I am going to argue for a robust realism about magnitudes, as irreducible elements in our ontology. This realistic attitude, I will argue, gives a better metaphysics than the alternatives. It suggests some new options in the philosophy of science. It also provides the materials for a better account of the mind’s relation to the world, in particular its perceptual relations.

Natural properties are those that carve reality at the joints. The notion of carving reality at the joints, however, is somewhat obscure, and is often understood in terms of making for similarity, conferring causal powers, or figuring in the laws of nature. I develop and assess an account of the third sort according to which carving reality at the joints is understood as having the right level of determinacy relative to nomic roles. The account has the attraction of involving very (...) weak metaphysical presuppositions, but fails to capture several features that natural properties are presumed to have. (shrink)

Within the metaphysics of quantity, the debate rages between Absolutism and Comparativism. In retrospect, Armstrong appears to be an absolutist, for he claims that magnitudes like being 1 kg in mass are intrinsic properties of particulars, in virtue of which relations like being twice as massive as hold. More importantly, his theory is an instance of what I call ‘Radical Absolutism’, for he does not merely argue that relations are grounded in magnitudes, but also tries to explain how they “flow (...) from” the intrinsic features of magnitudes. The goal of the paper is not to support his theory, but to better understand why it fails, and why this must be of concern to contemporary absolutists. (shrink)

The philosophy of measurement studies the conceptual, ontological, epistemic, and technological conditions that make measurement possible and reliable. A new wave of philosophical scholarship has emerged in the last decade that emphasizes the material and historical dimensions of measurement and the relationships between measurement and theoretical modeling. This essay surveys these developments and contrasts them with earlier work on the semantics of quantity terms and the representational character of measurement. The conclusions highlight four characteristics of the emerging research program in (...) philosophy of measurement: it is epistemological, coherentist, practice oriented, and model based. (shrink)

When discrepancies are discovered between the outcomes of different measurement procedures, two sorts of explanation are open to scientists. Either some of the outcomes are inaccurate or the procedures are not measuring the same quantity. I argue that, due to the possibility of systematic error, the choice between and is underdetermined in principle by any possible evidence. Consequently, foundationalist criteria of quantity individuation are either empty or circular. I propose a coherentist, model-based account of measurement that avoids the underdetermination problem, (...) and use this account to explain how scientists individuate quantities in practice. (shrink)

Contrary to the claim that measurement standards are absolutely accurate by definition, I argue that unit definitions do not completely fix the referents of unit terms. Instead, idealized models play a crucial semantic role in coordinating the theoretical definition of a unit with its multiple concrete realizations. The accuracy of realizations is evaluated by comparing them to each other in light of their respective models. The epistemic credentials of this method are examined and illustrated through an analysis of the contemporary (...) standardization of time. I distinguish among five senses of ‘measurement accuracy’ and clarify how idealizations enable the assessment of accuracy in each sense. (shrink)

It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the (...) phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here. (shrink)

Physical theories often characterize their observables with real number precision. Many non-fundamental theories do so needlessly: they are more precise than they need to be to capture the physical matters of fact about their observables. A natural expectation is that a truly fundamental theory will require its full precision in order to exhaustively capture all of the fundamental physical matters of fact. I argue against this expectation and I show that we do not have good reason to expect that the (...) standard of precision set by successful theories, or even by a truly fundamental theory, will match the granularity of the physical facts. (shrink)

The thesis that numbers are ratios of quantities has recently been advanced by a number of philosophers. While adequate as a definition of the natural numbers, it is not clear that this view suffices for our understanding of the reals. These require continuous quantity and relative to any such quantity an infinite number of additive relations exist. Hence, for any two magnitudes of a continuous quantity there exists no unique ratio. This problem is overcome by defining ratios, and hence real (...) numbers, as binary relations between infinite standard sequences. This definition leads smoothly into a new definition of measurement consonant with the traditional view of measurement as the discovery or estimation of numerical relations. The traditional view is further strengthened by allowing that the additive relations internal to a quantity are distinct from relations observed in the behaviour of objects manifesting quantities. In this way the traditional theory can accommodate the theory of conjoint measurement. This is worth doing because the traditional theory has one great strength lacked by its rivals: measurement statements and quantitative laws are able to be understood literally. 1 This paper was completed in 1990-1. while the author was a visiting scholar at the Irvine Research Unit in Mathematical Behavioral Sciences. University of California. Irvine. The author wishes to thank the Director. Professor R. D. Luce, for the generous provision of space and facilities within the Unit and for his critical comments upon some of the ideas expressed herein: Professor L. Narens. for his trenchant criticisms: and the University of Sydney, for granting Special Study Leave and financial assistance to make the visit possible. (shrink)

