Unless one embraces activities as foundational, understanding activities in mechanisms requires an account of the means by which entities in biological mechanisms engage in their activities—an account that does not merely explain activities in terms of more basic entities and activities. Recent biological research on molecular motors exemplifies such an account, one that explains activities in terms of free energy and constraints. After describing the characteristic “stepping” activities of these molecules and mapping the stages of those steps onto the stages (...) of the motors’ hydrolytic cycles, researchers pieced together from images of the molecules in different hydrolyzation states accounts of how the chemical energy in ATP is transformed in the constrained environments of the motors into the characteristic activities of the motors. We argue that New Mechanism’s standard set of analytic categories—entities, activities, and organization—should be expanded to include constraints and energetics. Not only is such an expansion required descriptively to capture research on molecular motors but, more importantly from a philosophical point of view, it enables a non-regressive account of activities in mechanisms. In other words, this expansion enables a philosophical account of mechanistic explanation that avoids a regress of entities and activities “all the way down.” Rather, mechanistic explanation bottoms out in constraints and energetics. (shrink)

Autoinhibition is a design principle realized in many molecular mechanisms in biology. After explicating the notion of a design principle and showing that autoinhibition is such a principle, we focus on how researchers discovered instances of autoinhibition, using research establishing the autoinhibition of the molecular motors kinesin and dynein as our case study. Research on kinesin and dynein began in the fashion described in accounts of mechanistic explanation but, once the mechanisms had been discovered, researchers discovered that they exhibited a (...) second phenomenon, autoinhibition. The discovery of autoinhibition not only reverses the pattern in terms of which philosophers have understood mechanism discovery but runs counter to the one phenomenon-one mechanism principle assumed to relate mechanisms and the phenomena they explain. The ubiquity of autoinhibition as a design principle, therefore, necessitates a philosophical understanding of mechanisms that recognizes how they can participate in more than one phenomenon. Since mechanisms with this design are released from autoinhibition only when they are acted on by control mechanisms, we advance a revised account of mechanisms that accommodates attribution of multiple phenomena to the same mechanism and distinguishes them from other processes that control them. (shrink)

The paper takes a novel approach to a classic problem—Hempel’s Raven Paradox. A standard approach to it supposes the solution to consist in bringing our inductive logic into “reflective equilibrium” with our intuitive judgements about which inductive inferences we should license. This approach leaves the intuitions as a kind of black box and takes it on faith that, whatever the structure of the intuitions inside that box might be, it is one for which we can construct an isomorphic formal edifice, (...) a system of inductive logic. By popping open the box we can see whether that faith is misplaced. I aim, therefore, to characterize our pre-theoretical, intuitive understanding of generalizations like “ravens are black” and argue that, intuitively, we take them to mean, for instance: “ravens are black by some indeterminate yet characteristic means.” I motivate and explicate this formulation and bring it to bear on Hempel’s Problem. (shrink)

A review of Andrew Melnyk, A Physicalist Manifesto: Thoroughly Modern Materialism (Cambridge University Press, 2003).

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Many philosophers accept both of the following claims: (1) consciousness matters morally, and (2) species membership doesn’t matter morally. In other words, many reject speciesism but accept what we might call 'sentientism'. But do the reasons against speciesism yield analogous reasons against sentientism, just as the reasons against racism and sexism are thought to yield analogous reasons against speciesism? This paper argues that speciesism is disanalogous to sentientism (as well as racism and sexism). I make a case for the following (...) asymmetry: (a) some non-humans clearly have interests, but (b) no non-conscious entities clearly have interests. This asymmetry, I argue, renders sentientism resistant to the standard argument against speciesism. (shrink)

The view that folk psychology is primarily mindreading beliefs and desires has come under challenge in recent years. I have argued that we also understand others in terms of individual properties such as personality traits and generalizations from past behavior, and in terms of group properties such as stereotypes and social norms (Andrews 2012). Others have also argued that propositional attitude attribution isn’t necessary for predicting others’ behavior, because this can be done in terms of taking Dennett’s Intentional Stance (Zawidzki (...) 2013), appealing to social structures (Maibom 2007), shared norms (McGeer 2007) or via solution based heuristics for reaching equilibrium between social partners (Morton 2003). But it isn’t only prediction that can be done without thinking about what others think; we can explain and understand people in terms of their personality traits, habitual behaviors, and social practices as well. The decentering of propositional attitude attributions goes hand in hand with a move away from taking folk psychology to be primarily a predictive device. While experiments examining folk psychological abilities in children, infants, and other species still rest on asking subjects to predict behavior, theoretical investigations as to the evolutionary function of folk psychology have stressed the role of explanation (Andrews 2012) and regulative functions (McGeer 2007, Zawidzki 2013, Fenici 2011). In this paper I argue that an explanatory role for folk psychology is also a regulative role, and that language is not required for these regulative functions. I will start by drawing out the relationship between prediction, explanation, and regulation of behavior according to both mindreading approaches to folk psychology and the pluralistic account I defend. I will argue that social cognition does not take the form of causal reasoning so much as it does normative reasoning, and will introduce the folk psychological spiral. Then I will examine the cognitive resources necessary for participating in the folk psychological spiral, and I will argue that these cognitive resources can be had without language. There is preliminary evidence that some other species understand one another through a normative lens that, through looping effects, creates expectations that community members strive to live up to. (shrink)

