account in a conceptualist framework according to which the two canonical classes of non-veridical experience involve error in the basic sense that how they represent the world as being is not how the world is. In (...) hallucination this is due to the misapplication of categories and in illusion to the misapplication of empirical concepts. Yet there is also room in this framework for a distinction in terms of cognitive functionality between the level of experience, which is merely judgementally structured, and that of judgement proper, which involves the free action of a conscious agent. This distinction enables Kant to allow for the otherwise problematic phenomenon of self-aware non-veridicality. (shrink)

It is often claimed that anti-realism is a form of transcendental idealism or that Kant is an anti-realist. It is also often claimed that anti-realists are committed to some form of knowability principle and that such principles have problematic consequences. It is therefore natural to ask whether Kant is so committed, and if he is, whether this leads him into difficulties. I argue that a standard reading of Kant does indeed have him committed to the claim that all empirical truths (...) are knowable and that this claim entails that there is no empirical truth that is never known. I extend the result to a priori truths and draw some general philosophical lessons from this extension. However, I then propose a re-examination of Kant’s notion of experience according to which he carefully eschews any commitment to empirical knowability. Finally I respond to a remaining problem that stems from a weaker, justified believability principle. (shrink)

Our aim in this chapter is to shed light on Kant’s account of the pure forms of sensibility by focusing on a somewhat neglected issue: Kant’s restriction of his claims about space and time to the case of human sensibility. Kant argues that space and time are the pure forms of sensibility for human cognizers. But he also says that we cannot know whether space and time are likewise the pure forms of sensibility for all discursive cognizers. A great deal (...) of attention has focused on the first of these claims, both on how Kant argues for it and how it relates to transcendental idealism. But a satisfactory interpretation must also account for the second claim, and it must account for the fact that Kant endorses both of them. What we need is an explanation of why Kant thinks our knowledge that space and time are the pure forms of sensibility extends to all human beings but no further. (shrink)

In this extended critical discussion of 'Kant's Modal Metaphysics' by Nicholas Stang (OUP 2016), I focus on one central issue from the first chapter of the book: Stang’s account of Kant’s doctrine that existence is not a real predicate. In §2 I outline some background. In §§3-4 I present and then elaborate on Stang’s interpretation of Kant’s view that existence is not a real predicate. For Stang, the question of whether existence is a real predicate amounts to the question: ‘could (...) there be non-actual possibilia?’ (p.35). Kant’s view, according to Stang, is that there could not, and that the very notion of non-actual or ‘mere’ possibilia is incoherent. In §5 I take a close look at Stang’s master argument that Kant’s Leibnizian predecessors are committed to the claim that existence is a real predicate, and thus to mere possibilia. I argue that it involves substantial logical commitments that the Leibnizian could reject. I also suggest that it is danger of proving too much. In §6 I explore two closely related logical commitments that Stang’s reading implicitly imposes on Kant, namely a negative universal free logic and a quantified modal logic that invalidates the Converse Barcan Formula. I suggest that each can seem to involve Kant himself in commitment to mere possibilia. (shrink)

Recent debates in the interpretation of Kant’s theoretical philosophy have focused on the nature of Kantian intuition and, in particular, on the question of whether intuitions depend for their existence on the existence of their objects. In this paper we show how opposing answers to this question determine different accounts of the nature of Kantian cognition and we suggest that progress can be made on determining the nature of intuition by considering the implications different views have for the nature of (...) cognition. (shrink)

There is a tension at the heart of Lucy Allaiss transcendental idealism. The problem arises from her use of two incompatible theories in contemporary philosophy - relationalism about perception, or naïve realism, and relationalism about colour, or more generally relationalism about any such perceptual property. The problem is that the former requires a more robust form of realism about the properties of the objects of perception than can be accommodated in the partially idealistic framework of the latter. On Allais’ interpretation, (...) Kant’s notorious attempt to balance realism and idealism remains unstable. (shrink)

