While it seems to be evident that the vision of the eternal return of the same is the solution to the riddle mentioned in "On the vision and the riddle," exactly what constitutes the riddle is anything but clear. Li ke all good riddles the solution demands a paradigm shift. Nietzsche's riddle is solved by a radical rethinking of the concept of time, from a straight line to a circle. I give a detailed account of how Nietzsche's riddle is formulated (...) in such a way tha t the eternal return of the same is the only possible solution. (shrink)

This analysis shows Cantor's diagonal definition in his 1891 paper was not compatible with his horizontal enumeration of the infinite set M. The diagonal sequence was a counterfeit which he used to produce an apparent exclusion of a single sequence to prove the cardinality of M is greater than the cardinality of the set of integers N.

Orthodox semantics for natural language modals give rise to two puzzles for their interactions with disjunction: Ross’s puzzle and the puzzle of free choice permission. It is widely assumed that each puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from the truth of a possibility or necessity modal with an embedded disjunction, hearers infer that each disjunct is compatible with the relevant set of worlds. I argue that Diversity inferences are too weak to explain the full (...) range of data. Instead, I argue, modals with embedded disjunctions license ‘Independence’ inferences: from the truth of a modal with an embedded disjunction, hearers infer that each disjunct is an independent alternative among the relevant set of worlds. I then develop a bilateral inquisitive semantics for modals that predicts the validity of these Independence inferences. My account vindicates common intuitions about both Ross’s puzzle and the puzzle of free choice permission, and explains the full range of data. (shrink)

Some years ago, Machery, Mallon, Nichols, and Stich reported the results of experiments that reveal, they claim, cross-cultural differences in speaker’s ‘intuitions’ about Kripke’s famous Gödel–Schmidt case. Several authors have suggested, however, that the question they asked their subjects is ambiguous between speaker’s reference and semantic reference. Machery and colleagues have since made a number of replies. It is argued here that these are ineffective. The larger lesson, however, concerns the role that first-order philosophy should, and more importantly should not, (...) play in the design of such experiments and in the evaluation of their results. (shrink)

So-called 'Frege cases' pose a challenge for anyone who would hope to treat the contents of beliefs (and similar mental states) as Russellian propositions: It is then impossible to explain people's behavior in Frege cases without invoking non-intentional features of their mental states, and doing that seems to undermine the intentionality of psychological explanation. In the present paper, I develop this sort of objection in what seems to me to be its strongest form, but then offer a response to it. (...) I grant that psychological explanation must invoke non-intentional features of mental states, but it is of crucial importance which such features must be referenced. -/- It emerges from a careful reading of Frege's own view that we need only invoke what I call 'formal' relations between mental states. I then claim that referencing such 'formal' relations within psychological explanation does not undermine its intentionality in the way that invoking, say, neurological features would. The central worry about this view is that either (a) 'formal' relations bring narrow content in through back door or (b) 'formal' relations end up doing all the explanatory work. Various forms of each worry are discussed. The crucial point, ultimately, is that the present strategy for responding to Frege cases is not available either to the 'psycho-Fregean', who would identify the content of a belief with its truth-value, nor even to someone who would identify the content of a belief with a set of possible worlds. It requires the sort of rich semantic structure that is distinctive of Russellian propositions. There is therefore no reason to suppose that the invocation of 'formal' relations threatens to deprive content of any work to do. (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)

Nietzsche announces his intentions to publish a “physiology of aesthetics”, namely a naturalistic explanation for how aesthetic judgements are grounded in the physiology of both the one experiencing the work, and the creator of it. But as well as the physiological reduction of aesthetic judgements, Nietzsche in many places across his oeuvre frames the apparatus of physiology, especially the prescriptive dimension of self-cultivation, in terms amenable to being treated as ‘aesthetic’. The first section will mount a (re-) defense of the (...) use of aestheticized language for discussing Nietzschean self-cultivation. The second section demonstrates an aesthetic evaluation of capacities that make possible the acquisition and removal of instinctual components, ultimately arguing for Nietzsche’s qualified indeterminism regarding the capacity for self-cultivation. The third section will assess the pres- ence of another aesthetic measure, this time in terms of envisaging one’s psycho-physiology by reference to an external spectacle. The final section discusses metaethical questions stemming from Nietzsche’s prescriptive language regarding the aestheticization of our physiology. (shrink)

to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) -/- L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, Harman (...) 2015) — I call our argument the Fine-Graining Response. Paul has her own reply to this response, which we might call the Authenticity Reply. But Sarah Moss has recently offered an alternative reply to the Fine-Graining Response on Paul’s behalf (Moss 2017) — we’ll call it the No Knowledge Reply. This appeals to the knowledge norm of action, together with Moss’ novel and intriguing account of probabilistic knowledge. In this paper, I consider Moss’ reply and argue that it fails. I argue first that it fails as a reply made on Paul’s behalf, since it forces us to abandon many of the features of Paul’s challenge that make it distinctive and with which Paul herself is particularly concerned. Then I argue that it fails as a reply independent of its fidelity to Paul’s intentions. (shrink)

