This paper develops an interpretation of what is essential to kant's doctrine of the highest good, Which defends it while also explaining why it is often rejected. While it is commonly viewed as a theological ideal in which happiness is proportioned to virtue, The paper gives an account in which neither feature appears. The highest good is best understood as a state of affairs to be achieved through human agency, Containing the moral perfection of all individuals and the satisfaction of (...) their permissible ends-I.E., One in which all act from the moral law and in doing so achieve their intended ends. The paper shows that the texts contain two distinct conceptions not distinguished by kant-Both a theological and a secular (political) notion. The standard objections apply to the theological, But the secular conception is consistent with kant's conception of moral conduct. Moreover, That the highest good is introduced as an end to be constructed out of the moral law indicates that the secular version is the essential notion. (shrink)

One aim of the Critique of Practical Reason is to establish that reason alone can determine the will. To show that it can, it suffices to show that there are practical principles given by reason alone – what Kant terms ‘practical laws’, or (roughly) requirements of reason on action. Chapter I of the Analytic accomplishes this aim by arguing that the moral law is an authoritative practical principle given as a ‘fact of reason’. The chapter begins in section 1 with (...) a ‘Definition’ (Erklärung) of a practical law as a practical principle that.. (shrink)

The primary concern of this paper is to outline an explanation of how Kant derives morality from reason. We all know that Kant thought that morality comprises a set of demands that are unconditionally and universally valid. In addition, he thought that to support this understanding of moral principles, one must show that they originate in reason a priori, rather than in contingent facts about human psychology, or the circumstances of human life. But do we really understand how he tries (...) to establish that moral principles originate in reason? In at least two passages in the second section of the Groundwork, Kant insists upon the importance of grounding the moral law in practical reason a priori, and subsequently states a conception of practical reason from which he appears to extract a formulation of the Categorical Imperative. The reasoning employed in these passages would appear to be of central importance to the overall argument of the Groundwork, but in each case the route travelled from the definition of practical reason to the ensuing formulation of the moral law is obscure. My goal is to work out a plausible reconstruction of this portion of Kant’s argument. At the very least, I hope that my interpretation will illuminate the distinctive structure of the Kantian approach to questions of justification in ethics. What I understand of Kant’s view leads me to believe that its aims and overall shape are different in important respects from what is often assumed. It also represents an approach to foundational issues in ethics, which provides an alternative to many contemporary attempts to ground morality in reason. (shrink)

This chapter examines Kant's moral philosophy, which is developed principally in three major works: the Groundwork of the Metaphysics of Morals, the Critique of Practical Reason, and The Metaphysics of Morals. It begins with an overview of Kant's foundational theory, and then turns, more briefly, to his normative theory.

Kant’s project in ethics is to defend the conception of morality that he takes to be embedded in ordinary thought. The principal aims of his foundational works in ethics – the Groundwork of the Metaphysics of Morals and the Critique of Practical Reason – are to state the fundamental principle of morality, which he terms the “Categorical Imperative”, and then to give an account of its unconditional authority – why we should give moral requirements priority over non-moral reasons – by (...) grounding it in the nature of free rational agency. Roughly the principle of morality gets its authority from the fact that it is by acting from this principle that we exercise our free agency. In these works Kant develops a distinctive account of the content of moral requirement (which is filled out in his later work, The Metaphysics of Morals). According to one version of the Categorical Imperative, we determine what sorts of actions are permissible or required in various situations by asking whether a principle of action is rationally willed as universal law for agents with autonomy. A second version of the Categorical Imperative derives the content of morality from the principle that we are to respect “humanity”, or “rational nature”, as an “end in itself” and never merely as a means. “Humanity” is the capacity for autonomous rational choice, and it includes the capacity to act from one’s own judgment of what one has reason to do, to set ends for oneself, and to guide one’s actions by values one finds it reasonable to accept. To hold that this capacity is an end in itself is to claim that it has an absolute value – a value that Kant terms “dignity” – that sets limits on the.. (shrink)

This paper discusses three inter-related themes in Barbara Herman's Moral Literacy norm-constituted power completes’ practical reason or rational agency.

