Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.

Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used (...) several keywords such as "active intuition" and "self-reflection" from Nishida's philosophy. In this paper, we aim to describe a general outline of our project to investigate Takeuti's philosophy of mathematics. In particular, after reviewing Takeuti's proof-theoretic results briefly, we describe some key elements in Takeuti's texts. By explaining these texts, we point out the connection between Takeuti's proof theory and Nishida's philosophy and explain the future goals of our project. (shrink)

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and (...) proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim. (shrink)

Many mathematicians have cited depth as an important value in their research. However, there is no single widely accepted account of mathematical depth. This article is an attempt to bridge this gap. The strategy is to begin with a discussion of Szemerédi's theorem, which says that each subset of the natural numbers that is sufficiently dense contains an arithmetical progression of arbitrary length. This theorem has been judged deep by many mathematicians, and so makes for a good case on which (...) to focus in analyzing mathematical depth. After introducing the theorem, four accounts of mathematical depth will be considered. (shrink)

This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.

Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy in Kyoto's (...) school. For the proving the consistency of such systems, it is crucial to prove the well-foundedness of ordinals called "ordinal diagrams" developed for it. Takeuti presented such arguments several times in order to show that they are admitted in his stand point. As a starting point of investigating his finitist stand point, we formulate the system of ordinal notations up to ε0 and reconstruct the well-foundedness arguments of them. (shrink)

Why do mathematics often give several proofs of the same theorem? This is the question raised in this article, introducing the notion of an epistemic ideal and discussing two such ideals, the explanatoriness and purity of proof.

Over the years many mathematicians have voiced a preference for proofs that stay “close” to the statements being proved, avoiding “foreign”, “extraneous”, or “remote” considerations. Such proofs have come to be known as “pure”. Purity issues have arisen repeatedly in the practice of arithmetic; a famous instance is the question of complex-analytic considerations in the proof of the prime number theorem. This article surveys several such issues, and discusses ways in which logical considerations shed light on these issues.

Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...) naïf, il semblerait que la première soit pure et la seconde impure. Des objections à cette vue naïve sont ici considérées et réfutées. Concernant la preuve euclidienne, la question relève de la logique, notamment de la définissabilité arithmétique de l’addition en termes de successeur et de divisibilité telle que démontrée par Julia Robinson, tandis qu’en ce qui concerne la preuve topologique, la question relève de la sémantique, notamment pour tout ce qui touche au problème de savoir ce qui est « inclus » dans le contenu d’énoncés particuliers.A proof is pure, roughly, if it draws only on what is « close » or « intrinsic » to the statement being proved. The infinitude of prime numbers, a classical theorem of arithmetic, is a rich case study for philosophical investigation of purity. Two different proofs of this result are considered, namely the classical Euclidean proof and a more recent « topological » proof by Furstenberg. Naively the former would seem to be pure and the latter to be impure. Objections to these naive views are considered and met. In the case of the former the issue rests on logical matters, specifically the arithmetic definability of addition in terms of successor and divisibility shown by Julia Robinson, while in the case of the latter the issue rests on semantic matters, specifically with respect to what is « contained » in the content of particular statements. (shrink)

In this paper I begin by extending two results of Solovay; the first characterizes the possible Turing degrees of models of True Arithmetic (TA), the complete first-order theory of the standard model of PA, while the second characterizes the possible Turing degrees of arbitrary completions of P. I extend these two results to characterize the possible Turing degrees of m-diagrams of models of TA and of arbitrary complete extensions of PA. I next give a construction showing that the conditions Solovay (...) identified for his characterization of degrees of models of arbitrary completions of PA cannot be dropped (I showed that these conditions cannot be simplified in the paper. (shrink)

We review Solomon Feferman's 1998 essay collection In The Light of Logic (Oxford University Press).

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late nineteenth century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis (in the sense of the infinitesimal calculus) received much attention in the nineteenth century. They helped instigate what Hans Hahn called a “crisis of intuition”, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this “crisis” as (...) follows: Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof... (p. 67) Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called “logicization”, “when the discipline requires nothing but purely logical fundamental concepts and propositions for its development.” On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals to visual representations. This would be a radical reformation of past practice, necessary, according to its advocates, for avoiding “unclarities and mistakes” like the one exposed by Peano. (shrink)