In this paper, we attempt to show that if Plantinga’s free will defence succeeds, his O Felix Culpa theodicy fails. For if every creaturely essence suffers from transworld depravity, then given that Jesus has a creaturely essence (as we attempt to show), it follows that Incarnation and Atonement worlds cannot be actualized by God, in which case we have anything but a felix culpa.

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...

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...) acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

This article reviews and criticizes Joseph Heath’s market failures approach (MFA) to business ethics. Our criticism is organized into three sections. First, we argue that, even under the ideal assumptions of perfect competition, when markets generate Pareto-efficient distributions, Heath’s approach does not rule out significant harms. Second, we show that, under nonideal conditions, the MFA is either too demanding, if efficiency is to be attained, or not sufficiently demanding, if the goal of Pareto efficiency is abandoned. Finally, we argue that (...) Heath’s appeal to regulations and specific moral requirements as a remedy for market failures is unlikely to safeguard efficiency and exposes a number of general worries regarding the moral force of the MFA. We end this article with a constructive suggestion on how to adjust the MFA to avoid these problems while preserving its contractualist and Paretian spirit. (shrink)

Upward monotonic semantics for necessity modals give rise to Ross’s Puzzle: they predict that □φ entails □(φ ∨ ψ), but common intuitions about arguments of this form suggest they are invalid. It is widely assumed that the intuitive judgments involved in Ross’s Puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from □(φ ∨ ψ), interpreters infer that the truth of each disjunct (φ, ψ) is compatible with the relevant set of worlds. I introduce two pieces of (...) data that this analysis fails to explain. Analyzing this data, I argue, suggests that necessity modals with embedded disjunctions license ‘Independence’ inferences: from the truth of □(φ ∨ ψ), interpreters infer that φ-without-ψ and ψ-without-φ are each compatible with the relevant set of worlds. I outline a bilateral inquisitive semantics for necessity modals that predicts the validity of the Independence inferences. I then argue that the resulting theory should be understood as one on which disjunctions denote pluralities of propositions, and necessity modals behave like collective predicates applied to these pluralities. (shrink)

This paper applies a virtue epistemology approach to using the Internet, as to improve our information-seeking behaviours. Virtue epistemology focusses on the cognitive character of agents and is less concerned with the nature of truth and epistemic justification as compared to traditional analytic epistemology. Due to this focus on cognitive character and agency, it is a fruitful but underexplored approach to using the Internet in an epistemically desirable way. Thus, the central question in this paper is: How to use the (...) Internet in an epistemically virtuous way? Using the work of Jason Baehr, it starts by outlining nine intellectual or epistemic virtues: curiosity, intellectual autonomy, intellectual humility, attentiveness, intellectual carefulness, intellectual thoroughness, open-mindedness, intellectual courage and intellectual tenacity. It then explores how we should deploy these virtues and avoid the corresponding vices when interacting with the Internet, particularly search engines. Whilst an epistemically virtuous use of the Internet will not guarantee that one will acquire true beliefs, understanding or even knowledge, it will strongly improve one’s information-seeking behaviours. The paper ends with arguing that teaching and assessing online intellectual virtues should be part of school and university curricula, perhaps embedded in critical thinking courses, or even better, as individual units. (shrink)

If a Zen Master kills a kitten, and does not hear its scream, does it make a sound? In this essay, I use the Zen story of Master Nansen's killing of a kitten as an entree into a reflection on the Zen experience of enlightenment. I argue that the story of Nansen and the cat, as presented in the Zen tradition, raises many questions and problems that must be resolved if we are to envision the enlightenment experience in a clear (...) way. (shrink)

Much of our information comes to us indirectly, in the form of conclusions others have drawn from evidence they gathered. When we hear these conclusions, how can we modify our own opinions so as to gain the benefit of their evidence? In this paper we study the method known as geometric pooling. We consider two arguments in its favour, raising several objections to one, and proposing an amendment to the other.

