Existence as the Possibility of Reference

The mere fact that ontological debates are possible requires us to address the question, what is it to claim that a certain entity or kind of entity exists—in other words, what do we do when we make an existence-claim? I develop and defend one candidate answer to this question, namely that to make an existence-claim with regard to Fs is to claim that we can refer to Fs. I show how this theory can fulfil the most important explanatory desiderata for a theory of existence; I also defend it against the charges of illegitimate ‘semantic ascent’ and of making existence counterfactually dependent on human linguistic ability.     

Dispositional Monism and the Circularity Objection

Three basic positions regarding the nature of fundamental properties are: dispositional monism, categorical monism and the mixed view. Dispositional monism apparently involves a regress or circularity, while an unpalatable consequence of categorical monism and the mixed view is that they are committed to quidditism. I discuss Alexander Bird's defence of dispositional monism based on the structuralist approach to identity. I argue that his solution does not help standard dispositional essentialism, as it admits the possibility that two distinct dispositional properties can possess the same stimuli and manifestations. Moreover, Bird's argument can be used to support the mixed view by relieving it of its commitment to quidditism. I briefly analyse an alternative defence of dispositional essentialism based on Leon Horsten's approach to the problem of circularity and impredicativity. I conclude that the best option is to choose Bird's solution but amend the dispositional perspective on properties. According to my proposal, the essences of dispositions are determined not directly by their stimuli and manifestations but by the role each property plays in the structure formed by the stimulus/manifestation relations.     

Experience and Time

In this discussion, I claim that the debate over ‘the bias towards the present’ turns on an axiological question. Is the value of a present experience greater than its value when past? I argue not and hold that our bias towards the present, understood as a pure time preference, is irrational.     

Using DEA to assess NATO burden-sharing

As the member making many of the most visible contributions to NATO, the USA has often claimed that they shoulder the heaviest ‘burden’ in maintaining the objectives of the alliance. This claim has been backed by research which has concentrated on contributions such as defence expenditure and benefits such as protection from external threats. However, modern alliances entail the exchange of multiple forms of alliance benefits and liabilities and therefore the study of ‘burden-sharing’ in these alliances is a more complicated accounting problem than has been acknowledged by previous research. In this paper, burden-sharing is studied using Data Envelopment Analysis (DEA). This is a novel application of DEA. Instead of calculating relative ‘efficiencies’, the analysis produces a ‘net-burden index’ for each member nation of NATO. The results of the analysis indicate that whilst the USA shoulders a heavy burden, some other member nations, including Canada and Spain, may in fact shoulder a heavier burden.     

Perdurance, Endurance, and ‘Having a Property Atemporally’

In this paper, I argue that both perdurance theory and the ‘relations-to-times’ endurantist view rely on an atemporal notion of property instantiation and relation bearing. I distinguish two possible meanings of ‘atemporal’ which result in two different understandings of what it is for an object to have a property or to bear a relation atemporally. I show that standard presentations of the theories considered are indeterminate as to which of these two understandings is the intended one. I claim that even if both understandings are admissible, one of them is more attractive and has more to recommend than the other.     

Critical perspectives of the ‘new’ difference equation solution method of Rivera-Figueroa and Rivera-Rebolledo

Recently, claims of a ‘new and straightforward’ method of solution to second-order linear difference equations have appeared in the mathematics education literature from Rivera-Figueroa and Rivera-Rebolledo. The claim of novelty is based on an assumption that ‘since the equation is worked in its canonical form’, the method within this context must be new. In addition, the assertion of straightforwardness is based on the position that ‘the solution comes naturally’ through this method, rather than artificially. In this article, we subject these claims and assumptions to closer scrutiny, examination and analysis. We note that the method has been published before, and we present the method in a more succinct form. We also discuss how the method can be extended to solve difference equations with non-constant coefficients, illustrating this via a discussion of an example.     

The metalogic of economic predictions,calculations and propositions

Indeterminacy is a matter of concern in the analysis of ideal forms and this paper shows that Gödel incompleteness and undecidability directly pertain to the analysis of theoretical economic systems - specifically, that certain solution concepts such as ‘predictions of characteristics of policy outcomes guided by a social welfare function’, ‘the existence of equilibrium’, ‘the existence of welfare optima’ are subject to Gödel undecidability. This consideration brings into question the convention of a finite decision unit or economic actor, and the paper considers more-appropriate (metatheoretic) assumption structures and the implications of specifying richer information structures in microeconomics and choice theory.     

A Note on Belief Reports and Context Dependence

The aim of this paper is to pose a problem for theories that claim that belief reports are context dependent. Firstly, I argue that the claim (interpreted in the spirit of moderate contextualism) is committed to verbalism, a theory that derives the context sensitivity of belief reports from the context sensitivity of the psychological verbs used in such reports. Secondly, I argue that verbalism is not an attractive theoretical option because it is in conflict with the non-proto-rigidity of verbs like ‘believe’. Finally, I describe various consequences that the argument has for invariantism and moderate contextualism.     