The essays in this volume explore those aspects of Kant’s writings which concern issues in the philosophy of mind. These issues are central to any understanding of Kant’s critical philosophy and they bear upon contemporary discussions in the philosophy of mind. Fourteen specially written essays address such questions as: What role does mental processing play in Kant’s account of intuition? What kinds of empirical models can be given of these operations? In what sense, and in what ways, are intuitions object-dependent? (...) How should we understand the nature of the imagination? What is inner sense, and what does it mean to say that time is the form of inner sense? Can we cognize ourselves through inner sense? How do we self-ascribe our beliefs and what role does self-consciousness play in our judgments? Is the will involved in judging? What kind of knowledge can we have of the self ? And what kind of knowledge of the self does Kant proscribe? These essays showcase the depth of Kant’s writings in the philosophy of mind, and the centrality of those writings to his wider philosophical project. Moreover, they show the continued relevance of Kant’s writings to contemporary debates about the nature of mind and self. Contents: 0. Introduction Anil Gomes and Andrew Stephenson 1. Kant, The Philosophy Of Mind, And Twentieth Century Analytic Philosophy Anil Gomes 2. Synthesis And Binding Lucy Allais 3. Understanding Non-Conceptual Representation Of Objects: Empirical Models Of Sensibility’s Operation Katherine Dunlop 4. Are Kantian Intuitions Object-Dependent? Stefanie Grüne 5. Intuition And Presence Colin McLear 6. Imagination And Inner Intuition Andrew Stephenson 7. Inner Sense And Time Ralf M. Bader 8. Can’t Kant Cognize Himself? Or, A Problem For (Almost) Every Interpretation Of The Refutation Of Idealism Andrew Chignell 9. A Kantian Critique Of Transparency Patricia Kitcher 10. Judging For Reasons: On Kant And The Modalities Of Judgment Jessica Leech 11. Kant On Judging And The Will Jill Vance Buroker 12. Self and Selves Ralph C. S. Walker 13. Subjects Of Kant’s First Paralogism Tobias Rosefeldt 14. The Lessons Of Kant’s Paralogisms Paul Snowdon. (shrink)

Review of Markus Willaschek, Kant on the Sources of Metaphysics: The Dialectic of Pure Reason. Cambridge: Cambridge University Press, 2018.

Is a human more conscious than an octopus? In the science of consciousness, it’s oftentimes assumed that some creatures (or mental states) are more conscious than others. But in recent years, a number of philosophers have argued that the notion of degrees of consciousness is conceptually confused. This paper (1) argues that the most prominent objections to degrees of consciousness are unsustainable, (2) examines the semantics of ‘more conscious than’ expressions, (3) develops an analysis of what it is for a (...) degreed property to count as degrees of consciousness, and (4) applies the analysis to various theories of consciousness. I argue that whether consciousness comes in degrees ultimately depends on which theory of consciousness turns out to be correct. But I also argue that most theories of consciousness entail that consciousness comes in degrees. (shrink)

Empirical work has lately confirmed what many philosophers have taken to be true: people are ‘biased toward the future’. All else being equal, we usually prefer to have positive experiences in the future, and negative experiences in the past. According to one hypothesis, the temporal metaphysics hypothesis, future-bias is explained either by our beliefs about temporal metaphysics—the temporal belief hypothesis—or alternatively by our temporal phenomenology—the temporal phenomenology hypothesis. We empirically investigate a particular version of the temporal belief hypothesis according to (...) which future-bias is explained by the belief that time robustly passes. Our results do not match the apparent predictions of this hypothesis, and so provide evidence against it. But we also find that people give more future-biased responses when asked to simulate a belief in robust passage. We take this to suggest that the phenomenology that attends simulation of that belief may be partially responsible for future-bias, and we examine the implications of these results for debates about the rationality of future-bias. (shrink)

This paper examines the idea of "objective phenomenology," or a way of understanding the phenomenal character of conscious experiences that doesn’t require one to have had the kinds of experiences under consideration. My central thesis is that structural facts about experience—facts that characterize purely how conscious experiences are structured—are objective phenomenal facts. I begin by precisifying the idea of objective phenomenology and diagnosing what makes any given phenomenal fact subjective. Then I defend the view that structural facts about experience are (...) objective. I also argue that structural facts about experience, despite being objective, nevertheless still give rise to an explanatory gap. (shrink)

Empirical evidence suggests that a majority of people believe that time robustly passes, and that many also report that it seems to them, in experience, as though time robustly passes. Non-dynamists deny that time robustly passes, and many contemporary non-dynamists—deflationists—even deny that it seems to us as though time robustly passes. Non-dynamists, then, face the dual challenge of explaining why people have such beliefs and make such reports about their experiences. Several philosophers have suggested the stable-self explanation, according to which (...) what partly explains one or both of the explananda is that people believe themselves to have a stable persisting self which is imagined either as moving through time, or as being stationary, with time moving around it. This paper empirically investigates this explanation. We found, however, no evidential support for the stable-self explanation, leaving the non-dynamist but also, we will argue, the dynamist, with an extant explanatory challenge. (shrink)

This is a discussion of the state of discussion on pragmatic reasons for belief.