My aim in this paper is to explore different ways of understanding Kant’s Formula of Humanity as a formal principle. I believe that a formal principle for Kant is a principle that is constitutive of some domain of cognition or rational activity. It is a principle that both constitutively guides that activity and serves as its internal regulative norm. In the first section of this essay, I explain why it is desirable to find a way to understand the Formula of (...) Humanity as a formal principle in this sense. In sections II and III I discuss two interpretive approaches to Kant’s idea that rational nature or humanity is an end in itself, both of which may be construed as treating the Formula of Humanity as a formal principle. By focusing on the notion of formal principle, I hope to raise a set of issues about how to understand the idea of rational nature or humanity as an end in itself, and about the relation of the Formula of Humanity [FH] to the Formula of Universal Law [FUL]. I do not resolve the issues in this paper, though I briefly sketch some resolution at the end. (shrink)

Kantians often talk about the capacity to set ends for oneself through reason and those who do assume that Kant regarded the capacity to set ends as a rational power or a component of practical reason. ‘Natural perfection’, Kant says, ‘is the cultivation of any capacities whatever for furthering ends set forth by reason’, and he refers to ‘humanity’ as the ‘capacity to set oneself any end at all’ or ‘the capacity to realize all sorts of possible ends’.¹ ‘Humanity’ comprises (...) the full range of human rational capacities, one of which is the capacity to adopt a wide variety of ends, including ends that are not morally required by pure practical reason.² Likewise Kant refers to ‘culture’ as ‘the aptitude and skill for all sorts of ends for which he can use nature (internal and external)’, or as ‘the production of the aptitude of a rational being for any ends in general (thus those of his freedom).’³ Christine Korsgaard characterizes ‘humanity’ as follows. (shrink)

Paul Guyer’s Kant on Freedom, Law, and Happiness is a collection of essays written over a period of ten years on the roles of freedom, reason, law, and happiness in Kant’s practical philosophy. The centrality of these concepts has always been acknowledged, but Guyer proposes a different way to understand their interconnections. Kant extols respect for moral law and conformity to moral principle for its own sake while at the same time celebrating the value of human freedom and autonomy. Guyer (...) sees tensions between these two poles of Kant’s practical philosophy—obedience to law and the value of freedom. He argues: “A profound paradox can be avoided only if it can be shown that Kant intended obedience to universal law to be mandatory solely as the necessary condition for the realization of human freedom and through that freedom a systematic and unselfish distribution of happiness among all persons” and that “the sheer fact of adherence to universal law is not an end in itself but is rather the means to the realization of the human potential for autonomy or freedom in both choice and action” (p. 1). One guiding theme of Guyer’s book is that Kant’s practical philosophy is based on the fundamental, and hence indemonstrable, intrinsic value of freedom, which Guyer understands as a value that is prior to the moral law, providing both an end to be realized through conformity to universal law and the basis of the authority of moral principles. Conformity to universal law has no intrinsic value in itself; it is the means to the preservation, enhancement, and full realization of human freedom, and is required because of its instrumental connection to the prior value of freedom. As he says, “freedom of choice and its natural expression in action are what human beings value most, and the fundamental principle of morality and the rules for both po-. (shrink)

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)

A satisfactory theory of linguistic communication must explain how it is that, through the interpersonal exchange of auditory, visual, and tactile stimuli, the communicative preconditions for the acquisition of testimonial knowledge regularly come to be satisfied. Without an account of knowledge-yielding communication this success condition for linguistic theorizing is left opaque, and we are left with an incomplete understanding of testimony, and communication more generally, as a source of knowledge. This paper argues that knowledge-yielding communication should be modelled on knowledge (...) itself. It is argued that knowledge-yielding communication occurs iff interlocutors coordinate on truth values in a non-lucky and non-deviant way. This account is able to do significant explanatory work: it sheds light on the nature of referential communication, and it allows us to capture, in an informative way, the sense in which interlocutors must entertain similar propositions in order to communicate successfully. (shrink)

In this paper I argue that the enkratic principle in its classic formulation may not be a requirement of rationality. The investigation of whether it is leads to some important methodological insights into the study of rationality. I also consider the possibility that we should consider rational requirements as a subset of a broader category of agential requirements.