The transition from the traditional to the representational theory of measurement around the turn of the century was accompanied by little sustained criticism of the former. The most forceful critique was Bertrand Russell''s 1897 Mind paper, On the relations of number and quantity. The traditional theory has it that real numbers unfold from the concept of continuous quantity. Russell''s critique identified two serious problems for this theory: (1) can magnitudes of a continuous quantity be defined without infinite regress; and (2) (...) can additive relations between such magnitudes exist if magnitudes are not divisible? The present paper shows how the traditional theory answers these questions and compares the traditional and representational theories as contributions to our understanding of the logic of application. (shrink)

Actualism is the doctrine that the only things there are, that have being in any sense, are the things that actually exist. In particular, actualism eschews possibilism, the doctrine that there are merely possible objects. It is widely held that one cannot both be an actualist and at the same time take possible world semantics seriously — that is, take it as the basis for a genuine theory of truth for modal languages, or look to it for insight into the (...) modal structure of reality. For possible world semantics, it is supposed, commits one to possibilism. In this paper I take issue with this view. To the contrary, I argue that one can take possible world semantics seriously without any commitment to possible worlds or possibilism and hence remain in full compliance with actualist scruples. Moreover, one can do so without without invoking either "ersatz" worlds or haecceities. (shrink)

Are concrete objects in some sense made up of the properties they exemplify? A distinguished tradition holds they are. I begin by defending the distinction: there is a real and not just semantic distinction between asserting and denying that concrete objects have their properties as parts. I then argue in favor of the view that concrete objects are not made up of their parts. First, this view has less ontological baggage than its opponent. Next, the supposed advantages of the alternative (...) view—its superiority in understanding persistence, exemplification, or the possibility of diverse duplicates—dissipate under analysis. (shrink)

Quantities like mass and temperature are properties that come in degrees. And those degrees (e.g. 5 kg) are properties that are called the magnitudes of the quantities. Some philosophers (e.g., Byrne 2003; Byrne & Hilbert 2003; Schroer 2010) talk about magnitudes of phenomenal qualities as if some of our phenomenal qualities are quantities. The goal of this essay is to explore the anti-physicalist implication of this apparently innocent way of conceptualizing phenomenal quantities. I will first argue for a metaphysical thesis (...) about the nature of magnitudes based on Yablo’s proportionality requirement of causation. Then, I will show that, if some phenomenal qualities are indeed quantities, there can be no demonstrative concepts about some of our phenomenal feelings. That presents a significant restriction on the way physicalists can account for the epistemic gap between the phenomenal and the physical. I’ll illustrate the restriction by showing how that rules out a popular physicalist response to the Knowledge Argument. (shrink)

Several prominent ethical philosophers have attempted to demonstrate that there exist instances or types of value that are of crucial moral significance but which cannot legitimately be compared with one another. Bernard Williams and Michael Stocker, for example, argue that it can sometimes be rational to regret having chosen the all-things-considered better of two alternatives, and that this sense of regret entails that the goodness of the worse option is not made up for by and is therefore incommensurable with that (...) of the better. Joseph Raz and others have made similar points. In this paper, I propose a theory of value that is monistic in that it countenances just one sort of morally crucial value, but pluralistic in that several distinct properties bearer this value. I then explain how this view avoids incommensurable values without doing violence to the core intuitions that seemed to necessitate them, and how it fits into a larger conception of morality, right conduct, and moral psychology. (shrink)

The relation between two systems of attitude ascription that capture all the empirically significant aspects of an agents thought and speech may be analogous to that between two systems of magnitude ascription that are equivalent relative to a transformation of scale. If so, just as an objects weighing eight pounds doesnt relate that object to the number eight (for a different but equally good scale would use a different number), similarly an agents believing that P need not relate her to (...) P (for a different but equally adequate interpretive scheme could use a different proposition). In either case the only reality picked out by any system of ascription is what is common to all equivalent rivals. By emphasizing some contrasts between decision theory and belief-desire psychology, it is argued that if attitude ascription is appropriately analogous to measurement then not only is being related to a proposition an artifact of the system of representation chosen, so are belief and desire. (shrink)

Recently, there has been a revival in taking empirical magnitudes seriously. Weights, heights, velocities and the like have been accepted as abstract entities in their own right rather than just equivalence classes of objects. The aim of my paper is to show that this revival should include value magnitudes. If we posit such magnitudes, important value comparisons can be easily explained; it becomes easier to satisfy the axioms for measurement of value; goodness, badness, and neutrality can be given univocal definitions; (...) value aggregation can be given a non-mathematical understanding which allows for Moorean organic unities. Of course, this does not come for free. One has to accept a rich ontology of abstract value magnitudes, but, to quote David Lewis, ‘The price is right; the benefits in theoretical unity and economy are well worth the entities.’. (shrink)

A number of issues connected with the nature of applied mathematics are discussed. Among the claims are these: mathematics "hooks onto" the world by providing models or representations, not by describing the world; classic platonism is to be preferred to structuralism; and several issues in the philosophy of science are intimately connected to the nature of applied mathematics.

