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.

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)

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)

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.

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)

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)

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.

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)

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)

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.

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

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)

While more species are being identified as cultural on a regular basis, stark differences between human and animal cultures remain. Humans are more richly cultural, with group-specific practices and social norms guiding almost every element of our lives. Furthermore, human culture is seen as cumulative, cooperative, and normative, in contrast to animal cultures. One hypothesis to explain these differences is grounded in the observation that human children across cultures appear to spontaneously over-imitate silly or causally irrelevant behaviors that they observe. (...) The few studies on over-imitation in other species are largely taken as evidence that spontaneous over-imitation is not present in other species. This leads to the over-imitation hypothesis – that the differences between human culture and animal cultures can be traced to the human unique tendency to over-imitate. In this paper, we analyze the current state of the literature on animal over-imitation and challenge the adequacy of the over-imitation hypothesis for the differences between humans and animal cultures. To make this argument, we first argue that the function of human over-imitation is norm-learning and that over-imitation, like skill-learning, should be subject to selective social learning effects. Then we review the empirical evidence against animal over-imitation and argue that these studies do not take into account the relevant variables given the normative and selective nature of over-imitation. We then analyze positive empirical evidence of over-imitation in great apes and canids from the experimental literature and conclude that the current body of evidence suggests that some canids and primates may have the capacity for over-imitation. This paper offers a methodological suggestion for how to study animal over-imitation, and a theoretical suggestion that over-imitation might be much more widely found among species. The larger implication for claims about human uniqueness suggests that if we do find widespread evidence of over-imitation across species, many of the current theories of human uniqueness that focus on human hyper-cooperation or social norms may have only identified a difference of degree, not of kind, between humans and other animals. (shrink)

Deflationists hold that it does not seem to us, in experience, as though time robustly passes. There is some recent empirical evidence that appears to support this contention. Equally, empirical evidence suggests that we naïvely represent time as dynamical. Thus deflationists are faced with an explanatory burden. If, as they maintain, the world seems to us in experience as though it is non-dynamical, then why do we represent time as dynamical? This paper takes up the challenge of investigating, on the (...) part of the deflationist, one candidate explanation. We hypothesise that people’s belief that the future is what we call deliberatively open partly explains why they represent time as dynamical. In a series of two experiments we test this hypothesis. We find no evidence that beliefs about deliberative openness explain why people represent time as dynamical. Hence there remains an explanatory burden for the deflationist to discharge. (shrink)

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of a (...) substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

In this paper I will introduce a new compatibilist account of free action: indirect conscious control compatibilism, or just indirect compatibilism for short. On this account, actions are free either when they are caused by compatibilist‐friendly conscious psychological processes, or else by sub‐personal level processes influenced in particular ways by compatibilist‐friendly conscious psychological processes. This view is motivated by a problem faced by a certain family of compatibilist views, which I call conscious control views. These views hold that we act (...) freely when we act in a way that is caused by certain conscious psychological processes. One problem for such views is that current neuroscience suggests that most of our actions are not caused by such processes. Instead, many of the actions we typically suppose are free are caused by sub‐personal level processes and hence would count as not free according to contemporary conscious control views. I argue, contra these views, that many actions caused by these sub‐personal level processes are indirectly free. Further, most of the actions we ordinarily judge to be free are free in this indirect manner. (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)

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 ...

Many philosophers hold that ‘one-instant worlds’—worlds that contain a single instant—fail to contain time. We experimentally investigate whether these worlds satisfy the folk concept of time. We found that ~50% of participants hold that there is time in such worlds. We argue that this suggests one of two possibilities. First, the population disagree about whether at least one of the A-, B-, or C-series is necessary for time, with there being a substantial sub-population for whom the presence of neither an (...) A-, B-, nor C-series, is necessary for time, and hence those folk have a radically more minimal concept of time than has been attributed to them by philosophers. Or, second, the population do not disagree about whether at least one of the A-, B-, or C-series is necessary for time, but disagree about what it takes for a world to fail to contain even a C-series. (shrink)

We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about (...) their logical behaviour. We also wield the framework to probe the conditions under which a logicist account of necessities is possible, in which the theory is completely reducible to logic. (shrink)

The usual way of discussing normativity and naturalism is by running through a standard range of issues: the relations of fact and value, objectivity, reason and emotion, is and ought, and the so-called ‘naturalistic fallacy’. This is a naturalism that is virtually silent on nature. I outline an alternative approach that relates normativity to our nature as living beings, for whom specific things are good or bad for us. Our nature as evaluative beings is shown to be rooted in and (...) emergent from this biological normativity. There is also significant downward causation, such that our brain-bodies are continually modified by our experience and thoughts. Cultures, as emergent from the affordances of our brain-bodies, create further extensive, irreducible sources of normativity, albeit ones which do not wholly escape biological normativity and can impact back on it. (shrink)

