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

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)

This paper argues that both a limited doxastic voluntarism and anti-evidentialism are consistent with the views that the aim of belief is truth or knowledge and that this aim plays an important role in norm-setting for beliefs. More cautiously, it argues that limited doxastic voluntarism is (or would be) a useful capacity for agents concerned with truth tracking to possess, and that having it would confer some straightforward benefits of both an epistemic and non-epistemic variety to an agent concerned with (...) truth tracking. (shrink)

This paper shows that strict evidentialism about normative reasons for belief is inconsistent with taking truth to be the source of normative reasons for belief. It does so by showing that there are circumstances in which one can know what truth requires one to believe, yet still lack evidence for the contents of that belief.

This entry discusses the notion of a unit of normativity. This notion may be understood in two distinct ways. One way to understand a unit of normativity is as some particular type of assignment of normative status, e.g., a requirement, an ought, a reason, or a permission. A second way to understand a unit of normativity is as a measure of a quantity of normativity, perhaps associated with the numerical assignment given to the strength of reasons. This entry outlines some (...) basic differences among units of normativity in the first sense, noting that they vary slightly depending on whether one is talking about normativity in a more general or more robust sense. This entry also discusses in more detail the question of whether there might be a unit of normativity in the second sense. It discusses the relevant metaphysical questions. It also provides an explanation of why reasons can be assigned numerical strengths, even if there are no units of normativity in the sense of measurements of quantities of normativity. (shrink)

This chapter explores two kinds of testimonial trust, what we call ‘evidential trust’ and ‘non-evidential trust’ with the aim of asking how testimonial trust could provide epistemic reasons for belief. We argue that neither evidential nor non-evidential trust can play a distinctive role in providing evidential reasons for belief, but we tentatively propose that non-evidential trust can in some circumstances provide a novel kind of epistemic reason for belief, a reason of epistemic facilitation. The chapter begins with an extensive discussion (...) of standard accounts of both kinds of trust and criticises especially the standard accounts of non-evidential trust. A new account of non-evidential trust is offered that avoids a number of difficulties that plague the standard accounts by rejecting what we call ‘attitude-liability assumptions’. (shrink)

In tradition linked to Aristotle and Kant, many contemporary philosophers treat practical and theoretical normativity as two genuinely distinct domains of normativity. In this paper I consider the question of what it is for normative domains to be distinct. I suggest that there are two different ways that the distinctness thesis might be understood and consider the different implications of the two different distinctness theses.

This paper considers the relation between the sources of normativity, reasons, and normative conflicts. It argues that common views about how normative reasons relate to their sources have important consequences for how we can understand putative normative conflicts.

This paper outlines a new pluralistic theory of normative reasons for belief, welfarist pluralism, which aims to explain how there can be basic alethic/epistemic reasons for belief and basic pragmatic/non-alethic reasons for belief that can combine to determine what one ought to believe. The paper shows how this non-derivative first-order pluralism arises from a purely welfarist account of the foundations of theoretical normativity, thereby combining foundational pragmatism with non-derivative pluralism about normative reasons for belief. In addition, this paper outlines how (...) welfarist pluralism provides a new and potentialy attractive account of the value of truth (or its indicators), namely that the value of truth (or its indicators) is its direct contribution to individuals' personal good or wellbeing. (shrink)

In this paper I introduce an objection to normative evidentialism about reasons for belief. The objection arises from difficulties that evidentialism has with explaining our reasons for belief in unstable belief contexts with a single fixed point. I consider what other kinds of reasons for belief are relevant in such cases.

This chapter addresses an ambiguity in some of the literature on rational peer disagreement about the use of the term 'rational'. In the literature 'rational' is used to describe a variety of normative statuses related to reasons, justification, and reasoning. This chapter focuses most closely on the upshot of peer disagreement for what is rationally required of parties to a peer disagreement. This follows recent work in theoretical reason which treats rationality as a system of requirements among an agent's mental (...) states. It is argued that peer disagreement has either no, or a very limited, affect on what rationality requires of an agent in a given circumstance. This is in part because of difficulties generated by a novel example of evidence of evidence of p being evidence against p. This example calls into question the mechanisms whereby peer disagreement might affect what is rationally required of an agent. The chapter also reevaluates the importance of actual peer disagreement against the backdrop of prior expectations about whether disagreement is believed to be likely, arguing that peer disagreement is most likely to change what is rationally required of an agent when it is believed to be unlikely. (shrink)

In this paper it is argued that the buck-passing analysis (BPA) of final value is not a plausible analysis of value and should be abandoned. While considering the influential wrong kind of reason problem and other more recent technical objections, this paper contends that there are broader reasons for giving up on buck-passing. It is argued that the BPA, even if it can respond to the various technical objections, is not an attractive analysis of final value. It is not attractive (...) for two reasons: the first being that the BPA lacks the features typical of successful conceptual analyses and the second being that it is unable to deliver on the advantages that its proponents claim for it. While not offering a knock-down technical refutation of the BPA, this paper aims to show that there is little reason to think that the BPA is correct, and that it should therefore be given up as an analysis of final value. (shrink)