Virtue theories of argumentation (VTA) emphasize the roles arguers play in the conduct and evaluation of arguments, and lay particular stress on arguers’ acquired dispositions of character, that is, virtues and vices. The inspiration for VTA lies in virtue epistemology and virtue ethics, the latter being a modern revival of Aristotle’s ethics. Aristotle is also, of course, the father of Western logic and argumentation. This paper asks to what degree Aristotle may thereby be claimed as a forefather by VTA.

An important advance in normativity research over the last decade is an increased understanding of the distinction, and difference, between normativity and rationality. Normativity concerns or picks out a broad set of concepts that have in common that they are, put loosely, guiding. For example, consider two commonly used normative concepts: that of a normative reason and that of ought. To have a normative reason to perform some action is for there to be something that counts in favour of performing (...) that action. Likewise with ought, when there is sufficient evidence for something, one ought to believe it (at least under normal circumstances). Not all guidance need be directed towards a specific state or a specific action. Subject to the requirements of normativity, too, are relations. It is commonly believed, for example, that we ought not to hold contradictory beliefs.1 At least some of the requirements that concern relations amongst an agent’s mental states are, or seem, distinctive. Agents who fail to satisfy these requirements are considered, at least to some degree, irrational. On many current views, being irrational is distinct in some way from not being how one ought to be; rationality is a concept distinct from normativity. Much of the literature on this topic over the last decade stems from attempts to capture the characteristic features of the requirements of rationality. Two influential views in particular did much to set the agenda. The first of these two was put forward John Broome.2 His view, the particulars of which I shall discuss in more detail below, is that the requirements of rationality could be expressed using a normative relation, which he calls a ‘normative requirement’. Normative requirements are conditionals governed by an all-thingsconsidered ought. In the case of rationality, the conditional is made up entirely of mental states.. (shrink)

A list of resources for virtue theories of argumentation. Last updated October 31st, 2023.

In this chapter, I present and explore various arguments for skepticism that are related to memory. My focus will be on the aspects of the arguments that are unique to memory, which are not shared, for example, by the more often explored skeptical arguments related to perception. -/- Here are some interesting upshots. First, a particular problem for justifiably concluding that one's memory is reliable is that any reasoning in favor of this conclusion will either result in epistemically circularity or (...) not be sufficient to justify the conclusion. Second, since many beliefs stored in memory do not appear to be based on evidence, it might also appear to follow that they are not justified. Third, although many stored memory beliefs are not based on stored memory experiences in the same way that perceptual beliefs are based on perceptual experiences, skeptical scenarios loom just as problematically for memory beliefs as they do for perceptual beliefs. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, (...) as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

A number of `no-proposition' approaches to the liar paradox find themselves implicitly committed to a moderate disquotational principle: the principle that if an utterance of the sentence `$P$' says anything at all, it says that $P$ (with suitable restrictions). I show that this principle alone is responsible for the revenge paradoxes that plague this view. I instead propose a view in which there are several closely related language-world relations playing the `semantic expressing' role, none of which is more central to (...) semantic theorizing than any other. I use this thesis about language and the negative result about disquotation to motivate the view that people do say things with utterances of paradoxical sentences, although they do not say the proposition you'd always expect, as articulated with a disquotational principle. (shrink)

