This paper presents a Least Square Monte Carlo approach for accurately calculating credit value adjustment (CVA). In contrast to previous studies, the model relies on the probability distribution of a default time/jump rather than the default time itself, as the default time is usually inaccessible. As such, the model can achieve a high order of accuracy with a relatively easy implementation. We find that the valuation of a defaultable derivative is normally determined via backward induction when their payoffs could be (...) positive or negative. Moreover, the model can naturally capture wrong or right way risk. (shrink)

This paper presents a new model for pricing OTC derivatives subject to collateralization. It allows for collateral posting adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives. Using a unique dataset, we find empirical evidence that credit risk alone is not overly important in determining credit-related spreads. Only accounting for both collateral arrangement and credit risk can sufficiently explain unsecured credit costs. This (...) finding suggests that failure to properly account for collateralization may result in significant mispricing of derivatives. We also empirically gauge the impact of collateral agreements on risk measurements. Our findings indicate that there are important interactions between market and credit risk. (shrink)

This article presents a new methodology for pricing and hedging commodity derivatives. A generic model calibration is provided. The calibration procedure consists of an offline step where the mean reversion rates, the ratio of the long and short factor volatilities and the correlation between the long and short factors are determined via historical analysis. This offline step is performed relatively infrequently. There’s also an online step of the calibration which happens every time the model is used to price an option (...) or to simulate price paths. Empirical study shows that the model is quite accurate. (shrink)

Equity-linked securities with a guaranteed return become popular in a volatile market environment. This paper presents a new model for valuing guaranteed equity-linked notes. We consider a security whose value depends on the performance of a basket of equities averaged over certain points in time, but that is floored by a guaranteed amount. We show that the security’s price is given by the sum of the guaranteed amount plus the price of an Asian style option on the basket above. The (...) model provides analytical formulas for the security’s price as well as for corresponding hedge ratios; these respective formulas appear to be accurate over a wide range of underlying security parameter values, based on numerical testing against a Monte Carlo benchmark, Finally, we apply our method to value a type of segregated fund with a maturity guarantee. (shrink)

This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the literature, we emphasize that the market value of a defaultable derivative is actually a risky value rather than a risk-free value. Credit value adjustment (CVA) is also (...) elaborated. A practical framework is developed for pricing defaultable derivatives and calculating their CVAs at a portfolio level. (shrink)

This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in (...) the CDS market. (shrink)

This article presents a comprehensive framework for valuing financial instruments subject to credit risk. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats in financial markets. We analyze how swap rates are affected by bilateral counterparty credit risk, and how CDS spreads depend on the trilateral credit risk of the buyer, seller, and reference entity in a contract. Moreover, we study the effect of collateralization on (...) valuation, since the majority of OTC derivatives are collateralized. The model shows that a fully collateralized swap is risk-free, whereas a fully collateralized CDS is not equivalent to a risk-free one. (shrink)

This paper presents an analytical model for valuing interest rate swaps, subject to bilateral counterparty credit risk. The counterparty defaults are modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

This article presents a new model for valuing financial contracts subject to credit risk and collateralization. Examples include the valuation of a credit default swap (CDS) contract that is affected by the trilateral credit risk of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to (...) a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market. (shrink)

During the lifetime of a structured product, payment events and cancellation events mainly affect the value of the option. This article presents a model for pricing generic cancellable option. The model is used to build most common kinds of cancellation schedules and compute the cancellation probability.