This collection of essays explores what makes modern mathematics ‘modern’, where ‘modern mathematics’ is understood as the mathematics done in the West from roughly 1800 to 1970. This is not the trivial matter of exploring what makes recent mathematics recent. The term ‘modern’ (or ‘modernism’) is used widely in the humanities to describe the era since about 1900, exemplified by Picasso or Kandinsky in the visual arts, Rilke or Pound in poetry, or Le Corbusier or Loos in architecture (a building (...) by the latter graces the cover of this book’s dust jacket). (shrink)

When mathematicians think of the philosophy of mathematics, they probably think of endless debates about what numbers are and whether they exist. Since plenty of mathematical progress continues to be made without taking a stance on either of these questions, mathematicians feel confident they can work without much regard for philosophical reflections. In his sharp–toned, sprawling book, David Corfield acknowledges the irrelevance of much contemporary philosophy of mathematics to current mathematical practice, and proposes reforming the subject accordingly.

Review of Dowek, Gilles, Computation, Proof, Machine, Cambridge University Press, Cambridge, 2015. Translation of Les Métamorphoses du calcul, Le Pommier, Paris, 2007. Translation from the French by Pierre Guillot and Marion Roman.

This paper argues that phenomenal consciousness is what makes an entity a welfare subject. I develop a variety of motivations for this view, and then defend it from objections concerning death, non-conscious entities that have interests (such as plants), and conscious entities that necessarily have welfare level zero. I also explain how my theory of welfare subjects relates to experientialist and anti-experientialist theories of welfare goods.

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)

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

Kant's speculative theistic proof rests on a distinction between “logical” and “real” modality that he developed very early in the pre-critical period. The only way to explain facts about real possibility, according to Kant, is to appeal to the properties of a unique, necessary, and “most real” being. Here I reconstruct the proof in its historical context, focusing on the role played by the theory of modality both in motivating the argument (in the pre-critical period) and, ultimately, in undoing it (...) as a source of knowledge of God's existence (in the critical period). Along the way I examine Kant's version of the now-popular “actualist” thesis that facts about what is possible must be explained by facts about what is actual. I conclude by discussing why the critical Kant claims both that there are rational grounds for accepting the conclusion of his theistic proof, and that such acceptance can not count as knowledge. This is important, I argue, because the same considerations ultimately motivate his prohibition on knowledge of things-in-themselves generally. -/- . (shrink)

This work was written for the Midlands Conference of Critical Thought which took place on 5–6th April 2024 at Nottingham Trent University. It was presented for a session on productivity, process, and the value of making, organised by the Vienna Contemporary Art Space. The work provides an overview of two of the presenter’s essays, Content and Operation and Instinct and Intelligence, to show how the process of philosophy can be the subject matter of philosophical works.

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)

The virtues and vices of argument are now an established part of argumentation theory. They have helped direct attention to hitherto neglected aspects of how we argue. However, it remains controversial whether a virtue theory can contribute to some of the central questions of argumentation theory. Notably, Harvey Siegel disputes whether what he calls ‘arguments in the abstract propositional sense’ can be evaluated meaningfully within a virtue theory. This paper explores the prospects for grounding an account of argument evaluation in (...) arguers’ virtues and vices by examination of a corresponding debate in virtue ethics: Can an ethics of virtue guide our actions? It is thereby argued that an affirmative answer is possible: virtues suffice for argument evaluation. (shrink)

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 ...

In this paper I look at the much-discussed case of disabled parents seeking to conceive disabled children. I argue that the permissibility of selecting for disability does not depend on the precise impact the disability will have on the child’s wellbeing. I then turn to an alternative analysis, which argues that the permissibility of selecting for disability depends on the impact that disability will have on the child’s future opportunities. Nearly all bioethicists who have approached the issue in this way (...) have argued that disabilities like deafness unacceptably constrain a child’s opportunities. I argue, however, that this conclusion is premature for several reasons. Most importantly, we don’t have a good way of comparing opportunity sets. Thus, we can’t conclude that deaf children will grow up to have a constrained set of opportunities relative to hearing children. I conclude by suggesting that bioethicists and philosophers of disability need to spend more time thinking carefully about the relationship between disability and opportunity. (shrink)

This paper empirically investigates one aspect of the folk concept of time by testing how the presence or absence of directedness impacts judgements about whether there is time in a world. Experiment 1 found that dynamists, showed significantly higher levels of agreement that there is time in dynamically directed worlds than in non-dynamical non-directed worlds. Comparing our results to those we describe in Latham et al., we report that while ~ 70% of dynamists say there is time in B-theory worlds, (...) only ~ 45% say there is time in C-theory worlds. Thus, while the presence of directedness makes dynamists more inclined to say there is time in a world, a substantial subpopulation of dynamists judge that there is time in non-directed worlds. By contrast, a majority of non-dynamists judged that there was time in both growing block worlds and C-theory worlds, with no significant differences between the means. Experiment 2 found that when participants are only presented with non-dynamical worlds—namely, a directed world and a non-directed world—they report significantly higher levels of agreement that there is time in B-theory worlds. However, the majority of participants still judge that there is time in C-theory worlds. We conclude that while the presence of directedness bolsters judgements that there is time, most people do not judge it to be necessary for time. (shrink)