Summary Background Self-binding directives instruct clinicians to overrule treatment refusal during future severe episodes of illness. These directives are promoted as having potential to increase autonomy for individuals with severe episodic mental illness. Although lived experience is central to their creation, service users’ views on self-binding directives have not been investigated substantially. This study aimed to explore whether reasons for endorsement, ambivalence, or rejection given by service users with bipolar disorder can address concerns regarding self-binding directives, decision-making capacity, and human (...) rights. Methods This study used qualitative data from an internet-based survey distributed to the mailing list of the UK charity Bipolar UK, which contained multiple closed and open questions on advance decision-making in bipolar disorder. Quantitative analysis of a closed question about self-binding directives had already demonstrated endorsement amongst a very high proportion of participants with bipolar disorder who completed the survey. We conducted thematic analysis of responses from those participants who answered a subsequent open question about reasons for their view. Research was co-produced within a multi-disciplinary team, with clinical, legal, and ethical expertise, and lived experience of bipolar disorder. Ideas and methodologies associated with all these areas of expertise were used in the analysis of these reasons and to gain insight into the thoughts of individuals with bipolar disorder about self-binding directives and associated issues. Findings Between Oct 23 and Dec 5, 2017, 932 individuals with a self-reported clinical diagnosis of bipolar disorder completed the internet survey, with 565 (154 men; 400 women; 11 transgender or other) providing free text answers to the open question. A large majority of respondents endorsed self-binding directives, nearly all describing a determinate shift to types of distorted thinking and decision-making when unwell as their key justification. Responses indicating ambivalence were dominated by logistical concerns about the drafting and implementation of self-binding directives, while those who rejected self-binding directives also cited logistical concerns, validity of their thinking when unwell, and potential contravention of human rights. Interpretation This study is, to our knowledge, the first large study of reasons why mental health service users might endorse or reject the use of self-binding directives. The findings provide empirical support for introducing self-binding directives into mental health advance decision-making practice and policy and may help to address enduring ethical concerns surrounding possible implementation of the directive while a person retains decision-making capacity. The opinions expressed here in responses given by multiple service users with bipolar disorder challenge a prominent view within international disability rights debates that involuntary treatment and recognition of impaired mental capacity constitute inherent human rights violations. Funding The Wellcome Trust . (shrink)

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which (...) a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

Conscious experiences are characterized by mental qualities, such as those involved in seeing red, feeling pain, or smelling cinnamon. The standard framework for modeling mental qualities represents them via points in geometrical spaces, where distances between points inversely correspond to degrees of phenomenal similarity. This paper argues that the standard framework is structurally inadequate and develops a new framework that is more powerful and flexible. The core problem for the standard framework is that it cannot capture precision structure: for example, (...) consider the phenomenal contrast between seeing an object as crimson in foveal vision versus merely as red in peripheral vision. The solution I favor is to model mental qualities using regions, rather than points. I explain how this seemingly simple formal innovation not only provides a natural way of modeling precision, but also yields a variety of further theoretical fruits: it enables us to formulate novel hypotheses about the space and structures of mental qualities, formally differentiate two dimensions of phenomenal similarity, generate a quantitative model of the phenomenal sorites, and define a measure of discriminatory grain. A noteworthy consequence is that the structure of the mental qualities of conscious experiences is fundamentally different from the structure of the perceptible qualities of external objects. (shrink)

This paper argues that new light may be shed on mathematical reasoning in its non-pathological forms by careful observation of its pathologies. The first section explores the application to mathematics of recent work on fallacy theory, specifically the concept of an ‘argumentation scheme’: a characteristic pattern under which many similar inferential steps may be subsumed. Fallacies may then be understood as argumentation schemes used inappropriately. The next section demonstrates how some specific mathematical fallacies may be characterized in terms of argumentation (...) schemes. The third section considers the phenomenon of correct answers which result from incorrect methods. This turns out to pose some deep questions concerning the nature of mathematical knowledge. In particular, it is argued that a satisfactory epistemology for mathematical practice must address the role of luck. (shrink)

I want to say something about the sort of arguments that it is possible to lose, and whether losing arguments can be done well. I shall focus on losing philosophical arguments, and I will be talking about arguments in the sense of acts of arguing. This is the sort of act that one can perform on one’s own or with one other person in private. But in either of these cases it is difficult to win—or to lose. So I shall (...) concentrate on arguments with audiences. We may think of winning or losing such arguments in terms of whether the audience is convinced. Of course, this doesn’t necessarily have anything to do with who is in the right. That means that there are two sorts of loser: real losers, who lose the argument deservedly, because they are in the wrong, and mere losers, who lose the argument undeservedly, because they are in the right. Hence there must also be two sorts of winner: real winners, who win the argument deservedly, because they are in the right, and mere winners, who win the argument undeservedly, because they are in the wrong. An optimal outcome for arguments with losers would be if all the losers are real losers. (shrink)

Kant’s “primacy of the practical” doctrine says that we can form morally justified commitments regarding what exists, even in the absence of sufficient epistemic grounds. In this paper I critically examine three different varieties of Kant’s “moral proof” that can be found in the critical works. My claim is that the third variety—the “moral-psychological argument” based in the need to sustain moral hope and avoid demoralization—has some intriguing advantages over the other two. It starts with a premise that more clearly (...) coheres with Kant’s mature account of moral motivation, and it invokes plausible empirical-psychological theses to motivate a commitment to the full-blown classical deity—the result Kant clearly wanted. From the point of view of its structure, I think this third variety of moral argument also has the most by way of contemporary interest. (shrink)