Higher-order logic augments first-order logic with devices that let us generalize into grammatical positions other than that of a singular term. Some recent metaphysicians have advocated for using these devices to raise and answer questions that bear on many traditional issues in philosophy. In contrast to these 'higher-order metaphysicians', traditional metaphysics has often focused on parallel, but importantly different, questions concerning special sorts of abstract objects: propositions, properties and relations. The answers to the higher-order and the property-theoretic questions may coincide (...) sometimes but will often come apart. I argue that when they do, the higher-order questions are closer to the metaphysical action and so it would be better for these debates to proceed in higher-order terms. (shrink)

Virtue theories have become influential in ethics and epistemology. This paper argues for a similar approach to argumentation. Several potential obstacles to virtue theories in general, and to this new application in particular, are considered and rejected. A first attempt is made at a survey of argumentational virtues, and finally it is argued that the dialectical nature of argumentation makes it particularly suited for virtue theoretic analysis.

I discuss whether "sentience" (i.e., phenomenal consciousness) comes in degrees.

Andrews argues for a pluralistic folk psychology that employs different kinds of practices and different kinds of cognitive tools (including personality trait attribution, stereotype activation, inductive reasoning about past behavior, and ...

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)

What should a virtue theory of argumentation say about fallacious reasoning? If good arguments are virtuous, then fallacies are vicious. Yet fallacies cannot just be identified with vices, since vices are dispositional properties of agents whereas fallacies are types of argument. Rather, if the normativity of good argumentation is explicable in terms of virtues, we should expect the wrongness of bad argumentation to be explicable in terms of vices. This approach is defended through analysis of several fallacies, with particular emphasis (...) on the ad misericordiam. (shrink)

Recent research (Latham, Miller and Norton, forthcoming) reveals that a majority of people represent actual time as dynamical. But do they, as suggested by McTaggart and Gödel, represent time as essentially dynamical? This paper distinguishes three interrelated questions. We ask (a) whether the folk representation of time is sensitive or insensitive: i.e., does what satisfies the folk representation of time in counterfactual worlds depend on what satisfies it actually—sensitive—or does is not depend on what satisfies it actually—insensitive, and (b) do (...) those who represent actual time as dynamical, represent time in all possible worlds as dynamical—what we call insensitive dynamism—or do they represent time in all possible worlds as dynamical only conditional on the actual world in fact being dynamical—what we call sensitive dynamism and (c) do dynamists and non-dynamists deploy two different representations of time, or deploy the same representation, but disagree about what actually satisfies that representation? We found no evidence that the folk representation of time is sensitive, or that the folk representation of time is essentially dynamical in either sense, though we did find evidence of a shared representation, on which dynamical features are sufficient, but not necessary, for time. (shrink)

A list of resources for virtue theories of argumentation. Last updated April 19th, 2022.

Deep disagreements are characteristically resistant to rational resolution. This paper explores the contribution a virtue theoretic approach to argumentation can make towards settling the practical matter of what to do when confronted with apparent deep disagreement, with particular attention to the virtue of courage.

Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready to (...) meet them, who have explicitly invoked virtues in discussing what is necessary for a mathematician to succeed. In both ethics and epistemology, virtue theory tends to emphasize character virtues, the acquired excellences of people. But people are not the only sort of thing whose excellences may be identified as virtues. Theoretical virtues have attracted attention in the philosophy of science as components of an account of theory choice. Within the philosophy of mathematics, and mathematics itself, attention to virtues has emerged from a variety of disparate sources. Theoretical virtues have been put forward both to analyse the practice of proof and to justify axioms; intellectual virtues have found multiple applications in the epistemology of mathematics; and ethical virtues have been offered as a basis for understanding the social utility of mathematical practice. Indeed, some authors have advocated virtue epistemology as the correct epistemology for mathematics (and perhaps even as the basis for progress in the metaphysics of mathematics). This topical collection brings together several of the researchers who have begun to study mathematical practices from a virtue perspective with the intention of consolidating and encouraging this trend. (shrink)