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...) is mysterious why we care about justification, for neither of the accounts explains how justification is connected to anything of epistemic value. We will call this the Connection Problem. I begin by describing Dunn’s process reliabilism and Tang’s indicator reliabilism. I argue that, understood correctly, they are, in fact, extensionally equivalent. That is, Dunn and Tang reach the top of the same mountain, albeit by different routes. However, I argue that both face the Connection Problem. In response, I offer my own version of reliabilism, which is both process and indicator, and I argue that it solves that problem. Furthermore, I show that it is also extensionally equivalent to Dunn’s reliabilism and Tang’s. Thus, I reach the top of the same mountain as well. (shrink)

In this critical review I explore the anti-intentionalist stance Adorno offers in his aesthetics, specifically focusing on his Notes to Literature, and the internal limits to this stance. Adorno rejects the primacy of authorial intentionalism: The presuppositions of its aesthetic methodology, he claims, place the individual in a position of epistemic priority, without exploring the social totalities which constitute the conditions of the presentation of aesthetic knowledge by any such individual. The role of the creator for Adorno is inherently mediated (...) within the context of such totalities. -/- This is not to wholly discount the role of creative intentions, however. Rather, Adorno frames the artist as a ‘bearer’ and a ‘representative of the total social subject’. In this context he allows for a qualified form of subjectivity, construed as a mode of creativity produced by a particular kind of “achieved self-awareness” or disposition of consciousness towards an “estrangement of meaning”. Indeed, the loss of the stronger presupposition that the subject acts as an authentic expository force can lead to a realization that objectivity by this means constitutes a “loss”, Adorno claims, which creates the possibility for pursuing a critical stance to facilitate the capacity for creating autonomous works of art. Creators of autonomous works acknowledge “the paradoxical relationship of the autonomous work to its commodity character” (‘Valery’s Deviations’), namely an awareness of their inherent reification. The self-alienating yet autonomous work is described by Adorno as possessing and demonstrating tacit yet genuine ‘wants’, but this is framed by the demands of the human condition to recognize how ill-fitting the forces of social production are upon and towards securing them. Aesthetic intentions and the subjects which channel them can be critically valuable if they allude to or exposit the contradictions between these demands and those forces. (shrink)

In this brief essay, I argue that Anselm's ontological argument for the existence of God achieves its effect through the verbal equivalent of a magician's "sleight-of-hand." More technically, the argument commits the informal fallacy of equivocation. I provide a brief analysis of the argument's text to demonstrate this.

It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...) Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic". (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)

We provide a philosophical reconstruction and analysis of the debate on the scientific status of cosmic inflation that has played out in recent years. In a series of critical papers, Ijjas et al. have questioned the scientificality of the current views on cosmic inflation. Proponents of cosmic inflation have in turn defended the scientific credentials of their approach. We argue that, while this defense, narrowly construed, is successful against Ijjas et al., the latter's reasoning does point to a significant epistemic (...) issue that arises with respect to inflation. A broadening of the concept of theory assessment is needed to address that issue in an adequate way. (shrink)

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

C. Stephen Layman contends that an argument supporting theism over naturalism can be constructed based on three defensible, non–question-begging premises about the moral order. Previous critics of Layman’s argument have challenged the truth of these premises. We stipulate them arguendo but go on to show that there is a deeper problem: a fourth premise introduced to complete the argument—the “completion premise,” as we call it—is true only if we assume that God exists or we concede that there is no afterlife. (...) We close with suggestions for how Layman’s argument must be strengthened to meet with dialectical success. (shrink)

A discussion of John Dewey's theory of inquiry and what it does and does not imply concerning good educational practice.

The discovery of a 1932 typewriter apparently signed by Heidegger raises questions about its authenticity and purpose, and prompts us to reconsider the validity of Heidegger’s portrayal of typewriters as devices that alienate writing from the hand and exemplify the modern oblivion of being.

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)

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...) proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

The main focus of my comments is the role played in Dickie's view by the idea that "the mind has a need to represent things outside itself". But there are also some remarks about her (very interesting) suggestion that descriptive names can sometimes fail to refer to the object that satisfies the associated description.

David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...) little attention, and on a number of philosophical reconstructions of the viewpoint (in particular, by Hand, Kitcher, and Tait). (shrink)

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.