This three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximally coarse-grained view that coextensiveness is sufficient for (...) identity), and some which take the view in the direction of fineness of grain (whose endpoint is the maximally fine-grained theory containing all distinctness claims compatible with Classicism). The third part introduces some techniques for constructing models of Classicism, and uses them to prove the consistency of many of the extensions of Classicism introduced in the second part. (shrink)

Much work in MKM depends on the application of formal logic to mathematics. However, much mathematical knowledge is informal. Luckily, formal logic only represents one tradition in logic, specifically the modeling of inference in terms of logical form. Many inferences cannot be captured in this manner. The study of such inferences is still within the domain of logic, and is sometimes called informal logic. This paper explores some of the benefits informal logic may have for the management of informal mathematical (...) knowledge. (shrink)

It is difficult for prioritarians to explain the degree to which justice requires redress for misfortune in a way that avoids imposing unreasonably high costs on more advantaged individuals whilst also economising on intuitionist appeals to judgment. An appeal to hypothetical insurance may be able to solve the problems of cost and judgment more successfully, and can also be defended from critics who claim that resource egalitarianism is best understood to favour the ex post elimination of envy over individual endowments.u.

In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that empirical science characteristically exhibits inglorious revolutions but that revolutions in mathematics are at most glorious [2]. Here are three possible responses: 0. Accept that empirical science and mathematics are methodologically discontinuous; 1. Argue that mathematics can exhibit inglorious revolutions; 2. Deny that inglorious revolutions are (...) characteristic of science. Where Aberdein and Read take option 1, option 2 is preferred by Mizrahi [3]. This paper seeks to resolve this disagreement through consideration of some putative mathematical revolutions. [1] Andrew Aberdein and Stephen Read, The philosophy of alternative logics, The Development of Modern Logic (Leila Haaparanta, ed.), Oxford University Press, Oxford, 2009, pp. 613-723. [2] Donald Gillies (ed.), Revolutions in Mathematics, Oxford University Press, Oxford, 1992. [3] Moti Mizrahi, Kuhn's incommensurability thesis: What's the argument?, Social Epistemology 29 (2015), no. 4, 361-378. (shrink)

Commentators typically neglect the distinct nature and role of hope in Kant’s system, and simply lump it together with the sort of Belief that arises from the moral proof. Kant himself is not entirely innocent of the conflation. Here I argue, however, that from a conceptual as well as a textual point of view, hope should be regarded as a different kind of attitude. It is an attitude that we can rationally adopt toward some of the doctrines that are not (...) able to be proved from within the bounds of mere reason – either theoretical or practical. This does not mean that hope is unconstrained; there are rational limits, as we shall see. In fact one of my central claims here is that a crucial difference between knowledge, rational Belief, and rational hope is that they are governed by different modal constraints; section II discusses those constraints and the kind of modality involved. In section III, I return to Religion and offer what I take to be Kant’s account of the main objects of rational hope in that text – namely, “alleged outer experiences (miracles)”;a “supposed inner experience(effect of grace)”;and a future collective experience (the construction of a truly ethical society). (shrink)

Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

This paper considers Kant's views on how it can be rational to hope for God's assistance in becoming morally good. If I am fully responsible for making myself good and can make myself good, then my moral condition depends entirely on me. However, if my moral condition depends entirely on me, then it cannot depend on God, and it is therefore impossible for God to provide me with any assistance. But if it is impossible for God to provide me with (...) any assistance, it is irrational for me to hope for such assistance. I address this conundrum by providing an analysis of one necessary condition of rational hope: hope is rational only if the subject is not in a position to be certain that p is really impossible. I then offer several different strategies on which it might be rational to hope that God provides moral assistance, with the most radical of these strategies suggesting that, given our ignorance of the laws of the intelligible world, for all human beings know it is metaphysically possible that God perform a noumenal miracle on their moral character. -/- . (shrink)

Some philosophers think that life is worth living not merely because of the goods and the bads within it, but also because life itself is good. I explain how this idea can be formalized by associating each version of such of a view with a function from length of life to the value generated by life itself. Then I argue that every version of the view that life itself is good faces some version of the following dilemma: either (1) good (...) human lives are worse than very long lives wholly devoid of pleasure, desire-satisfaction, knowledge, or any other goods, or (2) very short lives containing nothing but suffering are worth living. Since neither result is plausible, we ought to reject the view that life itself is good. On the view I favor, any given life may be worth living because of the goods that it contains, but life itself is neutral. (shrink)