Commitment to sparseness amounts to the idea that there is an objective, worldly privileging of certain properties over others that makes the privileged properties suited to play certain roles, and is responsible for their playing such roles. In this chapter I offer a brief, opinionated overview of sparseness. I begin by examining a set of problems that I call “problems of abundance”, which generate canonical motivations for sparseness. I then survey some influential approaches to sparseness and (...) the roles that they attribute to sparse properties, noting that on most approaches sparse properties are deeply connected to inquiry. Finally I consider some problems for sparseness, focusing on the purported connections between sparseness and inquiry, particularly in philosophy of science and inquiry into the social world. (shrink)

In the past fifteen years or so there has been a lot of attention paid to theories of “sparse” universals, particularly because of the work of D. M. Armstrong. These theories are of particular interest to those of us concerned with the distinction between natural and non-natural properties, since, as David Lewis has observed, it seems possible to analyze naturalness in terms of sparse universals. Moreover, Armstrong claims that we should conceive of universals as being “immanent” as opposed to “transcendent”, (...) and if universals are immanent then, as we will see, there is pressure to admit they are sparse as well. But I will argue that neither of these alleged reasons to accept a sparse conception of universals succeeds: the outlook for a fully general analysis of naturalness in terms of universals is not good, and the apparent advantages of immanence over transcendence are illusory. (shrink)

Commitment to sparseness amounts to the idea that there is an objective, worldly privileging of certain properties over others that makes the privileged properties suited to play certain roles, and is responsible for their playing such roles. In this chapter I offer a brief, opinionated overview of sparseness. I begin by examining a set of problems that I call “problems of abundance”, which generate canonical motivations for sparseness. I then survey some influential approaches to sparseness and (...) the roles that they attribute to sparse properties, noting that on most approaches sparse properties are deeply connected to inquiry. Finally I consider some problems for sparseness, focusing on the purported connections between sparseness and inquiry, particularly in philosophy of science and inquiry into the social world. (shrink)

Answers are given to two questions concerning the existence of some sparse subsets of $\mathscr{H} = \{0, 1,..., H - 1\} \subseteq * \mathbb{N}$ , where H is a hyperfinite integer. In § 1, we answer a question of Kanovei by showing that for a given cut U in H, there exists a countably determined set $X \subseteq \mathscr{H}$ which contains exactly one element in each U-monad, if and only if U = a · N for some $a \in \mathscr{H} (...) \backslash \{0\}$ . In §2, we deal with a question of Keisler and Leth in [6]. We show that there is a cut $V \subseteq \mathscr{H}$ such that for any cut U, (i) there exists a U-discrete set $X \subseteq \mathscr{H}$ with X + X = H (mod H) provided $U \subsetneqq V$ , (ii) there does not exist any U-discrete set $X \subseteq \mathscr{H}$ with X + X = H (mod H) provided $\supsetneqq V$ . We obtain some partial results for the case U = V. (shrink)

Sparse languages play an important role in classical structural complexity theory. In this paper we introduce a natural definition of sparse problems for parameterized complexity theory. We prove an analog of Mahaney's theorem: there is no sparse parameterized problem which is hard for the tth level of the W hierarchy, unless the W hierarchy itself collapses up to level t. The main result is proved for the most general form of parametric many:1 reducibility, where the parameter functions are not assumed (...) to be recursive. This provides one of the few instances in parameterized complexity theory of a full analog of a major classical theorem. The proof involves not only the standard technique of left sets, but also substantial circuit combinatorics to deal with the problem of small weft, and a diagonalization to cope with potentially nonrecursive parameter functions. The latter techniques are potentially of interest for further explorations of parameterized complexity analogs of classical structural results. (shrink)

Are the sparse properties drawn from all the levels of nature, or only the fundamental level? I discuss the notion of sparse property found in Armstrong and Lewis, show that there are tensions in the roles they have assigned the sparse properties, and argue that the sparse properties should be drawn from all the levels of nature.