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage is mainly due (...) to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price. (shrink)

This paper presents a new model for valuing hybrid defaultable financial instruments, such as, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence (...) supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price. (shrink)

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing a shifted forward measure and several novel fast drift approximation methods. This model should achieve the best performance without losing much accuracy. Moreover, the calibration (...) is almost automatic and it is simple and easy to implement. Adding this model to the valuation toolkit is actually quite useful; especially for risk management or in the case there is a need for a quick turnaround. (shrink)

The incremental risk charge (IRC) is a new regulatory requirement from the Basel Committee in response to the recent financial crisis. Notably few models for IRC have been developed in the literature. This paper proposes a methodology consisting of two Monte Carlo simulations. The first Monte Carlo simulation simulates default, migration, and concentration in an integrated way. Combining with full re-valuation, the loss distribution at the first liquidity horizon for a subportfolio can be generated. The second Monte Carlo simulation is (...) the random draws based on the constant level of risk assumption. It convolutes the copies of the single loss distribution to produce one year loss distribution. The aggregation of different subportfolios with different liquidity horizons is addressed. Moreover, the methodology for equity is also included, even though it is optional in IRC. (shrink)

This paper attempts to assess the economic significance and implications of collateralization in different financial markets, which is essentially a matter of theoretical justification and empirical verification. We present a comprehensive theoretical framework that allows for collateralization adhering to bankruptcy laws. As such, the model can back out differences in asset prices due to collateralized counterparty risk. This framework is very useful for pricing outstanding defaultable financial contracts. By using a unique data set, we are able to achieve a clean (...) decomposition of prices into their credit risk factors. We find empirical evidence that counterparty risk is not overly important in credit-related spreads. Only the joint effects of collateralization and credit risk can sufficiently explain unsecured credit costs. This finding suggests that failure to properly account for collateralization may result in significant mispricing of financial contracts. We also analyze the difference between cleared and OTC markets. (shrink)

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a (...) better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread. (shrink)

Shadow pictures radically changed the modern understanding of pictorial concepts. Tim Otto Roth’s broadly based cultural history traces the consequences of this revolution of methods of vision and image production in the sciences and the arts. By means of abundant image and text sources he develops a picture theory based on physics and projective geometry. This definitive book comprising 500 pages provides a generally understandable and vivid insight in the history of shadowgraphs from the 19th century until the present age. (...) A crucial role play scientific processes as the X-ray technique, but also the artistic examination of space and body. (shrink)

Both motivational internalism and externalism need to explain why sometimes moral judgments tend to motivate us. In this paper, I argue that Dreier’ second-order desire model cannot be a plausible externalist alternative to explain the connection between moral judgments and motivation. I explain that the relevant second-order desire is merely a constitutive requirement of rationality because that desire makes a set of desires more unified and coherent. As a rational agent with the relevant second-order desire is disposed towards coherence, she (...) will have some motivation to act in accordance with her moral judgments. Dreier’s second-order desire model thus collapses into a form of internalism and cannot be a plausible externalist option to explain the connection between moral judgments and motivation. (shrink)

I advocate scepticism about epistemic blame; the view that we have good reason to think there is no distinctively epistemic form of blame. Epistemologists often find it useful to draw a distinction between blameless and blameworthy norm violation. In recent years, this has led several writers to develop theories of ‘epistemic blame.’ I present two challenges against the very idea of epistemic blame. First, everything that is supposedly done by epistemic blame is done by epistemic evaluation, at least according to (...) a prominent view about the social role of epistemic evaluation. Parsimony considerations count against introducing an idle mechanism that does the same work as an existing one. Second, no current theory of epistemic blame includes a plausible account of the force of epistemic blame or the practices that could express it. I conclude that we should give up the notion of epistemic blame. (shrink)

Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...) STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

Tim Button explores the relationship between words and world; between semantics and scepticism. -/- A certain kind of philosopher – the external realist – worries that appearances might be radically deceptive. For example, she allows that we might all be brains in vats, stimulated by an infernal machine. But anyone who entertains the possibility of radical deception must also entertain a further worry: that all of our thoughts are totally contentless. That worry is just incoherent. -/- We cannot, then, be (...) external realists, who worry about the possibility of radical deception. Equally, however, we cannot be internal realists, who reject all possibility of deception. We must position ourselves somewhere between internal realism and external realism, but we cannot hope to say exactly where. We must be realists, for what that is worth, and realists within limits. -/- In establishing these claims, The Limits of Realism critically explores and develops several themes from Hilary Putnam’s work: the model-theoretic arguments; the connection between truth and justification; the brain-in-vat argument; semantic externalism; and conceptual relativity. The book establishes the continued significance of these topics for all philosophers interested in mind, logic, language, or the possibility of metaphysics. (shrink)