Previously, we introduced a capability approach to assess the responsible use of brain-computer interface. In this commentary, we say more about the ethical basis of our capability view and respond to three objections. The first objection holds that by stressing that capability lists are provisional and subject to change, we threaten the persistence of human dignity, which is tied to capabilities. The second objection states that we conflate capabilities and abilities. The third objection claims that the goal of using neuroenhancements (...) should be preserving capabilities, not altering them. (shrink)

This is part 1 on a paper whose final variation of parts shall be titled,”The Universal Theory of Existence: The Sashu, Pharaohs, and the al-Mahdī”. The first part of this series sets the premise for a proposed ”Theory of Everything” that will be the foundation for encompassing many different topics. Since, the beginning of time, a singularity existed. This singularity is what we call an origin point of everything. Beyond, this origin point for time is different depending on position, being (...) outside of the singularity, or the idea that multiple universes exists with different time dilation, and likely different laws. Existence in essence is centered around the idea of what is prior to the origin point of time, and in theory, what is the space-time complexity together, in regards to how civilization come to be. From a physics standpoint, there are multiple theories around this. For starters, the author of this paper coined QSOPR Theorem, MDQBT, QSICT, and how this relates to Time/Multiverse Dilation and Origin Points. Quantum Similarity on a molecular, atomic, theoretical, and chemical level is one of these vast things humanity should be trying to explore. (shrink)

Intelligent neurotechnology is an emerging field that combines neurotechnologies like brain-computer interface (BCI) with artificial intelligence. This paper introduces a capability framework to assess the responsible use of intelligent BCI systems and provide practical ethical guidance. It proposes two tests, the threshold and flourishing tests, that BCI applications must meet, and illustrates them in a series of cases. After a brief introduction (Section 1), Section 2 sets forth the capability view and the two tests. It illustrates the threshold test using (...) examples from clinical medicine of BCI applications that enable patients with profound disabilities to function at a threshold level through computer mediation. Section 3 illustrates the flourishing test by exploring possible future applications of BCI involving neuroenhancements for healthy people, using examples adapted from research currently underway in the US military. Section 3 applies a capability lens to a complex case involving dual effects, both therapeutic and non-therapeutic, showing how the threshold and flourishing tests resolve the case. Section 4 replies to three objections: neurorights are the best tool for assessing BCI; the two tests are moving targets; and the analysis utilizes a capability view to do work it is not designed for. The paper concludes that a capability view offers unique advantages and gives practical guidance for evaluating the responsible use of present and future BCI applications. Extrapolating from our analysis may help guide other emerging technologies, such as germline gene editing, expected to impact central human capabilities. (shrink)

Critical comments on David Papineau's idea that people find physicalism about phenomenal consciousness unbelievable because they commit what he calls the 'antipathetic fallacy'.

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 goal of this paper is to show that Thomas Aquinas, in his _Disputed Questions on Evil_, presents a theory of free will that is compatibilist but still involves a version of the principle of alternative possibilities (PAP) and even requires alternative possibilities for a certain kind of responsibility. In Aquinas’ view, choosing between possibilities is not the primary power of the will. Rather, choice arises through the complex interaction of various parts of human psychology, in particular through the indeterminacy (...) of the intellect and through the interaction between reason and passion. Both of these ways provide cases where Aquinas not only allows for alternative possibilities but thinks that they are necessary for moral responsibility, all the while remaining, strictly speaking, a compatibilist. (shrink)

Religious dietary practices foster a sense of communal identity, certainly, but traditionally they are also regarded as pleasing to God (or the gods, or the ancestors) and spiritually beneficial. In other words, for many religious people, the effects of fasting go well beyond what is immediately observed or empirically measurable, and that is a large part of what motivates participation in the practice. The goal of this chapter is to develop that religious way of thinking into a response to a (...) motivational problem that arises from our awareness of the insensitivity of contemporary food supply chains. If someone can have faith, or at least tenacious hope, that the significance of her food choices goes well beyond what is immediately observed or empirically measurable, then she may be less demoralized by the apparent inefficacy of those choices. The chapter concludes by considering a way in which this broadly religious way of thinking might be available to secular people as well. (shrink)

One debate surrounding Derk Pereboom’s (2001, 2014) four-case argument against compatibilism focuses on whether, and why, we judge manipulated agents to be neither free nor morally responsible. In this paper, we propose a novel explanation. The four-case argument features cases where an agent is the only individual in her universe who has been manipulated. Let us call manipulation whose scope includes at least one but not all agents existential manipulation. Contrast this with universal manipulation, which affects all agents within a (...) universe. We propose that we find agents in Pereboom’s manipulation cases less free and morally responsible in part because they are the target of existential manipulation. We empirically tested this hypothesis and found that people’s free will and moral responsibility judgments were sensitive to the scope of manipulation: people judged existentially manipulated agents significantly less free and responsible than universally manipulated agents. (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)

