On a currently popular reading of Locke, an idea represents its cause, or what God intended to be its cause. Against Martha Bolton and my former self (among others), I argue that Locke cannot hold such a view, since it sins against his epistemology and theory of abstraction. I argue that Locke is committed to a resemblance theory of representation, with the result that ideas of secondary qualities are not representations.

Disputes over territory are a major contributing factor to the disruption of international relations. We believe that a cumulative, integrated, and continuously updated resource providing information about such disputes in an easily accessible form would be of benefit to intelligence analysts, military strategists, political scientists, and also to historians and others concerned with international disputes. We propose an ontology-based strategy for creating such a resource. The resource will contain information about territorial disputes, arguments for and against claims pertaining to sovereignty, (...) proffered evidence for such claims, political and military motives (overt or hidden), and associated conflicts. Our approach is designed to address several issues surrounding the representation of geopolitical conflict, including the tracking and individuation of disputes and the validation of disseminated information. (shrink)

How language works — its functions, mechanisms, and limitations — matters to the early moderns as much as it does to contemporary philosophers. Many of the moderns make reflection on language central to their philosophical projects, both as a tool for explaining human cognition and as a weapon to be used against competing views. Even in philosophers for whom language is less central, we can find important connections between their views on language and their other philosophical commitments.

Two kinds of people might find this useful: first, those interested in the modern debate over ideas and representation who don’t happen to read French, or who do, but would like to have in one place the relevant excerpts, to see whether looking at the originals is worth their time. Second are teachers of modern philosophy. The back-and-forth among these figures makes for a refreshing change from the massive, often self-contained works that characterize much of the rest of such a (...) course. For example, one could easily work in chapter 3 (the high point of the debate, from my point of view) between Descartes and Berkeley. (shrink)

This article canvases the main areas of controversy: the nature of Lockean signification and his position on propositions and particles.

Like their contemporary counterparts, early modern philosophers find themselves in a predicament. On one hand, there are strong reasons to deny that sensations are representations. For there seems to be nothing in the world for them to represent. On the other hand, some sensory representations seem to be required for us to experience bodies. How else could one perceive the boundaries of a body, except by means of different shadings of color? I argue that Nicolas Malebranche offers an extreme -- (...) and ultimately unworkable -- attempt to solve this riddle. Most commentators claim that Malebranche defends an adverbial theory of sensation, according to which a sensation is merely a way in which an act of sensing happens. The adverbial reading is wrong, or so I argue. Once we arrive at a more accurate reading, we shall see that his position is much more strange than is currently thought. Nevertheless, Malebranche’s view is similar to the adverbial theory in one respect, albeit it at a very high level of generality. His view thus inherits two of the main problems that afflict adverbial theories. Although Malebranche fails to solve them, his ingenious attempts to do so are instructive. (shrink)

What we value, like, endorse, want, and prefer changes over the course of our lives. Richard Pettigrew presents a theory of rational decision making for agents who recognise that their values will change over time and whose decisions will affect those future times.

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

In recent years there has been a number of promising technical and institutional developments regarding use of ontologies in industry. At the same time, however, most industrial ontology development work remains within the realm of academic research and is without significant uptake in commercial applications. In biomedicine, by contrast, ontologies have made significant inroads as valuable tools for achieving interoperability between data systems whose contents derive from widely heterogeneous sources. In this position paper, we present a set of principles learned (...) from the successful Open Biomedical Ontologies (OBO) Foundry initiative to guide the design and development of the Industrial Ontologies Foundry (IOF), which is a counterpart to the OBO Foundry initiative for the manufacturing industry. We also illustrate the potential utility of these principles by sketching the conceptual design of a framework for sustainable IOF development. (shrink)

Although the last decade has seen a proliferation of ontological approaches to arguments, many of them employ ad hoc solutions to representing arguments, lack interoperability with other ontologies, or cover arguments only as part of a broader approach to evidence. To provide a better ontological representation of arguments, we present the Arguments Ontology (ArgO), a small ontology for arguments that is designed to be imported and easily extended by researchers who work in different upper-level ontology frameworks, different logics, and different (...) approaches to argument evaluation. Unlike most ontological approaches to arguments, ArgO utilizes Basic Formal Ontology (BFO) as an upper-level ontology, and may be used alongside other commonly used ontologies in the BFO framework, including boththe Information Artifact Ontology (IAO), and the Information Entity Ontology (INFO). Critically, our proposal is principled, based on rigorous definitions and formal axioms out of which characterizations of arguments naturally fall. It is our hope that ArgO may assist researchers in many projects, including: integrating heterogeneous sources of evidence, structuring the content of semantic wikis, and enhancing semantic reasoning. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