Philosophers have long noted, and empirical psychology has lately confirmed, that most people are “biased toward the future”: we prefer to have positive experiences in the future, and negative experiences in the past. At least two explanations have been offered for this bias: belief in temporal passage and the practical irrelevance of the past resulting from our inability to influence past events. We set out to test the latter explanation. In a large survey, we find that participants exhibit significantly less (...) future bias when asked to consider scenarios where they can affect their own past experiences. This supports the “practical irrelevance” explanation of future bias. It also suggests that future bias is not an inflexible preference hardwired by evolution, but results from a more general disposition to “accept the things we cannot change”. However, participants still exhibited substantial future bias in scenarios in which they could affect the past, leaving room for complementary explanations. Beyond the main finding, our results also indicate that future bias is stake-sensitive and that participants endorse the normative correctness of their future-biased preferences and choices. In combination, these results shed light on philosophical debates over the rationality of future bias, suggesting that it may be a rational response to empirical realities rather than a brute, arational disposition. (shrink)

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)

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)

This entry summarizes arguments for and against the thesis that knowledge entails belief.

While many aspects of cognition have been shown to be shared between humans and non-human animals, there remains controversy regarding whether the capacity to mentally time travel is a uniquely human one. In this paper, we argue that there are four ways of representing when some event happened: four kinds of temporal representation. Distinguishing these four kinds of temporal representation has five benefits. First, it puts us in a position to determine the particular benefits these distinct temporal representations afford an (...) organism. Second, it provides the conceptual resources to foster a discussion about which of these representations is necessary for an organism to count as having the capacity to mentally time travel. Third, it enables us to distinguish stricter from more liberal views of mental time travel that differ regarding which kind(s) of temporal representation is taken to be necessary for mental time travel. Fourth, it allows us to determine the benefits of taking a stricter or more liberal view of mental time travel. Finally, it ensures that disagreement about whether some species can mentally time travel is not merely the product of unrecognised disagreement about which temporal representation is necessary for mental time travel. We argue for a more liberal view, on the grounds that it allows us to view mental time travel as an evolutionarily continuous phenomenon, and to recognise that differences in the ways that organisms mentally time travel might reflect different temporal representations, or combinations thereof, that they employ. Our ultimate aim, however, is to create the conceptual framework for further discussion regarding what sorts of temporal representations are required for mental time travel. (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)

Frans de Waal (1948-2024) transformed our understanding of primate cognition and social behavior, shaping the perspectives of scientists, philosophers, and the general public through his groundbreaking research and engaging popular books.

To be conscious—according to a common metaphor—is for the “lights to be on inside.” Is this a good metaphor? I argue that the metaphor elicits useful intuitions while staying neutral on controversial philosophical questions. But I also argue that there are two ways of interpreting the metaphor. Is consciousness the inner light itself? Or is consciousness the illuminated room? Call the first sense subjectivity (where ‘consciousness’ =def what makes an entity feel some way at all), and the second sense phenomenal (...) character (where ‘consciousness’ =def what it feels like to be an entity). I use this distinction—as well as the metaphor of the inner light—to clarify some philosophical questions about whether consciousness comes in degrees, whether consciousness is multidimensional, and whether there are borderline cases of consciousness. (shrink)

Most elpistologists now agree that hope for a specific outcome involves more than just desire plus the presupposition that the outcome is possible. This paper argues that the additional element of hope is a disposition to focus on the desired outcome in a certain way. I first survey the debate about the nature of hope in the recent literature, offer objections to some important competing accounts, and describe and defend the view that hope involves a kind of focus or attention. (...) I then suggest that this account makes sense of the intuitive thought that there are moral and pragmatic norms on hope that go beyond the norms on desires and modal presuppositions. I conclude by considering some key questions. (shrink)