The attention economy — the market where consumers’ attention is exchanged for goods and services — poses a variety of threats to individuals’ autonomy, which, at minimum, involves the ability to set and pursue ends for oneself. It has been argued that the threat wireless mobile devices pose to autonomy gives rise to a duty to oneself to be a digital minimalist, one whose interactions with digital technologies are intentional such that they do not conflict with their ends. In this (...) paper, we argue that there is a corresponding duty to others to be an attention ecologist, one who promotes digital minimalism in others. Although the moral reasons for being an attention ecologist are similar to those that motivate the duty to oneself, the arguments diverge in important ways. We explore the application of this duty in various domains where we have special obligations to promote autonomy in virtue of the different roles we play in the lives of others, such as parents and teachers. We also discuss the consequences of our arguments for employers, software developers, and policy makers. (shrink)

Much recent discussion has focused on the nature of artifacts, particularly on whether artifacts have essences. While the general consensus is that artifacts are at least intention-dependent, an equally common view is function essentialism about artifacts, the view that artifacts are essentially functional objects and that membership in an artifact kind is determined by a particular, shared function. This paper argues that function essentialism about artifacts is false. First, the two component conditions of function essentialism are given a clear and (...) precise formulation, after which counterexamples are offered to each. Second, ways to handle the counterexamples suggested by Randall Dipert and Simon Evnine are considered and rejected. Third, I then consider the prospects for restricting function essentialism to so-called technical artifacts, as Lynne Baker does, and argue that this, too, fails. This paper thereby consolidates the scattered literature on function essentialism and shows that, despite the seeming plausibility of the thesis, it should be rejected as an account of artifact essences. (shrink)

The phenomenal character of perceptual experience involves the representation of colour, shape and motion. Does it also involve the representation of high-level categories? Is the recognition of a tomato as a tomato contained within perceptual phenomenality? Proponents of a conservative view of the reach of phenomenal content say ’No’, whereas those who take a liberal view of perceptual phenomenality say ’Yes’. I clarify the debate between conservatives and liberals, and argue in favour of the liberal view that high-level content can (...) directly inform the phenomenal character of perception. (shrink)

I defend the intention-dependence of artifacts, which says that something is an artifact of kind K only if it is the successful product of an intention to make an artifact of kind K. I consider objections from two directions. First, that artifacts are often mind- and intention-dependent, but that this isn’t necessary, as shown by swamp cases. I offer various error theories for why someone would have artifact intuitions in such cases. Second, that while artifacts are necessarily mind-dependent, they aren’t (...) necessarily intention-dependent. I consider and reject three kinds of cases which purport to show this: accidental creation, automated production, and mass production. I argue that intentions are present in all of these cases, but not where we would normally expect. (shrink)

In “Models and Reality” (1980), Putnam sketched a version of his internal realism as it might arise in the philosophy of mathematics. Here, I will develop that sketch. By combining Putnam’s model-theoretic arguments with Dummett’s reflections on Gödelian incompleteness, we arrive at (what I call) the Skolem-Gödel Antinomy. In brief: our mathematical concepts are perfectly precise; however, these perfectly precise mathematical concepts are manifested and acquired via a formal theory, which is understood in terms of a computable system of proof, (...) and hence is incomplete. Whilst this might initially seem strange, I show how internal categoricity results for arithmetic and set theory allow us to face up to this Antinomy. This also allows us to understand why “Models are not lost noumenal waifs looking for someone to name them,” but “constructions within our theory itself,” with “names from birth.”. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, that (...) if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