In this paper I defend what I call the argument from epistemic reasons against the moral error theory. I argue that the moral error theory entails that there are no epistemic reasons for belief and that this is bad news for the moral error theory since, if there are no epistemic reasons for belief, no one knows anything. If no one knows anything, then no one knows that there is thought when they are thinking, and no one knows that they (...) do not know everything. And it could not be the case that we do not know that there is thought when we believe that there is thought and that we do not know that we do not know everything. I address several objections to the claim that the moral error theory entails that there are no epistemic reasons for belief. It might seem that arguing against the error theory on the grounds that it entails that no one knows anything is just providing a Moorean argument against the moral error theory. I show that even if my argument against the error theory is indeed a Moorean one, it avoids Streumer's, McPherson's and Olson's objections to previous Moorean arguments against the error theory and is a more powerful argument against the error theory than Moore's argument against external world skepticism is against external world skepticism. (shrink)

Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those (...) covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R. A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs and Pettigrew in Noûs, 2018). In both cases, these arguments proceed by first establishing a very general reflection principle. (shrink)

Many philosophers nowadays believe Frege was right about belief, but wrong about language: The contents of beliefs need to be individuated more finely than in terms of Russellian propositions, but the contents of utterances do not. I argue that this 'hybrid view' cannot offer no reasonable account of how communication transfers knowledge from one speaker to another and that, to do so, we must insist that understanding depends upon more than just getting the references of terms right.

All humans have an equal basic moral status. They possess the same fundamental rights, and the comparable interests of each person should count the same in calculations that determine social policy. Neither supposed racial differences, nor skin color, sex, sexual orientation, ethnicity, intelligence, nor any other differences among humans negate their fundamental equal worth and dignity. These platitudes are virtually universally affirmed. A white supremacist racist or an admirer of Adolf Hitler who denies them is rightly regarded as beyond the (...) pale of civilized dialogue. However, a very simple line of argument developed by Peter Singer challenges our understanding of these platitudes and forces us to rethink the basis and nature of the moral equality of all humans. What I call the “Singer Problem” arises if one accepts that the morally significant cognitive capacities that are relevant to the determination of the fundamental moral status of a being vary from individual to individual by degree. The problem is to specify a moral principle determining fundamental moral status that assigns a superior status to humans compared to other animals on the basis of the superior cognitive capacities of humans but also assigns all human persons an equal fundamental moral status regardless of their differing cognitive capacities. More broadly posed, the problem is to specify moral principles that yield intuitively satisfactory implications for the treatment of human individuals and other individual animals given that cognitive capacities differ across species and individuals. A search for a resolution of the Singer problem leads to disappointing results. (shrink)

This paper is concerned with neo-Fregean accounts of reference to abstract objects. It develops an objection to the most familiar such accounts, due to Bob Hale and Crispin Wright, based upon what I call the 'proliferation problem': Hale and Wright's account makes reference to abstract objects seem too easy, as is shown by the fact that any equivalence relation seems as good as any other. The paper then develops a response to this objection, and offers an account of what it (...) is for abstracta to exist that is Fregean in spirit but more robust than familiar views. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

An investigation of Frege’s various contributions to the study of language, focusing on three of his most famous doctrines: that concepts are unsaturated, that sentences refer to truth-values, and that sense must be distinguished from reference.

Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.

The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

This paper discusses Frege's account of definition by induction in Grundgesetze and the two key theorems Frege proves using it.

Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our resources, are those that focus on (i) ensuring a long future for humanity, and perhaps sentient or intelligent life more generally, and (ii) improving the quality of the lives that inhabit that long future. While it is by no means the only one, the argument most commonly given for this conclusion is that these interventions have greater expected goodness (...) per unit of resource devoted to them than each of the other available interventions, including those that focus on the health and well-being of the current population. In this paper, I argue that, even if we grant the consequentialist ethics upon which this argument depends, and even if we grant one of the axiologies that are typically paired with that ethics to give the argument, we are not morally required to choose an option that maximises expected utility; indeed, we might not even be permitted to do so. Instead, I will argue, if the argument's consequentialism is correct, we should choose using a decision theory that is sensitive to risk, and allows us to give greater weight to worse-case outcomes than expected utility theory does. And, I will show, such decision theories do not always recommend longtermist interventions. Indeed, sometimes, they recommend exactly the opposite: sometimes, they recommend hastening human extinction. Many, though not all, will take this as a reductio of the consequentialism or the axiology of the argument. I remain agnostic on the conclusion we should draw. (shrink)

The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais Paradox. In this paper we solve these problems by extending Richard Jeffrey's decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability maximising. (...) We end the paper by investigating the conditions necessary and sufficient for a desirability function to be an expected utility. It turns out that the additional conditions imply highly implausible epistemic principles. (shrink)

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...