I develop and defend a sense-datum theory of perception. My theory follows the spirit of classic sense-datum theories: I argue that what it is to have a perceptual experience is to be acquainted with some sense-data, where sense-data are private particulars that have all the properties they appear to have, that are common to both perception and hallucination, that constitute the phenomenal characters of perceptual experiences, and that may be aptly described as pictures in-side one’s head. But my theory also (...) diverges from conventional sense-datum theories in some key respects: on my view, (1) sense-data are first-person presentations of neural states, (2) the sensational qualities of sense-data differ in kind from the sensible qualities of external objects, and (3) sense-data are the vehicles in virtue of which we perceive, rather than the objects that we perceive. I argue that this package of claims is appropriately labeled ‘sense-datum theory’, and that the resultant view ought to be a live contender in contemporary philosophy of perception. (shrink)

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

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)

It has widely been assumed, by philosophers, that most people unambiguously have a phenomenology as of time passing, and that this is a datum that philosophical theories must accommodate. Moreover, it has been assumed that the greater the extent to which people have said phenomenology, the more likely they are to endorse a dynamical theory of time. This paper is the first to empirically test these assumptions. Surprisingly, our results do not support either assumption. One experiment instead found the reverse (...) correlation: people were more likely to report having passage phenomenology if they endorsed a non-dynamical theory of time. Given that people do not have an unambiguous phenomenology as of time passing, we conclude that this is suggestive evidence in favor of veridical non-dynamism—the view that our phenomenology is veridical, and that it does not unambiguously represent that time passes. Instead, our phenomenology veridically has some quite different content. (shrink)

Let a smooth experience be an experience with perfectly gradual changes in phenomenal character. Consider, as examples, your visual experience of a blue sky or your auditory experience of a rising pitch. Do the phenomenal characters of smooth experiences have continuous or discrete structures? If we appeal merely to introspection, then it may seem that we should think that smooth experiences are continuous. This paper (1) uses formal tools to clarify what it means to say that an experience is continuous (...) or discrete, and (2) develops a discrete model of the phenomenal characters of smooth experiences. As a result, I'll argue that introspection leaves open whether smooth experiences are continuous or discrete. Yet I’ll also argue—perhaps surprisingly—that the discrete theory may better fit our introspective evidence. (shrink)

It is important to note that certain mental health disorders are classified as rare conditions, and they have their own ‘cultural concepts of distress’ as defined in the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM 5). Cultural concepts of distress are a recent attempt to understand psychological distress influenced by culture, separate from biomedical diagnoses that require equal attention and support for individuals and their families, both physically and emotionally. [1].

In recent years, the science and the philosophy of consciousness has seen growing interest in structural questions about consciousness. This is the Editorial Introduction for a special volume for Philosophy and the Mind Sciences on “Structuralism in Consciousness Studies.”.

Our reasons for emotions such as sadness, anger, resentment, and guilt often remain long after we cease experiencing these emotions. This is puzzling. If the reasons for these emotions persist, why do the emotions not persist? Does this constitute a failure to properly respond to our reasons? In this paper we provide a solution to this puzzle. Our solution turns on the close connection between the rationality of emotion and the rationality of attention, together with the differing reasons to which (...) attention and emotion are properly responsive. (shrink)

In this paper, I present counterexamples to the evidence thesis, the thesis that S knows that p at t only if S believes that p on the basis of evidence at t. The outline of my paper is as follows. In section 1, I explain the evidence thesis and make clear what a successful counterexample to the evidence thesis will look like. In section 2, I show that instances of non-occurrent knowledge are counterexamples to the evidence thesis. At the end (...) of section 2, I consider the primary thesis of my paper — that the evidence thesis is false — to be successfully defended. In section 3, I consider three variations of the evidence thesis. The first variation restricts the evidence thesis to occurrent knowledge; the second requires for knowledge that one’s belief could be based on evidence; and the third requires for knowledge that the belief was based on evidence at a suitable prior time. The secondary thesis of this paper is that these variations are also subject to serious objections. (shrink)

In this article I discuss the moral-coherence reading of Kant’s moral argument offered by Allen Wood in his recent book _Kant and Religion_, display some of the challenges that it faces and suggest that a moral-psychological formulation is preferable.

In his recent book, Bernecker (Memory, 2010) has attacked the following prominent view: (RK) S remembers that p only if S knows that p. An attack on RK is also an attack on Timothy Williamson’s view that knowledge is the most general factive stative attitude. In this paper, I defend RK against Bernecker’s attacks and also advance new arguments in favor of it. In Sect. 2, I provide some background on memory. In Sect 3, I respond to Bernecker’s attacks on (...) RK and develop a new argument for RK. In Sects. 4 and 5, I develop two more new arguments for RK. (shrink)