Norman forms the belief that the president is in New York by way of a clairvoyance faculty he doesn’t know he has. Many agree that his belief is unjustified but disagree about why it is unjustified. I argue that the lack of justification cannot be explained by a higher-level evidence requirement on justification, but it can be explained by a no-defeater requirement. I then explain how you can use cognitive faculties you don’t know you have. Lastly, I use lessons from (...) the foregoing to compare Norman’s belief, formed by clairvoyance, with Sally’s theistic belief, formed by a sensus divinitatis. (shrink)

Virtue theories have lately enjoyed a modest vogue in the study of argumentation, echoing the success of more far-reaching programmes in ethics and epistemology. Virtue theories of argumentation (VTA) comprise several conceptually distinct projects, including the provision of normative foundations for argument evaluation and a renewed focus on the character of good arguers. Perhaps the boldest of these is the pursuit of the fully satisfying argument, the argument that contributes to human flourishing. This project has an independently developed epistemic analogue: (...) eudaimonistic virtue epistemology. Both projects stress the importance of widening the range of cognitive goals beyond, respectively, cogency and knowledge; both projects emphasize social factors, the right sort of community being indispensable for the cultivation of the intellectual virtues necessary to each project. This paper proposes a unification of the two projects by arguing that the intellectual good life sought by eudaimonistic virtue epistemologists is best realized through the articulation of an account of argumentation that contributes to human flourishing. (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 précis of my book Pragmatist Quietism: A Meta-Ethical System (OUP, 2022); forthcoming in Analysis along with commentaries and my replies.

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)

In their article, Thom Scott‐Phillips, Stefaan Blancke, and Christophe Heintz do a commendable job summarizing the position and misunderstandings of “cultural attraction theory” (CAT). However, they do not address a longstanding problem for the CAT framework; that while it has an encompassing theory and some well‐worked out case studies, it lacks tools for generating models or empirical hypotheses of intermediate generality. I suggest that what the authors diagnose as misunderstandings are instead superficial interpretive errors, resulting from researchers who have attempted (...) to extract generalizable hypotheses from CAT and bring them into contact with the analytical and inferential models of contemporary cultural evolutionary research. (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)

This article discusses the following question: what epistemic relation must audiences bear to the content of assertions in order to gain testimonial knowledge? There is a brief discussion of why this issue is of importance, followed by two counterexamples to the most intuitive answer: that in order for an audience to gain testimonial knowledge that p they must know that the speaker has asserted p. It is then suggested that the argument generalises and can be made to work on different (...) sets of assumptions about the conditions for knowledge, and the conditions under which a proposition is asserted. (shrink)

This paper defines and defends a notion of teleological function which is fit to figure in explanations concerning how organic systems, and the items which compose them, are able to perform certain activities, such as surviving and reproducing or pumping blood. According to this notion, a teleological function of an item (such as the heart) is a typical way in which items of that type contribute to some containing system's ability to do some activity. An account of what it is (...) for an item to contribute to a containing system's ability to perform an activity is provided. I argue that the view acquires its normative status in virtue of the fact that it obeys a function-accident distinction and obeys a function-dysfunction distinction; that the view is ahistorical; and, that its ahistoricity provides it with an advantage over one of its main competitors. (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)

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.

This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed reform (...) program. Finally, the fourth case study is paraconsistent logic, perhaps the most controversial of serious proposals. (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)

Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory, but also psychology, education, and computer science. This introduction provides some background to their work.

We consider the relationship between neural and behavioural evidence for animal consciousness. We critically examine two recent studies: one neural and one behavioural. The first, on crows, finds different neural activity depending on whether a stimulus is reported as seen or unseen. However, to implicate this neural activity in consciousness, we must assume that a specific conditioned behaviour is a report of conscious experience. The second study, on macaques, records behaviours strikingly similar to patterns of conscious and unconscious perception in (...) humans. However, confounds are only ruled out in human subjects, presupposing substantial neural similarity between humans and macaques. Taken together, the two studies reveal a sense in which neural and behavioural research rely on each other. Looking ahead, these two types of evidence could prove to be either mutually reinforcing or mutually undermining. The science of animal consciousness needs both neural and behavioural evidence, ideally obtained as part of a single coordinated programme. (shrink)

There are two kinds of time-bias: near-bias and future-bias. While philosophers typically hold that near-bias is rationally impermissible, many hold that future-bias is rationally permissible. Call this normative hybridism. According to arbitrariness objections, certain patterns of preference are rationally impermissible because they are arbitrary. While arbitrariness objections have been levelled against both near-bias and future-bias, the kind of arbitrariness in question has been different. In this paper we investigate whether there are forms of arbitrariness that are common to both kinds (...) of preferences, and hence whether there are versions of the arbitrariness objection that are objections both to near-bias and future-bias. If there are, then this might go some way towards undermining normative hybridism and to defending a thorough-going time-neutralism. (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)