The thesis contains my early work arguing against evidentialism for reasons for belief (chapter 1), my early argument that rationality is not normative (chapter 2), an argument that rationality is not responding reasons, at least understood in one way (chapter 2), a general discussion of how normative conflicts might (appear to) arise in many different ways (chapter 3), a discussion of how to weigh pragmatic and evidential reasons for belief (chapter 4), and a discussion of the general structure of normativity (...) and its ramifications for understanding putative normative conflicts (chapter 4). At a more general level, the thesis aims to explore how putative normative conflicts might arise and whether they are genuine conflicts or only apparent. It also offers a defence of the view that there are genuine state-given reasons for propositional attitudes, including pragmatic reasons for belief. (shrink)

The Projectability Challenge states that a metaethical view must explain how ordinary agents can, on the basis of moral experience and reflection, accurately and justifiably apply moral concepts to novel situations. In this paper, we argue for two primary claims. First, paradigm nonnaturalism can satisfactorily answer the projectability challenge. Second, it is unclear whether there is a version of moral naturalism that can satisfactorily answer the challenge. The conclusion we draw is that there is an important respect in which nonnaturalism (...) holds an advantage over its most prominent naturalist rivals. The conclusion is interesting if only because it is widely assumed that naturalism has an easier time handling thorny problems in moral epistemology. We argue that there is at least one such problem of which this assumption is not true. (shrink)

This paper argues against the correctness of the more popular -first views (fittingness first, reasons first, and value first). The aim of this paper is to argue that there are at least two categories of normative properties that are basic and that one of those categories is value. Although the emphasis of this paper is on reductionist -first accounts, most of the arguments work equally well against weaker views that are only committed to different categories of normative properties' being linked (...) by a necessary bi-conditional. -/- . (shrink)

According to moral testimony pessimists, the testimony of moral experts does not provide non-experts with normative reasons for belief. Moral testimony optimists hold that it does. We first aim to show that moral testimony optimism is, to the extent such things may be shown, the more natural view about moral testimony. Speaking roughly, the supposed discontinuity between the norms of moral beliefs and the norms of non-moral beliefs, on careful reflection, lacks the intuitive advantage that it is sometimes supposed to (...) have. Our second aim is to highlight the difference in the nature of the pragmatic reasons for belief that support moral testimony optimism and moral testimony pessimism, setting out more clearly the nature and magnitude of the challenge for the pessimist. (shrink)

In this chapter we discuss some of the central ethical issues specific to eating and harvesting fish. We survey recent research on fish intelligence and cognition and discuss possible considerations that are distinctive to questions about the ethics of eating fish as opposed to terrestrial and avian mammals. We conclude that those features that are distinctive to the harvesting and consumption of fish, including means of capture and the central role that fishing plays in many communities, do not suggest that (...) eating fish is less morally problematic than eating terrestrial of avian animals. (shrink)

This paper offers a sketch of welfarist pluralism, a view that is intended to resolve a difficulty for non-derivative pluralists about normative reasons for belief. Welfarist pluralism is the view that all reasons for belief are rooted in wellbeing, and that wellbeing has as one of its components being in a positive epistemic state. The paper explores how this view can explain various pluralist intuitions and why it offers a plausible basis for combinatorial pluralists who believe that alethic and pragmatic (...) reasons for belief combine to determine what one ought to believe. The paper also considers the relationship between theoretical rationality and wellbeing, and provides a partial argument for the derivative normativity of at least some requirements of theoretical rationality. (shrink)

In this paper we argue that the use of survey data or intuitions about single person cases as a dialectically neutral data point for favouring telic egalitarianism over prioritarianism has dim prospects for success. We take as a case study Otsuka and Voorhoeve (2009)'s now well known paper and show that it either is either argumentatively irrelevant or question-begging, depending on whether the survey data about people's judgements concerning single-person cases is interpreted as being prudential or moral in character. We (...) suggest that this problem is likely to generalise to other ways of trying to use intuitions or survey data about single-person cases, where those data or intuitions are not just treated as further direct moral intuitions about prioritarianism and telic egalitarianism. (shrink)

