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)

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)

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)

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.

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)

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.

We are able to participate in countless different sorts of social practice. This indefinite set of capacities must be explainable in terms of a finite stock of capacities. This paper compares and contrasts two different explanations. A standard decomposition of the capacity to participate in social practices goes something like this: the interpreter arrives on the scene with a stock of generic practice-types. He looks at the current scene to fill-in the current tokens of these types. He looks at the (...) current state of these practice tokens to see what actions are available to him. He uses his current desires to choose between these various possible actions. I argue that this standard explanation is defective, drawing on arguments by Searle and Wittgenstein and Garfinkel. I propose an alternative explanation, in which the participants must continually show each other the state of the scene in order to maintain the scene’s intelligibility. I provide a simple formal language in which to describe this alternative approach, in which we can state quite precisely what someone is doing when they participate in a practice. This language is related to both deontic and epistemic logics, but it is much simpler – it does not include the classic propositional connectives, and it is driven by a very different set of assumptions. The inspirations for this formal language are Searle’s analysis of directions of fit, Wittgenstein’s remarks on rule-following and Garfinkel’s ethnomethodology. (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 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)

An investigation of what Frege means by his doctrine that functions (and so concepts) are 'unsaturated'. We argue that this doctrine is far less peculiar than it is usually taken to be. What makes it hard to understand, oddly enough, is the fact that it is so deeply embedded in our contemporary understanding of logic and language. To see this, we look at how it emerges out of Frege's confrontation with the Booleans and how it expresses a fundamental difference between (...) Frege's approach to logic and theirs. (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...

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)

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.

This paper explores the relationship between the questioning attitude of wondering and a class of attitudes I call 'epistemic desires'. Broadly, these are desires to improve one's epistemic position on some question. A common example is the attitude of wanting to know the answer to some question. I argue that one can have any kind of epistemic desire towards any question, Q, without necessarily wondering Q, but not conversely. That is, one cannot wonder Q without having at least some epistemic (...) desire directed towards Q. I defend this latter claim from apparent counterexamples due to Friedman (2013) and Drucker (2022), and finish with a proposal on which epistemic desires, particularly the desire for understanding, play an explanatory role in distinguishing wondering from other forms of question-directed thought. (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.

How should your opinion change in light of an epistemic peer's? We show that the pooling rule known as "upco" is the unique answer satisfying some natural desiderata. If your revised opinion will impact your other views by Jeffrey conditionalization, then upco is the only standard pooling rule that ensures the order in which peers are consulted makes no difference. Popular alternatives like linear pooling, geometric pooling, and harmonic pooling cannot boast the same. In fact, no alternative can that possesses (...) four minimal properties these proposals all share. (shrink)

Frege held that referring expressions in general, and demonstratives and indexicals in particular, contribute more than just their reference to what is expressed by utterances of sentences containing them. Heck first attempts to get clear about what the essence of the Fregean view is, arguing that it rests upon a certain conception of linguistic communication that is ultimately indefensible. On the other hand, however, he argues that understanding a demonstrative (or indexical) utterance requires one to think of the object denoted (...) in an appropriate way. This fact makes it difficult to reconcile the view that referring expressions are "directly referential" with any view that seeks (as Grice's does) to ground meaning in facts about communication. (shrink)

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 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)

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)

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)

My aim in this paper is to identify the wrong that is done in all cases of testimonial injustice, if there is one. Miranda Fricker (2007) proposes one account of this distinctive wrong, and Gaile Pohlhaus Jr. (2014) offers another. I think neither works. Nor does an account based on giving due respect to the testifier's epistemic competence. Nor does an account based on exposing the testifier to substantial risk of harm. Rachel Fraser (2023) describes a further account, and the (...) proposal I favour is a slight amendment of this. (shrink)

Many consider Nozick’s “utility monster”—a being more efficient than ordinary people at converting resources into wellbeing, with no upper limit—to constitute a damning counterexample to utilitarianism. But our intuitions may be reversed by considering a variation in which the utility monster starts from a baseline status of massive suffering. This suggests a rethinking of the force of the original objection.

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)

Adaptive preferences give rise to puzzles in ethics, political philosophy, decision theory, and the theory of action. Like our other preferences, adaptive preferences lead us to make choices, take action, and give consent. In 'False Consciousness for Liberals', recently published in The Philosophical Review, David Enoch (2020) proposes a criterion by which to identify when these choices, actions, and acts of consent are less than fully autonomous; that is, when they suffer from what Natalie Stoljar (2014) calls an 'autonomy deficit'. (...) According to Enoch, such actions are not protected in the usual way against interference by others; there is not the same prohibition against trying to prevent someone from acting in a particular way when that action is motivated by such adaptive preferences and is an attempt to satisfy them. In this note, I raise two concerns about Enoch's criterion. (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)

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

The concept of ‘Ethnicity’ still enjoys some currency in the historical and social science literature. However, the cogency of the idea remains disputed. First coming to prominence in the 1980s, the word is often used to depict the character of social relations in the context of conflicts over sovereignty. The case of Northern Ireland presents a paradigmatic example. This article is a rejoinder to Ian McBride’s contention that my scepticism about the notion lacks justification. With reference to disputes over the (...) state, I show in response that ‘ethnicity’ in effect means nationality. I further claim that the nation state is a successor to the dynastic state. In clarifying the meaning of this arrangement, the article brings out how the nation is a juridical rather than empirical category. More specifically, it derives from the notion of corporate personality in law. For this reason, its retrospective integrity is a matter of fabrication, depending on the fiction of ancestral continuity. At the same time, its future-oriented cohesiveness means that it must be invested with a unifying will. I conclude that the legitimacy of a nation state rests on its democratic will, whose coherence is expressed in the action of its government. (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)

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.

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 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.

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)

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)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

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)

There are three main moral theories: virtue ethics, the deontological approach and utilitarianism. The concern here is how they interrelate, why they come into focus at different times and places, and how they are configured in their application to a modern democratic society. Person-oriented virtue ethics was the dominant understanding in Ancient Greece but within the Western tradition this was later subordinated to the monotheism of Ancient Judaism as modified by Christianity. Of growing importance by the eighteenth century was rights (...) theory which was often still situated religiously. Kant’s principle of the categorical imperative has been highly influential but was challenged by the emerging nature of industrial and capitalist society. Utilitarianism, within which the moral rightness of activity resides in its tendency to promote happiness or unhappiness, represented the decisive move from the transcendental to the immanent approach. Although all three approaches to moral theory continue to be relevant to identifiable situations and aspects of modern society, there has been a substantial turn towards a heavily modified utilitarianism associated with parliamentary democracy and market economies founded on property ownership. The root cause of this is the ability of utilitarianism, as opposed to the other approaches, to handle considerations of number and probability. The concept of utility is fundamental in economics but the idea has evolved away from its origins to mean “preference”. There is a sense in which the straightforward appeal of basic utilitarianism has been “leased out” in modified form to a set of institutional arrangements. Certain “pressure points” in a modern society are noted which pose particular problems pertinent to moral theory. Bernard Williams argues persuasively for an appropriately modified form of virtue ethics. (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.

This is the second part of my theological dialogue with ChatGPT on the meaning of God. We explore the nature of God's agency, will, goodness, the problem of evil and suffering, the meaning of sin, and the meaning and nature of the redemptive act of Christ.

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)

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)

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)

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.

Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.

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)