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)

Kant holds that in order to have knowledge of an object, a subject must be able to “prove” that the object is really possible—i.e., prove that there is neither logical inconsistency nor “real repugnance” between its properties. This is (usually) easy to do with respect to empirical objects, but (usually) impossible to do with respect to particular things-in-themselves. In the first section of the paper I argue that an important predecessor of Kant’s account of our ignorance of real possibility can (...) be found in Locke’s Essay Concerning Human Understanding. In the middle sections I discuss the way in which our inability to prove the real possibility of things-in-themselves motivates Kant’s famous prohibition on certain kinds of knowledge-claims about them. In the final section I examine Hegel’s attempts to dissolve this problem of real repugnance and thereby remove an inherited obstacle to speculative knowledge of the supersensible. -/- . (shrink)

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

This paper argues that underlying social biases are able to affect the processes underlying linguistic interpretation. The result is a series of harms systematically inflicted on marginalised speakers. It is also argued that the role of biases and stereotypes in interpretation complicates Miranda Fricker's proposed solution to epistemic injustice.

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)

The fallacy fallacy is either the misdiagnosis of fallacy or the supposition that the conclusion of a fallacy must be a falsehood. This paper explores the relevance of these and related errors of reasoning for the appraisal of arguments, especially within virtue theories of argumentation. In particular, the fallacy fallacy exemplifies the Owl of Minerva problem, whereby tools devised to understand a norm make possible new ways of violating the norm. Fallacies are such tools and so are vices. Hence a (...) similar problem arises with argumentative vices. Fortunately, both instances of the problem have a common remedy. (shrink)

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.

David Lewis—famously—never tasted vegemite. Did he have any knowledge of what it's like to taste vegemite? Most say 'no'; I say 'yes'. I argue that knowledge of what it’s like varies along a spectrum from more exact to more approximate, and that phenomenal concepts vary along a spectrum in how precisely they characterize what it’s like to undergo their target experiences. This degreed picture contrasts with the standard all-or-nothing picture, where phenomenal concepts and phenomenal knowledge lack any such degreed structure. (...) I motivate the degreed picture by appeal to (1) limits in epistemic abilities such as recognition, imagination, and inference, and (2) the semantics of ‘knows what it’s like’ expressions. I argue that approximate phenomenal knowledge cannot be explained merely via determinable or vague phenomenal concepts. I develop a framework for systematizing approximate knowledge of phenomenal character. And I explain how my view challenges some standard assumptions about the acquisition conditions, requirements for mastery, and referential mechanisms of phenomenal concepts. (shrink)

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)

Disagreements that resist rational resolution, often termed “deep disagreements”, have been the focus of much work in epistemology and informal logic. In this paper, I argue that they also deserve the attention of philosophers of mathematics. I link the question of whether there can be deep disagreements in mathematics to a more familiar debate over whether there can be revolutions in mathematics. I propose an affirmative answer to both questions, using the controversy over Shinichi Mochizuki’s work on the abc conjecture (...) as a potential example of both phenomena. I conclude by investigating the prospects for the resolution of mathematical deep disagreements in virtue-theoretic approaches to informal logic and mathematical practice. (shrink)

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

I argue that assertoric content functions as a means for us to track the responsibilities undertaken by communicators, and that distinctively assertoric commitments are distinguished by being generated directly in virtue of the words the speaker uses. This raises two questions: (a) Why are speakers responsible for the content thus generated? (b) Why is it important for us to distinguish between commitments in terms of their manner of generation? I answer the first question by developing a novel responsibility based metasemantics. (...) I answer the second by reference to the conflicting pressures governing the resources we have available for appraising speech. (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)

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)

I argue that experiences can have microphenomenal structures, where the macrophenomenal properties we introspect are realized by non-introspectible microphenomenal properties. After explaining what it means to ascribe a microstructure to experience, I defend the thesis against its principal philosophical challenge, discuss how the thesis interacts with other philosophical issues about experience, and consider our prospects for investigating the microphenomenal realm.