Metaphysical Vagueness and Metaphysical Indeterminacy

The topic of this paper is whether there is metaphysical vagueness. It is shown that it is important to distinguish between the general phenomenon of indeterminacy and the more narrow phenomenon of vagueness (the phenomenon that paradigmatically rears its head in sorites reasoning). Relatedly, it is important to distinguish between metaphysical indeterminacy and metaphysical vagueness. One can wish to allow metaphysical indeterminacy but rule out metaphysical vagueness. As is discussed in the paper, central argument against metaphysical vagueness, like those of Gareth Evans and Mark Sainsbury, would if successful rule out metaphysical indeterminacy. One way to argue specifically against the possibility of metaphysical vagueness might be thought to be to argue for a specific theory of the nature of vagueness according to which vagueness is a semantic phenomenon. But it is shown that there are complications also pertaining to arguments with that structure. Toward the end of the paper, I discuss Trenton Merricks’ well-known argument against a semantic view on vagueness and for a metaphysical view.     

Global existence for degenerate parabolic equations with a non-local forcing

We establish local existence and comparison for a model problem which incorporates the effects of non-linear diffusion, convection and reaction. The reaction term to be considered contains a non-local dependence, and we show that local solutions can be obtained via monotone limits of solutions to appropriately regularized problems. Utilizing this construction, it is further shown that, under conditions of either ‘weak reaction’ or ‘sufficiently small’ initial mass, solutions exist for all time. Finally, we provide an alternative analysis of global existence and investigate blow up in finite time for the case of power law diffusion and convection. These results show the extent to which the assumption of weak reaction may be relaxed and still obtain global existence. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Uncertain volatility and the risk-free synthesis of derivatives

To price contingent claims in a multidimensional frictionless security market it is sufficient that the volatility of the security process is a known function of price and time. In this note we introduce optimal and risk-free strategies for intermediaries in such markets to meet their obligations when the volatility is unknown, and is only assumed to lie in some convex region depending on the prices of the underlying securities and time. Our approach is underpinned by the theory of totally non-linear parabolic partial differential equations (Krylov and Safanov, 1979; Wang, 1992) and the non-stochastic approach to Itô's formation first introduced by Föllmer (1981a,b).

In these more general conditions of unknown volatility, the optimal risk-free trading strategy will, necessarily, produce an unpredictable surplus over the minimum assets required at any time to meet the liabilities. This surplus, which could be released to the intermediary or to the client, is not required to meet the contingent claim. One sees that the effect of unknown volatility is the creation of a ‘with profits’ policy, where a premium is paid at the beginning, the contingent claim is collected at the terminal time, but that in addition an unpredictable surplus available as well.

The risk-free initial premium required to meet the contingent claim is given by the solution to the Dirichlet problem for a totally non-linear parabolic equation of the Pucci-Bellman type. The existence of a risk-free strategy starting with this minimum sum is dependent upon theorems ensuring the regularity of the solution and upon a non-probabilistic understanding of Itô's change of variable formulae.

To illustrate the ideas we give a very simple example of a one-dimensional barrier option where the maximum Black-Scholes price of the option over different fixed values for the volatility lying in an interval always underestimates the risk-free ‘price’ under the assumption that the volatility can vary within the same interval.

This paper puts together rather standard mathematical ideas. However, the author hopes that the overall result is more than the sum of its parts. The ability to hedge under conditions of uncertain volatility seems to be of considerable practical importance.

In addition it would be interesting if these ideas explained some features in the design of existing contracts.     

An extended maximin approach for decision analysis with uncontrollable factors

In this paper an extension to the maximin approach to decision analysis in the presence of uncontrollable factors is proposed. This extension is based on the assumption that probabilities of consequences are known. Using the language of stochastic dominance, one decision alternative is preferred to another if the cumulative distribution function of the first alternative dominates that of the second in some area of low value consequences. This approach is an extension of a standard lexicographic maximin procedure to a case in which decision alternatives are characterised by arbitrary, including continuous, sets of consequences. Applications of the suggested approach to an ‘attack–defence’ type game and to the problems of location of public facilities are discussed.     