This paper explores the implications of extended and distributed cognition theory for our notions of personal identity. On an extended and distributed approach to cognition, external information is under certain conditions constitutive of memory. On a narrative approach to personal identity, autobiographical memory is constitutive of our diachronic self. In this paper, I bring these two approaches together and argue that external information can be constitutive of one’s autobiographical memory and thus also of one’s diachronic self. To develop this claim, (...) I draw on recent empirical work in human-computer interaction, looking at lifelogging technologies in both healthcare and everyday contexts. I argue that personal identity can neither be reduced to psychological structures instantiated by the brain nor by biological structures instantiated by the organism, but should be seen as an environmentally-distributed and relational construct. In other words, the complex web of cognitive relations we develop and maintain with other people and technological artifacts partly determines our self. This view has conceptual, methodological, and normative implications: we should broaden our concepts of the self as to include social and artifactual structures, focus on external memory systems in the (empirical) study of personal identity, and not interfere with people’s distributed minds and selves. (shrink)

Derek Parfit was one of the most important and influential moral philosophers of the late 20th and early 21st centuries. This Element offers a critical introduction to his wide-ranging ethical thought, focusing especially on his two most significant works, Reasons and Persons and On What Matters, and their contribution to the consequentialist moral tradition. Topics covered include: rationality and objectivity, distributive justice, self-defeating moral theories, Parfit's Triple Theory, personal identity, and population ethics.

Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.

Rohwer & Marris claim that “many conservation biologists” believe that there is a prima facie duty to preserve the genetic integrity of species. (A prima facie duty is a necessary pro tanto moral reason.) They describe three possible arguments for that belief and reject them all. They conclude that the biologists they cite are mistaken, and that there is no such duty: duties to preserve genetic integrity are merely instrumental: we ought act to preserve genetic integrity only because doing so (...) is required by some other duty, such as the duty to preserve taxonomic biodiversity, or the duty to preserve the reproductive fitness of existing species. In permitting for instance the introgression of cattle genes into the genome of Bison bison we therefore do not necessarily fail in any respect ethically. I criticize the paper on three fronts. (shrink)

Co-authored letter to the APA to take a lead role in the recognition of teaching in the classroom, based on the participation in an interdisciplinary Conference on the Role of Advocacy in the Classroom back in 1995. At the time of this writing, the late Myles Brand was the President of Indiana University and a member of the IU Department of Philosophy.

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...) suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

The paradox of 'the One and the Many' might, more generally, be understood as the paradox of relationship. In order for there to be relationship there must be at least two parties in relation. The relation must, at once, hold the parties apart (otherwise they would collapse into unity) while holding them together (otherwise relationship itself would cease). It must do so, further, without itself becoming a third party which would then, itself, need to be related. This paper considers this (...) paradox as we find it manifest in the theories of quantum physics, the Socratic pursuit of universals, and, finally, at the very heart of human personhood - where we discover it at the core of interpersonal relationships, existential anxiety, and social distress. It is suggested, in the end, that though reason cannot resolve the terms of this paradox, there is a potential solution to the existential problems that spring from it, a solution lying in what Jesus calls, simply, 'faith.'. (shrink)

Written in 2002/2003 while I was a graduate student at the University of Connecticut and ultimately submitted as part of my qualifying exam for the Master Degree in philosophy. I argue that the causal relation is observable even if the necessity of the connection is not. This version (the only one that remains) was prepared for presentation at the New Jersey Regional Philosophy Association.

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)

Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts Frege’s claim that (...) his own view is completely different from Hankel’s formalism, and motivates a closer examination of where the differences lie. On the interpretation offered here, Frege shares important parts of the formalist perspective, but differs in recognizing a kind of content for arithmetical terms which can only be made available via proof from prior postulates. (shrink)

A general survey of Frege's views on truth, the paper explores the problems in response to which Frege's distinctive view that sentences refer to truth-values develops. It also discusses his view that truth-values are objects and the so-called regress argument for the indefinability of truth. Finally, we consider, very briefly, the question whether Frege was a deflationist.

Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...) number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting. (shrink)

David Rosenthal explains conscious mentality in terms of two independent, though complementary, theories—the higher-order thought (“HOT”) theory of consciousness and quality-space theory (“QST”) about mental qualities. It is natural to understand this combination of views as constituting a kind of representationalism about experience—that is, a version of the view that an experience’s conscious character is identical with certain of its representational properties. At times, however, Rosenthal seems to resist this characterization of his view. We explore here whether and to what (...) extent it makes sense to construe Rosenthal’s views as representationalist. Our goal is not merely terminological—discerning how best to use the expression ‘representationalism’. Rather, we argue that understanding Rosenthal’s account as a kind of representationalism permits us not only to make sense of broader debates within the philosophy of mind, but also to extend and clarify aspects of the view itself. (shrink)

In this essay I examine the moral message presented in Woody Allen's film, "Crimes and Misdemeanors.".

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)