This paper offers some refinements to a particular objection to act consequentialism, the “causal impotence” objection. According to proponents of the objection, when we find circumstances in which severe, unnecessary harms result entirely from voluntary acts, it seems as if we should be able to indict at least one act among those acts, but act consequentialism appears to lack the resources to offer this indictment. Our aim is to show is that the most promising response on behalf of act consequentialism, (...) the threshold argument, cannot offer a fully general prescription about what to do in cases of collective action. (shrink)

Amie Thomasson and Eli Hirsch have both attempted to deflate metaphysics, by combining Carnapian ideas with an appeal to ordinary language. My main aim in this paper is to critique such deflationary appeals to ordinary language. Focussing on Thomasson, I draw two very general conclusions. First: ordinary language is a wildly complicated phenomenon. Its implicit ontological commitments can only be tackled by invoking a context principle; but this will mean that ordinary language ontology is not a trivial enterprise. Second: ordinary (...) language often points in different directions simultaneously, so that a wide variety of existence questions cannot be deflated merely by appealing to ordinary language. (shrink)

There are empirical grounds to doubt the effectiveness of a common and intuitive approach to teaching debiasing strategies in critical thinking courses. We summarize some of the grounds before suggesting a broader taxonomy of debiasing strategies. This four-level taxonomy enables a useful diagnosis of biasing factors and situations, and illuminates more strategies for more effective bias mitigation located in the shaping of situational factors and reasoning infrastructure—sometimes called “nudges” in the literature. The question, we contend, then becomes how best to (...) teach the construction and use of such infrastructures. (shrink)

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...) abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

Craig Callender [2022] provides a novel challenge to the non-arbitrariness principle. His challenge plays an important role in his argument for the rational permissibility of a non-exponential temporal discounting rate. But the challenge is also of wider interest: it raises significant questions about whether we ought to accept the non-arbitrariness principle as a constraint on rational preferences. In this paper, I present two reasons to resist Callender’s challenge. First, I present a reason to reject his claim that the non-arbitrariness principle (...) only targets pure time preferences. Second, I criticize the inference Callender draws from a modest claim to a much stronger claim. The modest claim is that it can be hard to reveal the contents of an agent’s preferences. The stronger claim is that this provides us with a reason to reject a certain kind of normative constraint on rational preferences. I argue that the modest claim doesn’t motivate the stronger claim. The upshot of my two arguments is good news for those sympathetic to the non-arbitrariness principle: Callender’s challenge can be overcome, at least as it currently stands. (shrink)

Appeals to nature are ubiquitous in Epicurean ethics and politics. The foundation of Epicurean ethics is its claim that pleasure is the sole intrinsic good and pain the sole intrinsic evil, and this is supposedly shown by the behavior of infants who have not yet been corrupted, "when nature's judgement is pure and whole." Central to their recommendations about how to attain pleasure is their division between types of desires: the natural and necessary ones, the natural but non-necessary ones, and (...) the vain and empty ones. Elsewhere, the Epicureans talk about the "natural goods" of political power and fame, and they contrast "natural wealth" with wealth as "defined by empty opinion." Finally, in their politics, Epicurus claims that the "the justice of nature is a pledge of reciprocal usefulness, [i.e.,] neither to harm one another nor to be harmed." This paper explores two questions regarding these various appeals to nature. The first is: what is it for these things to be natural, i.e., what notion of "natural" or "nature" is at play here? (Furthermore, is there a single notion being used across these appeals, and if not, how are they related?) The second is: what normative work does a thing's being natural do? That is, what reason, if any, does a desire's being natural give me for pursuing the object of that desire and trying to fulfill that desire, as opposed to not doing so and trying to eliminate it, and similarly for the other appeals to nature? (shrink)