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)

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment (...) of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)

Frege-Geach worries about embedding and composition have plagued metaethical theories like emotivism, prescriptivism and expressivism. The sharpened point of such criticism has come to focus on whether negation and inconsistency have to be understood in descriptivist terms. Because they reject descriptivism, these theories must offer a non-standard account of the meanings of ethical and normative sentences as well as related semantic facts, such as why certain sentences are inconsistent with each other. This paper fills out such a solution to the (...) negation problems, following some of the original emotivist ideas about the interplay of interests in conversation. We communicate both to share information and coordinate our actions, and we use distinctively normative language like deontic ‘must’ and ‘may’ to negotiate what people are to do. The kinds of disagreement involved in such negotiation can illuminate the issues with negation and inconsistency. This paper outlines a dynamic semantic system in which these ideas can bear fruit, developing the scorekeeping model of conversation. The result is clarification about what Frege-Geach worries can mean for nondescriptive semantics. (shrink)

What makes a certain consideration an aesthetic reason rather than a reason of some other kind? Is it a solely a matter of the kind of attitude or activity that the reason supports? How fundamental or structural are such reasons? Do they contrast in a natural way with epistemic or practical reasons? Is skilled aesthetic achievement, whether interpretative or creative, a matter of recognizing the aesthetic reasons we have for a given response, and correctly according with such reasons? In this (...) paper, I offer a preliminary discussion of these topics. I argue that our account of aesthetic reasons should respect the fact that they play an important regulative role, over and above directly supporting aesthetic response. Such a role allows aesthetic reasons to moderate a wide range of practical and epistemic activities, but not by adding or substituting distinctively aesthetic ends or purposes for such activities. I then go on to argue against the view that skilled aesthetic achievement consists in correct recognition of and accord with aesthetic reasons, adapting a recent argument of Timothy Williamson’s. (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)

Reformed epistemology, roughly, is the thesis that religious belief can be rational without argument. After providing some background, I present Plantinga’s defense of reformed epistemology and its influence on religious debunking arguments. I then discuss three objections to Plantinga’s arguments that arise from the following topics: skeptical theism, cognitive science of religion, and basicality. I then show how reformed epistemology has recently been undergirded by a number of epistemological theories, including phenomenal conservatism and virtue epistemology. I end by noting that (...) a good objection to reformed epistemology must criticize either a substantive epistemological theory or the application of that theory to religious belief; I also show that the famous Great Pumpkin Objection is an example of the former. (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)

The notion of function is indispensable to our understanding of distinctions such as that between being broken and being in working order (for artifacts) and between being diseased and being healthy (for organisms). A clear account of the ontology of functions and functioning is thus an important desideratum for any top-level ontology intended for application to domains such as engineering or medicine. The benefit of using top-level ontologies in applied ontology can only be realized when each of the categories identified (...) and defined by a top-level ontology is integrated with the others in a coherent fashion. Basic Formal Ontology (BFO) has from the beginning included function as one of its categories, exploiting a version of the etiological account of function that is framed at a level of generality sufficient to accommodate both biological and artifactual functions. This account has been subjected to a series of criticisms and refinements. We here articulate BFO’s account of function, provide some reasons for favoring it over competing views, and defend it against objections. (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)

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.

What are the prospects (if any) for a virtue-theoretic account of inference? This paper compares three options. Firstly, assess each argument individually in terms of the virtues of the participants. Secondly, make the capacity for cogent inference itself a virtue. Thirdly, recapture a standard treatment of cogency by accounting for each of its components in terms of more familiar virtues. The three approaches are contrasted and their strengths and weaknesses assessed.

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)

Mereological nihilism (henceforth just "nihilism") is the thesis that composition never occurs. Nihilism has often been defended on the basis of its theoretical simplicity, including its ontological simplicity and its ideological simplicity (roughly, nihilism's ability to do without primitive mereological predicates). In this paper I defend nihilism on the basis of the theoretical unification conferred by nihilism, which is, roughly, nihilism's capacity to allow us to take fewer phenomena as brute and inexplicable. This represents a respect in which nihilism enjoys (...) greater theoretical simplicity than its rivals which has not yet been explored, and which is immune to many of the objections which have been leveled against previous arguments for nihilism from nihilism's theoretical simplicity. Composition as identity might be thought to confer a similar degree of theoretical unification as nihilism. I end the paper by arguing that this is not the case. (shrink)

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

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)