A famous mathematical theorem says that the sum of an infinite series of numbers can depend on the order in which those numbers occur. Suppose we interpret the numbers in such a series as representing instances of some physical quantity, such as the weights of a collection of items. The mathematics seems to lead to the result that the weight of a collection of items can depend on the order in which those items are weighed. But that is very hard (...) to believe. A puzzle then arises: How do we interpret the metaphysical significance of this mathematical theorem? I first argue that prior solutions to the puzzle lead to implausible consequences. Then I develop my own solution, where the basic idea is that the weight of a collection of items is equal to the limit of the weights of its finite subcollections contained within ever-expanding regions of space. I show how my solution is intuitively plausible and philosophically motivated, how it reveals an underexplored line of metaphysical inquiry about quantities and locations, and how it elucidates some classic puzzles concerning supertasks. (shrink)

How is it that a speaker _S_ can at once make it obvious to an audience _A_ that she intends to communicate some proposition _p_, and yet at the same time retain plausible deniability with respect to this intention? The answer is that _S_ can bring it about that _A_ has a high justified credence that ‘_S_ intended _p_’ without putting _A_ in a position to know that ‘_S_ intended _p_’. In order to achieve this _S_ has to exploit a (...) sense in which communication can be lottery-like. After defending this view of deniability I argue that it compares favorably to a rival account recently developed by Dinges and Zakkou (Mind, https://doi.org/10.1093/mind/fzac056, 2023 ). (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)

I intend to bring recent work applying virtue theory to the study of argument to bear on a much older problem, that of disagreements that resist rational resolution, sometimes termed "deep disagreements". Just as some virtue epistemologists have lately shifted focus onto epistemic vices, I shall argue that a renewed focus on the vices of argument can help to illuminate deep disagreements. In particular, I address the role of arrogance, both as a factor in the diagnosis of deep disagreements and (...) as an obstacle to their mutually acceptable resolution. Arrogant arguers are likely to make any disagreements to which they are party seem deeper than they really are and arrogance impedes the strategies that we might adopt to resolve deep disagreements. As a case in point, since arrogant or otherwise vicious arguers cannot be trusted not to exploit such strategies for untoward ends, any policy for deep disagreement amelioration must require particularly close attention to the vices of argument, lest they be exploited by the unscrupulous. (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)

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.

Once upon a time, not too long ago, the question about apes and ethics had to do with moral standing—do apes have interests or rights that humans ought to respect? Given the fifty years of research on great ape cognition, life history, social organization, and behavior, the answer to that question seems obvious. Apes have emotions and projects, they can be harmed, and they have important social relationships.

In this chapter I hope to persuade you that defective contexts are more ubiquitous than we typically assume. In doing, so I will draw attention to a number of pressing social and theoretical issues which arise once we start to consider defective contexts. I will proceed by pointing to a number of ways in which defective contexts can emerge without self-correcting in the manner envisioned by Stalnaker. First I will consider situations in which some, but not all interlocutors recognise that (...) the context is defective. I will then consider cases of opaquely defective contexts, and the question of what it is for a context to be “close enough” to being non-defective. (shrink)

Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of mathematical reasoning closely resemble patterns of reasoning in nonmathematical domains. Hence the tools developed to understand informal reasoning, collectively known as argumentation theory, are also applicable to much mathematical argumentation. This chapter investigates some of the details of that application. Consideration is given to the many contrasting meanings (...) of the word “argument”; to some of the specific argumentation-theoretic tools that have been applied to mathematics, notably Toulmin layouts and argumentation schemes; to some of the different ways that argumentation is implicated in mathematical practices; and to the social aspects of mathematical argumentation. (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)

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)