By definition, pain is a sensory and emotional experience that is felt in a particular part of the body. The precise relationship between somatic events at the site where pain is experienced, and central processing giving rise to the mental experience of pain remains the subject of debate, but there is little disagreement in scholarly circles that both aspects of pain are critical to its experience. Recent experimental work, however, suggests a public view that is at odds with this conceptualisation. (...) By demonstrating that the public does not necessarily endorse central tenets of the “mental” view of pain (subjectivity, privacy, and incorrigibility), experimental philosophers have argued that the public holds a more “body-centric” view than most clinicians and scholars. Such a discrepancy would have important implications for how the public interacts with pain science and clinical care. In response, we tested the hypothesis that the public is capable of a more “mind-centric” view of pain. Using a series of vignettes, we demonstrate that in situations which highlight mental aspects of pain the public can, and does, recognize pain as a mental phenomenon. We also demonstrate that the public view is subject to context effects, by showing that the public’s view is modified when situations emphasizing mental and somatic aspects of pain are presented together. (shrink)

The sensitivity condition on knowledge says that one knows that P only if one would not believe that P if P were false. Difficulties for this condition are now well documented. Keith DeRose has recently suggested a revised sensitivity condition that is designed to avoid some of these difficulties. We argue, however, that there are decisive objections to DeRose’s revised condition. Yet rather than simply abandoning his proposed condition, we uncover a rationale for its adoption, a rationale which suggests a (...) further revision that avoids our objections as well as others. The payoff is considerable: along the way to our revision, we learn lessons about the epistemic significance of certain explanatory relations, about how we ought to envisage epistemic closure principles, and about the epistemic significance of methods of belief formation. (shrink)

The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity. I show this by presenting Level Theory, a simplification of set theories (...) due to Scott, Montague, Derrick, and Potter. (shrink)

The phenomenology of agency has, until recently, been rather neglected, overlooked by both philosophers of action and philosophers of consciousness alike. Thankfully, all that has changed, and of late there has been an explosion of interest in what it is like to be an agent. 1 This burgeoning field crosses the traditional boundaries between disciplines: philosophers of psychopathology are speculating about the role that unusual experiences of agency might play in accounting for disorders of thought and action; cognitive scientists are (...) developing models of how the phenomenology of agency is generated; and philosophers of mind are drawing connections between the phenomenology of agency and the nature of introspection, phenomenal character, and agency itself. My aim in this paper is not to provide an exhaustive survey of this recent literature, but to provide a.. (shrink)

Much recent discussion has focused on the nature of artifacts, particularly on whether they have essences. While it is often held that artifacts are intention-dependent and necessarily have functions, it is equally commonly held, though far less discussed, that artifacts are the result of physical modification of some material objects. This paper argues that the physical modification condition on artifacts is false. First, it formulates the physical modification condition perspicuously for the first time. Second, it offers counterexamples to this condition, (...) both concrete and abstract. Third, it considers, and rejects, two responses to these counterexamples, one which appeals to the distinction between being a K and being used as a K and another which argues that the counterexamples are merely of functional, not artifactual, kinds. Finally, it considers, and rejects, a more general objection that appropriation makes artifact creation too easy. As a consequence, artifacts can be created by appropriating pre-existing objects and it sketches some success conditions for such appropriation. (shrink)

No-futurists ('growing block theorists') hold that that the past and the present are real, but that the future is not. The present moment is therefore privileged: it is the last moment of time. Craig Bourne (2002) and David Braddon-Mitchell (2004) have argued that this position is unmotivated, since the privilege of presentness comes apart from the indexicality of 'this moment'. I respond that no-futurists should treat 'x is real-as-of y' as a nonsymmetric relation. Then different moments are real-as-of different times. (...) This reunites privilege with indexicality, but entails that no-futurists must believe in ineliminably tensed facts. (shrink)

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly the same (...) relations to all objects (including themselves). I conclude that realistic structuralists must compromise and treat some structures eliminativistically. (shrink)