Contextualism,art, and rigidity: Levinson,Currie and Davies

The topic of this paper is the role played by context in art. In this regard I examine three theories linked to the names of J. Levinson, G. Currie and D. Davies. Levinson’s arguments undermine the structural theory. He finds it objectionable because it makes the individuation of artworks independent of their histories. Secondly, such a consequence is unacceptable because it fails to recognise that works are created rather than discovered. But, if certain general features of provenance are always work-constitutive, as it seems that Levinson is willing to claim, these features must always be essential properties of works. On the other hand, consideration of our modal practice suggests that whether a given general feature of provenance is essential or non-essential depends upon the particular work in question or is “work relative”. D. Davies builds his performance theory on the basis of the critical evaluation of Currie’s action-type hypotheses (ATH). Performances, says Davies, are not to be identified with “basic actions” to which their times belong essentially, but with “doings” that permit of the sorts of variation in modal properties required by the work-relativity of modality. He is also a fierce critic of the contextualist account. Contextualism is in his view unable to reflect the fact that aspects of provenance bear upon our modal judgements with variable force.In the second part of the paper I consider Davies’s “modality principle”. Davies is inclined to defend the claim that labels used for designation of works are rigid designators. Such a view offers a ground for discussion about the historicity of art. What has been meant when people claim that art is an historical concept? I argue that any historical theory implies a two-dimensional notion of “art”. At the end of the paper I suggest that Davies should embrace the theory of contingent identity and not the colocationist view about the relationship that exists between a particular artwork and its physical bearer.     

Where do we stand on measures of uncertainty,ambiguity, fuzziness,and the like?

It is argued in this paper that the theory of fuzzy sets involves at least four fundamentally different types of uncertainty. Each of these types requires a measure by which the degree of uncertainty of that type can be determined.Two main categories of uncertainty are connected with the terms ‘vagueness’ (or ‘fuzziness’) and ‘ambiguity’. In general, vagueness is associated with the difficulty of making sharp or precise distinctions in the world. Ambiguity, on the other hand, is associated with one-to-many relations, i.e., situations with two or more alternatives that are left unspecified. While the concept of a fuzzy set represents a basic mathematical framework for dealing with vagueness, the concept of a fuzzy measure is a general framework for dealing with ambiguity.Several classes of measures of vagueness, usually referred to as measures of fuzziness, have been proposed in the literature. Each class is based on some underlying conception of the degree of fuzziness. A general set of requirements for measures of fuzziness is formulated, followed by an overview of the measures proposed in the literature.Measures of ambiguity are discussed within the framework of plausibility and belief measures. Although it does not cover all fuzzy measures, this framework is sufficiently broad for most practical purposes, and represents a generalization of both probability theory and possibility theory.It is argued that three complementary measures of ambiguity should be employed. One of them is obtained by generalizing the Hartley measure of uncertainty; it measures the degree of nonspecificity in individual situations described by the various belief and plausibility measures. The other two are obtained by generalizing the well known Shannon measure of uncertainty; they measure the degree of dissonance and the degree of confusion in evidence, respectively. Basic mathematical properties of these measures are overviewed.It is also argued that each of the four types of uncertainty measures, which are fundamentally different from each other, can be used for measuring structural (syntactic) information in the same sense as the Hartley and Shannon measures have been used in this respect. As such, these measures are potentially powerful tools for dealing with systems problems such as systems modelling, analysis, simplification, or design.     

A thirteenth century ‘proof’ of the parallel postulate

Proposition I.14 of Witelo's Perspectiva purports to provide a proof of the claim contained in Euclid's fifth postulate. The Latin text of the proposition is presented and translated into English; a commentary on the nature of the ‘proof’ is also provided.     

Content essentialism

The paper offers some preliminary and rather unsystematic reflections about the question: Do Beliefs Have Their Contents Essentially? The question looks like it ought to be important, yet it is rarely discussed. Maybe that’s because content essentialism, i.e., the view that beliefs do have their contents essentially, is simply too obviously and trivially true to deserve much discussion. I sketch a common-sense argument that might be taken to show that content essentialism is indeed utterly obvious and/or trivial. Somewhat against this, I then point out that a “sexy” conclusion that is sometimes drawn from Putnam-Burge-style externalist arguments, namely that our mental states are not in our heads, presupposes content essentialism — which suggests that the view is not entirely trivial. Moreover, it seems intuitively that physicalists should reject the view: If beliefs are physical states, how could they have their propositional contents essentially? I distinguish three readings of the title question. Content essentialism does seem fairly obvious on the first two, but not so on the third. I argue that the common-sense argument mentioned earlier presupposes one of the first two readings but fails to apply to the third, on which ‘belief’ refers to belief-state tokens. That’s because ordinary belief individuation is silent about belief-state tokens. Token physicalists, I suggest, should indeed reject content essentialism about belief-state tokens. What about token dualists? One might think they ought to embrace content essentialism about belief-state tokens. I end with puzzling why this should be so.     

The Problem of Emotional Significance

What does it mean to say that an emotional response fits the situation? This question cannot be answered simply by specifying the core relational theme (loss or risk, say) associated with each emotion: we must also explain what constitutes an emotionally significant loss or risk. It is sometimes suggested that emotionally significant situations are those that bear on the subject’s interests or concerns. I accept that this claim is plausible for some emotional responses, and I propose a particular way of interpreting it. I suggest that, for many emotions, emotional significance is determined by the subject’s likes and dislikes – that is, settled dispositions to find a certain situation pleasant or distressing. I contrast this account with other preference-based accounts and with an account that appeals to the subject’s interests. I argue that we should prefer the likes-based account to these rival views.