The article advances a new way of thinking about classifications in general and the classification of mental disorders in particular. By applying insights from measurement practice to the context of classification, I defend a notion of epistemic accuracy that allows one to evaluate and improve classifications by comparing different classifying methods to each other. Progress in classification arises from the mutual development of classification systems and classifying methods. Based on this notion of accuracy, the article illustrates with an example how (...) psychiatric classifications can be improved via circumscribed comparisons of different perspectives on mental disorders, without relying on complete models of their complex aetiology. When applying this strategy, the traditional opposition between symptom-based and causal approaches is of little consequence for making progress in the epistemic accuracy of psychiatric classification. (shrink)

Since the publication of David Lewis's ''New Work for a Theory of Universals,'' the distinction between properties that are fundamental – or perfectly natural – and those that are not has become a staple of mainstream metaphysics. Plausible candidates for perfect naturalness include the quantitative properties posited by fundamental physics. This paper argues for two claims: (1) the most satisfying account of quantitative properties employs higher-order relations, and (2) these relations must be perfectly natural, for otherwise the perfectly natural properties (...) cannot play the roles in metaphysical theorizing as envisaged by Lewis. (shrink)

2020 update of the entry "Properties".

This work develops an epistemology of measurement, that is, an account of the conditions under which measurement and standardization methods produce knowledge as well as the nature, scope, and limits of this knowledge. I focus on three questions: (i) how is it possible to tell whether an instrument measures the quantity it is intended to? (ii) what do claims to measurement accuracy amount to, and how might such claims be justified? (iii) when is disagreement among instruments a sign of error, (...) and when does it imply that instruments measure different quantities? Based on a series of case studies conducted in collaboration with the US National Institute of Standards and Technology (NIST), I argue for a model-based approach to the epistemology of physical measurement. To measure a physical quantity, I argue, is to estimate the value of a parameter in an idealized model of a physical process. Such estimation involves inference from the final state (‘indication’) of a process to the value range of a parameter (‘outcome’) in light of theoretical and statistical assumptions. Contrary to contemporary philosophical views, measurement outcomes cannot be obtained by mapping the structure of indications. Instead, measurement outcomes as well as claims to accuracy, error and quantity individuation can only be adjudicated relative to a choice of idealized modelling assumptions. (shrink)

The topic of my dissertation is the hedonic calculus. The hedonic calculus presupposes that pleasure and pain come in amounts amenable to addition, subtraction, and aggregation operations. These operations are ones that utilitarianism and related normative ethical theories treat as central to moral phenomena. The first chapter is an introduction to the problem--in it, I explain what the hedonic calculus is, why it is important, and why it has recently come under disfavor. The second chapter explores the nature of hedonic (...) phenomena, arguing that pleasure and pain are propositional attitudes; they are not feelings or feeling-tones, nor are they fundamentally a matter of desire or motivation. The third and fourth chapters concern the nature of quantitative phenomena. I argue that quantities are determinate properties whose determinables enter into greater-than, less-than, or equal-to relationships that are homomorphic with the structure of the real number line. These structures include the presence of a unique order; the possibility of equal intervals; and a natural, non-arbitrary zero point. The fifth chapter is a defense of the thesis that there are exactly three relations of quantitative comparison from a recent attack. I argue that apparent instances of being on a par are in fact instances of vagueness or complexity and do not threaten the truth of the trichotomy thesis. The sixth chapter addresses arguments that pleasure and pain fail to meet these formal conditions. One argument stems from the observation that pleasures and pains are essentially transient and ephemeral. Another argument proceeds from the observation that interpersonal comparisons of pleasure and pain appear to be impossible. A third, closely related to the first two, argues that pleasure and pain are too heterogeneous to be quantitative. A final argument holds that, for a variety of reasons, the various mathematical operations constitutive of quantitativeness are not applicable to pleasure or pain. I argue that each argument suffers from at least one fatal flaw. Some arguments crucially involve a failure to distinguish between the existence of a quantity and our ability to perform reliable measurements of it. Others involve false analogies between hedonic and other sorts of phenomena. The seventh chapter addresses arguments in favor of the legitimacy of the calculus. Many philosophers, such as Bentham, Mill, Ross, and Plato, seem to assume, without any serious argument, that pleasure and pain are quantitative. Others attempt to argue that, for example, two people enjoying something must involve more pleasure than if just one person were enjoying it. A third type of argument rests on the claim that it is sometimes rational to be indifferent between a longer lasting, less intense episode of pleasure and a more intense but shorter episode. This suggests that since duration is clearly quantitative, intensity must be, too, because if it were not, there could be no equivalence between the brief but intense and the lengthy but mellow episodes. Several of these arguments are unsound or question-begging. Finally, I present an argument in favor of the hedonic calculus that I endorse, along with possible objections and my replies. I begin by acknowledging the central point of the "hedonic trade-offs" argument, and then proceed, via reductio, by pointing out the various absurd or unpalatable consequences of the denial of the thesis that pleasure and pain are quantitative. (shrink)

Paper responding to critique of Maurin (2002) presented by Herbert Hochberg in his “Relations, Properties and Particulars” (2004).