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)

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)

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

We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show (...) that some of these logics are non-degenerate. (shrink)

In this thesis, I will defend a new kind of compatibilist account of free action, indirect conscious control compatibilism (or indirect compatibilism for short), and argue that some of our actions are free according to it. My argument has three components, and involves the development of a brand new tool for experimental philosophy, and the use of cognitive neuroscience. The first component of the argument shows that compatibilism (of some kind) is a conceptual truth. Contrary to the current orthodoxy in (...) the free will literature, which is that our concept of free will is an incompatibilist concept - a concept according to which we have free will only if determinism is false - I will show that our concept of free will is in fact a compatibilist concept - a concept according to which we can have free will even if determinism is true - and I do so using a new experimental philosophy methodology inspired by two-dimensional semantics. -/- Of course, even if our concept of free will is a compatibilist concept, this does not mean that there are any free actions in the world: the current empirical evidence from the brain sciences appears to show that there might be no, or very few, free actions in the world, even on many compatibilist understandings of what it would take for there to be free will. The second component of the argument addresses this concern by extending our understanding of compatibilism. Agents act freely either when their actions are caused by compatibilistically acceptable psychological processes, or are indirectly caused by those same processes. Hence the name of my account: indirect compatibilism. -/- The final component of the argument defends my new account against some interesting objections and provides evidence from cognitive neuroscience that some of our actions count as free by the lights of indirect compatibilism. (shrink)

Stipulation gives us a degree of control over meaning. By stipulating how I will use a term I am able to determine the meaning it will receive on future occasions of use. My stipulation will affect the truth conditional content of my future utterances. But the mechanisms of stipulation are mysterious. As Cappelen (2018) argues, meaning is typically determined in an inscrutable way by a myriad of external factors beyond our control. How does stipulation override these factors? And the powers (...) of stipulation are limited. Firstly, the power of stipulation is typically short-lived. Sec-ondly, some stipulations simply don’t get off the ground. What explains the limits of stipulation? I consider two related approaches to stipulation and argue that they are unable to capture stipulation’s metasemantic effects. I then provide an explanation of the metasemantic effects of stipulation: Stipulation determines meaning by determining the word use it is fitting to hold the speaker to. This account is able to capture the mechanisms and limits of stipulation, whilst also explaining why we should care about stip-ulative success. I close by briefly drawing out some lessons for conceptual engineering. -/- . (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)

This paper proposes that virtue theories of argumentation and theories of visual argumentation can be of mutual assistance. An argument that adoption of a virtue approach provides a basis for rejecting the normative independence of visual argumentation is presented and its premisses analysed. This entails an independently valuable clarification of the contrasting normative presuppositions of the various virtue theories of argumentation. A range of different kinds of visual argument are examined, and it is argued that they may all be successfully (...) evaluated within a virtue framework, without invoking any novel virtues. (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)

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)

The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential (...) to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed. (shrink)

The study of animal cognition raises profound questions about the minds of animals and philosophy of mind itself. Aristotle argued that humans are the only animal to laugh, but in recent experiments rats have also been shown to laugh. In other experiments, dogs have been shown to respond appropriately to over two hundred words in human language. In this introduction to the philosophy of animal minds Kristin Andrews introduces and assesses the essential topics, problems and debates as they cut across (...) animal cognition and philosophy of mind. She addresses the following key topics: what is cognition, and what is it to have a mind? What questions should we ask to determine whether behaviour has a cognitive basis? the science of animal minds explained: ethology, behaviourist psychology, and cognitive ethology rationality in animals animal consciousness: what does research into pain and the emotions reveal? What can empirical evidence about animal behaviour tell us about philosophical theories of consciousness? does animal cognition involve belief and concepts; do animals have a ‘Language of Thought’? animal communication other minds: do animals attribute ‘mindedness’ to other creatures? moral reasoning and ethical behaviour in animals animal cognition and memory. Extensive use of empirical examples and case studies is made throughout the book. These include Cheney and Seyfarth’s ververt monkey research, Thorndike’s cat puzzle boxes, Jensen’s research into humans and chimpanzees and the ultimatum game, Pankseep and Burgdorf’s research on rat laughter, and Clayton and Emery’s research on memory in scrub-jays. Additional features such as chapter summaries, annotated further reading and a glossary make this an indispensable introduction to those teaching philosophy of mind, animal cognition. It will also be an excellent resource for those in fields such as ethology, biology and psychology. (shrink)