This chapter sets out a theory of how to weigh alethic and pragmatic (non-alethic) reasons for belief, or more precisely, to say how alethic and non-alethic considerations jointly determine what one ought to believe. It replaces my earlier (2008) weighing account. It is part of _The true and the good: a new theory of theoretical reason_, which develops a view, welfarist pluralism, which comprises central two theses. One is that there are both irreducibly alethic or epistemic reasons for belief and (...) irreducibly pragmatic (and non-alethic) reasons for belief. The other is that despite this, the source of all normativity is pragmatic in a particular way, i.e. that all reasons are reasons in virtue of their being conducive to wellbeing. The pluralist theory of reasons emerges from the irreducibly plural nature of the components of wellbeing, on of which is being in a positively-valenced epistemic state. This view also offers some insight into outstanding problems concerning the scope, chronicity, and normativity of the requirements of theoretical rationality as well. (Updated 10 May 2022). (shrink)

As Dworkin puts it: moral scepticism is a moral view. This is in contrast to the more popular idea that the real challenge for moral realism is external scepticism, scepticism which arises because of non-moral considerations about the metaphysics of morality. I, too, do not concur with Dworkin’s strongest conclusions about the viability of external scepticism. But, I think his criticism of error scepticism offers a much needed corrective to more traditional metaethical projects. My aim in this paper is to (...) split the difference between Dworkin’s view and more traditional views, concluding that Dworkin’s work in Justice for Hedgehogs contributes to metaethics for everyone. (shrink)

This is chapter 5 of the book project _The true and the good: a new theory of theoretical reason_, in which I explore the claim that both alethic and pragmatic reasons for belief are basic, but that they share a pragmatic foundation in a pluralist theory of wellbeing in which being in a positive epistemic state is a non-derivative component of wellbeing. This chapter argues that all three of fittingness first, reasons first, and value first views are false. It does (...) so by showing that fittingness and reasons both have unalike variance conditions with respect to value, i.e. that sometimes the value of something can switch from good to bad or bad to good without there being any change in whether it is fitting to favour it or whether there are reason to favour it. This is a form of an argument from under-generation following on earlier work by Krister Bykvist and Andrew Reisner, respectively. It is also more tentatively that reasons cannot be analysed in terms of correctness. Because the the arguments in this paper concern the extensional adequacy of the various bi-conditionals linking fittingness, reasons, and value, they suffice for rejecting even modest versions of '-first' views that do not purport to provide analyses, but rather only sets of correctness conditions for, e.g., reasons and value in terms of fittingness, or any two in terms of the third. (Updated 10 May 2022). (shrink)

[Please note, this paper has been for the most part superseded by 'Unifying the Requirements of Rationality'] In the last decade, it has become commonplace among people who work on reasons (although not uncontroversially so) to distinguish between normativity and rationality. Work by John Broome, Niko Kolodny, Derek Parfit, and Nicholas Shackel has helped to establish the view that rationality is conceptually distinct from reasons. The distinction allows us to make sense of the questions recently addressed by Broome, Kolodny, (...) class='Hi'>Reisner, and Shackel: is rationality normative, and if so, in what way? Kolodny’s ‘Why be Rational?’ answered the first of these questions by claiming that there is no reason to be rational. In order to argue for this conclusion, Kolodny argues for a process account of rationality. Kolodny’s view is that rational requirements govern mental processes. His view is set in direct contrast to Broome’s, who holds that rational requirements are primarily, and perhaps exclusively, concerned with relations among mental states at a time. (shrink)

A short encyclopaedia entry on John Broome.

One way to approach the question of whether there are non-derivative partial reasons of any kind is to give an account of what partial reasons are, and then to consider whether there are such reasons. If there are, then it is at least possible that there are partial reasons of friendship. It is this approach that will be taken here, and it produces several interesting results. The first is a point about the structure of partial reasons. It is at least (...) a necessary condition of a reason’s being partial that it has an explicit relational component. This component, technically, is a rela- tum in the reason relation that itself is a relation between the person to whom the reason applies and the person whom the action for which there is a reason concerns. The second conclusion of the paper is that this relational component is also required for a number of types of putatively impartial reasons. In order to avoid trivialising the distinction between partial and impartial rea- sons, some further sufficient condition must be applied. Finally, there is some prospect for a way of distinguishing between impartial reasons that contain a relational component and partial rea- sons, but that this approach suggests that the question of whether ethics is partial or impartial will be settled at the level of normative ethical discourse, or at least not at the level of discourse about the nature of reasons for action. (shrink)

This is the latest draft of chapter 1 of _A New Theory of Reasons for Belief: Pragmatic Foundations and Pluralistic Reasons_ (Under Contract with OUP). It outlines the view that is the focus of the book: Welfarist Pluralism. Welfarist pluralism is the view that all normative reasons for belief are grounded in wellbeing and that being in a positive epistemic state is one of the components of wellbeing. This chapter explains how one can develop a principled version of non-derivative pluralism (...) about normative reasons for belief while still accepting that theoretical reason has a single, unified pragmatic foundation. Updated 25 January 2023. (shrink)

A review of John Skorupski's The Domain of Reasons.

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)

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 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.

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)