We often learn the opinions of others without hearing the evidence on which they're based. The orthodox Bayesian response is to treat the reported opinion as evidence itself and update on it by conditionalizing. But sometimes this isn't feasible. In these situations, a simpler way of combining one's existing opinion with opinions reported by others would be useful, especially if it yields the same results as conditionalization. We will show that one method---upco, also known as multiplicative pooling---is specially suited to (...) this role when the opinions you wish to pool concern hypotheses about chances. The result has interesting consequences: it addresses the problem of disagreement between experts; and it sheds light on the social argument for the uniqueness thesis. (shrink)

Effective altruism sounds so innocuous—who could possibly be opposed to doing good more effectively? Yet it has inspired significant backlash in recent years. This paper addresses some common misconceptions and argues that the core “beneficentric” ideas of effective altruism are both excellent and widely neglected. Reasonable people may disagree on details of implementation, but all should share the basic goals or values underlying effective altruism.

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (shrink)

A framework is developed for understanding what is “taken for granted” both in philosophy and in life generally, which may serve to orient philosophical inquiry and make it more effective. The framework takes in language and its development, as well as mathematics, logic, and the empirical sphere with particular reference to the exigencies of life. It is evaluated through consideration of seven philosophical issues concerned with such topics as solipsism, sense data as the route to knowledge, the possible reduction of (...) geometry to logic, and the existence and status of human rights. Various dichotomies and the notion of continuity are evidently highly strategic. (shrink)

Basic Formal Ontology (BFO) is a top-level ontology consisting of thirty-six classes, designed to support information integration, retrieval, and analysis across all domains of scientific investigation, presently employed in over 350 ontology projects around the world. BFO is a genuine top-level ontology, containing no terms particular to material domains, such as physics, medicine, or psychology. In this paper, we demonstrate how a series of cases illustrating common types of change may be represented by universals, defined classes, and relations employing the (...) BFO framework. We provide discussion of these cases to provide a template for other ontologists using BFO, as well as to facilitate comparison with the strategies proposed by ontologists using different top-level ontologies. (shrink)

Religion emerged among early humans because both purposive and non-purposive explanations were being employed but understanding was lacking of their precise scope and limits. Given also a context of very limited human power, the resultant foregrounding of agency and purposive explanation expressed itself in religion’s marked tendency towards anthropomorphism and its key role in legitimizing behaviour. The inevitability of death also structures the religious outlook; with ancestors sometimes assigned a role in relation to the living. Subjective elements such as the (...) experience of dreams and the internalization of moral precepts also play their part. Two important sources of variation among religions concern the adoption of a dualist or non-dualist perspective, and whether or not the religion’s early political experience is such as to generate a systematic doctrine subordinating politics to religion. The near ubiquity and endurance of religion are further illuminated by analysis of its functions and ideological role. Religion tends to be socially conservative but has the potential to be revolutionary. (shrink)

Our values change. What we value, want, desire, prefer, and how much; for nearly everyone, these will be different at different times in their life. These changes can be gradual or abrupt; they can be long-lasting or short-lived; and they can be induced by forces outside yourself or they can come from within or they can have no specific catalyst at all. Such preference change raises a number of questions for our theorising about rational choice, and these have been discussed (...) at length. In §2 and §3, I’ll outline two of these questions along with some of the putative solutions that have been proposed. But preference change also raises questions for our theorising about autonomy, and these have hardly been considered at all. In §4, I’ll outline three problems for personal autonomy; and in §5, I’ll outline one problem for political autonomy. In §6, I conclude. (shrink)

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem (...) and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers. (shrink)

In this chapter we explain what experimental philosophy of science is, how it relates to the philosophy of science, and STS more broadly, and what sorts of contributions is can make to ongoing research in the philosophy of science.

This paper explores the relationship between Hume's Prinicple and Basic Law V, investigating the question whether we really do need to suppose that, already in Die Grundlagen, Frege intended that HP should be justified by its derivation from Law V.