Anaxarchus accompanied Pyrrho on Alexander the Great’s expedition to India and was known as “the Happy Man” because of his impassivity and contentment. Our sources on his philosophy are limited and largely consist of anecdotes about his interactions with Pyrrho and Alexander, but they allow us to reconstruct a distinctive ethical position. It overlaps with several disparate ethical traditions but is not merely a hodge-podge; it hangs together as a unified whole. Like Pyrrho, he asserts that things are indifferent in (...) value and that realizing this indifference leads to contentment. But this doctrine of indifference is rooted in Democritean atomism. And in his pursuit of pleasure and dismissiveness of conventional standards of what is just, noble, and pious, Anaxarchus is closer to fifth century thinkers such as Aristippus, Antiphon, and Critias. (shrink)

Many authors in ethics, economics, and political science endorse the Lottery Requirement, that is, the following thesis: where different parties have equal moral claims to one indivisible good, it is morally obligatory to let a fair lottery decide which party is to receive the good. This article defends skepticism about the Lottery Requirement. It distinguishes three broad strategies of defending such a requirement: the surrogate satisfaction account, the procedural account, and the ideal consent account, and argues that none of these (...) strategies succeed. The article then discusses and discharges some remaining grounds for resistance to these skeptical conclusions, as well as the possibility of defending a weaker version of a normative lottery principle. The conclusion is that we have no reason to believe that where equal claims conflict, we are morally required to hold a lottery, as opposed to simply picking one of the parties on more subjective grounds or out of pure whim. In addition to the practical consequences of this skeptical view, the article sketches some theoretical implications for debates about saving the greater number and about axiomatic utilitarianism. (shrink)

Tallant (2007) has challenged my recent defence of no-futurism (Button 2006), but he does not discuss the key to that defence: that no-futurism's primitive relation 'x is real-as-of y' is not symmetric. I therefore answer Tallant's challenge in the same way as I originally defended no-futurism. I also clarify no-futurism by rejecting a common mis-characterisation of the growing-block theorist. By supplying a semantics for no-futurists, I demonstrate that no-futurism faces no sceptical challenges. I conclude by considering the problem of how (...) to interpret the relation 'x is real-as-of y'. -/- (NB: A correction to this article appears in Analysis 68.1.). (shrink)

We argue that S is in a position to know that p iff S can know that p. Thus, what makes position-to-know-ascriptions true is just a special case of what makes ability-ascriptions true: compossibility. The novelty of our compossibility theory of epistemic modality lies in its subsuming epistemic modality under agentive modality, the modality characterizing what agents can do.

Suppose we can save either a larger group of persons or a distinct, smaller group from some harm. Many people think that, all else equal, we ought to save the greater number. This article defends this view (with qualifications). But unlike earlier theories, it does not rely on the idea that several people's interests or claims receive greater aggregate weight. The argument starts from the idea that due to their stakes, the affected people have claims to have a say in (...) the rescue decision. As rescuers, our primary duty is to respect these procedural claims, which we must do by doing what these people would decide, in a process where each is given an equal vote on the matter. So in cases where each votes in their own self-interest, respect for their equal right to decide, or their autonomy, will lead us to save the greater number. The argument is explained in detail, with special attention to the questions of how, exactly, it avoids aggregation, and of why majority rule is superior to lottery procedures. The view has further advantages. Especially, it explains the “partial” relevance of numbers in cases involving unequal harms, and it does so in a way that dissolves the appearance of paradox that besets theories of “partial aggregation.”. (shrink)

According to conventional wisdom, the split-brain syndrome puts paid to the thesis that consciousness is necessarily unified. The aim of this paper is to challenge that view. I argue both that disunity models of the split-brain are highly problematic, and that there is much to recommend a model of the split-brain—the switch model—according to which split-brain patients retain a fully unified consciousness at all times. Although the task of examining the unity of consciousness through the lens of the split-brain syndrome (...) is not a new one—such projects date back to Nagel’s seminal paper on the topic—the time is ripe for a re-evaluation of the issues. (shrink)

Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). -/- By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive (...) way of fleshing out this idea is synonymous with a ZF-like theory. -/- This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974). (shrink)