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

After a brief introduction and orientation (section I), this dialogue between Levinasian and Beckerian thought is approached along the lines of two major themes concerning consciousness which emerge in very different contexts and registers in their work (sections II and III), and one tantalizing question that is raised with great force by the dialogue (section IV). The two themes revolve around the subtle dialectical interplay that runs throughout the thought of both Levinas and Becker – the switching between internality and (...) externality, non-rational and rational; otherness and sameness; life and death – an interplay that is summed up in the dialectic between non-reflexive and reflexive consciousness. The Beckerian and Levinasian notions of the non-reflexive consciousness (section II) relate to their respective and in many ways convergent claims about a non-rational primal human state characterized by global vulnerability, awe and guilt, especially before the face of the other. Their analyses of reflexive consciousness (section III) relate to their interpretations of the problematic ideal of the free, self-constituting and self-mastering individual, and the impetus located therein towards the repression of what is Other to the self. Finally (section IV), the question is raised as to whether (and to what extent), following Levinas, sources of compelling ethical value might be legitimately understood as emerging out of Becker’s conception of primordial human vulnerability. (shrink)

When we abandon the neoliberal fiction that one is independent on the grounds that it is a-historic and antisocial, we realize that everyone is dependent and interdependent. In a media-driven society the self-identity of the individual is formed within the framework of the culture-ideology of consumerism from early childhood. As a result, both the environmental and social destruction have intensified. In the global era, or in the era of the global environmental crisis, self-identity as a precondition for environmentally sustainable care (...) of the self should be based on the culture-ideology of human rights and responsibilities, and on conscious self-limitation which realizes that one’s prosperity and security cannot come at the expense of others. Care of the self is about ensuring the habitability of the global environment as the primary interest of each individual. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

This paper presents a puzzle in the form of a tension between two things: (1) data points about what intuitively count as good guesses to a question given an agent's subjective probabilities, and (2) plausible strategic norms of inquiry that tell us how to go about answering a question. Recent theories of guessing and good guessing have acknowledged this puzzle in one form or another, and they aim to get around it by appealing to some sort of contextualism. But I (...) argue that the puzzle is more pressing than has been appreciated, that it makes it hard to understand how individually good guesses can form part of an overall rational inquiry, and that the appeal to contextualism in response to it relies on a very implausible kind of semantic blindness. In other words, I argue that the puzzle stands as a serious challenge to our understanding of how good guessing relates to rational inquiry. (shrink)

According to the phenomenal intentionality research program, a state’s intentional content is fixed by its phenomenal character. Defenders of this view have little to say about just how this grounding is accomplished. I argue that without a robust account of representation, the research program promises too little. Unfortunately, most of the well-developed accounts of representation – asymmetric dependence, teleosemantics, and the like – ground representation in external relations such as causation. Such accounts are inconsistent with the core of the phenomenal (...) intentionality program. I argue that, however counter-intuitive it may seem, the best prospect for explaining how phenomenal character represents appeals to resemblance. (shrink)

Parfit's On What Matters offers a rousing defence of non-naturalist normative realism against pressing metaphysical and epistemological objections. He addresses skeptical arguments based on (i) the causal origins of our normative beliefs, and (ii) the appearance of pervasive moral disagreement. In both cases, he concedes the first step to the skeptic, but draws a subsequent distinction with which he hopes to stem the skeptic's advance. I argue, however, that these distinctions cannot bear the weight that Parfit places on them. A (...) successful moral epistemology must take a harder line with the skeptic, insisting that moral knowledge can be had by those with the right kind of psychology -- no matter the evolutionary origin of the psychology, nor whether we can demonstrate its reliability over the alternatives. (shrink)

In this paper I examine the dispute between Hakwan Lau, Ned Block, and David Rosenthal over the extent to which empirical results can help us decide between first-order and higher-order theories of consciousness. What emerges from this is an overall argument to the best explanation against the first-order view of consciousness and the dispelling of the mythological notion of phenomenological overflow that comes with it.

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

Are non-natural properties worth caring about? I consider two objections to metaethical non-naturalism. According to the intelligibility objection, it would be positively unintelligible to care about non-natural properties that float free from the causal fabric of the cosmos. According to the ethical idlers objection, there is no compelling motivation to posit non-natural normative properties because the natural properties suffice to provide us with reasons. In both cases, I argue, the objection stems from misunderstanding the role that non-natural properties play in (...) the non-naturalist's understanding of normativity. The role of non-natural properties is not to be responded to, but to "mark" which natural properties it is correct for us to respond to in certain ways. (shrink)