Four dimensionalism, the thesis that persisting objects are four dimensional and thus extended in time as well as space, has become a serious contender as an account of persistence. While many four dimensionalists are mereological universalists, there are those who find mereological universalism both counterintuitive and ontologically profligate. It would be nice then, if there was a coherent and plausible version of four dimensionalism that was non-universalist in nature. I argue that unfortunately there is not. By its very nature four (...) dimensionalism embraces theses about the nature of objects and their borders that make any version of non-universalist four dimensionalism either incoherent or at least highly implausible. (shrink)

Zombies are bodies without minds: creatures that are physically identical to actual human beings, but which have no conscious experience. Much of the consciousness literature focuses on considering how threatening philosophical reflection on such creatures is to physicalism. There is not much attention given to the converse possibility, the possibility of minds without bodies, that is, creatures who are conscious but whose nature is exhausted by their being conscious. We can call such a ‘purely conscious’ creature a ghost.

This paper attacks two contrary views. One denies that nature has joints, taking the properties we call natural to be merely artefacts of our theories. The other accepts real natural properties but takes their naturalness to come by degrees. I argue that both are wrong: natural properties are real, and their naturalness no more comes by degrees than does the naturalness of the things that havethem.

David Lewis is typically interpreted as a class nominalist. One consequence of class nominalism, which he embraced, is that the reduction of ordered pairs, triples, etc to unordered sets of sets is conventional. The reaction by his Australian counterparts D.M. Armstrong and Peter Forrest was that Lewis was not being ontologically serious. This chapter evaluates this debate over serious ontology. It is argued that in one sense Lewis is ontologically serious, but that his additional commitment to structuralism about classes should (...) push him to adopt a trope-theoretic account of naturalness, which opens up another way to respond to the charge of not doing serious ontology. This conclusion is supported by certain remarks he makes in his correspondence, thus revealing how his thinking about properties appears to have evolved from property-egalitarianism to a sparse theory of tropes. (shrink)

Dispositional essentialism maintains that all sparse properties are essentially powerful. Two conceptions of sparse properties appear compatible with dispositional essentialism: sparse properties as pure powers or as powerful qualities. This paper compares the two views, criticizes the powerful qualities view, and then develops a new theory of pure powers, termed Point Theory. This theory neutralizes the main advantage powerful qualities appear to possess over pure powers—explaining the existence of powers during latency periods. The paper discusses the relation between powers and (...) space-time points, whether pure powers need to occupy space, and how to account for the movement of pure powers through space-time. Given Point Theory, dispositional essentialists should maintain that sparse properties are pure powers. (shrink)

Natural kind terms appear to behave like singular terms. If they were genuine singular terms, appearing in true sentences, that would be some reason to believe that there are entities to which the terms refer, the natural kinds. Paul Needham has attacked my arguments that natural kind terms are singular, referring expressions. While conceding the correctness of some of his criticisms, I defend and expand on the underlying view in this paper. I also briefly sketch an account of what natural (...) kinds in fact are—natural complexes of sparse (natural) universals. (shrink)

According to sparse modalism, the notion of essence can be analysed in terms of necessity and naturalness. In this paper, I develop and defend a version of sparse modalism that is equipped with a non-standard, relativized conception of naturalness. According to this conception, properties and relations can be natural to different degrees relative to different kinds of things, and relations can be natural to different degrees relative to different slots. I argue that this relativized version of sparse modalism can accommodate (...) various cases that the standard, non-relativized version can’t. The alternative version can accommodate cases where a relation is essential to a relatum but merely necessary to another, cases where a property is essential to an object but merely necessary to another, and cases where a less-than-perfectly natural property is essential to an object. (shrink)

A fundamental question in visual neuroscience is: Why are the response properties of visual neurons as they are? A modern approach to this problem emphasizes the importance of adaptation to ecologically valid input, and it proceeds by modeling statistical regularities in ecologically valid visual input (natural images). A seminal model was linear sparse coding, which is equivalent to independent component analysis (ICA), and provided a very good description of the receptive fields of simple cells. Further models based on modeling residual (...) dependencies of the ‘‘independent” components have later been introduced. These models lead to emergence of further properties of visual neurons: the complex cell receptive fields, the spatial organization of the cells, and some surround suppression and Gestalt effects. So far, these models have concentrated on the response properties of neurons, but they hold great potential to model various forms of inference and learning. (shrink)

Among those who posit properties, liberals (mostly nominalists) admit abundant, ontologically free properties, which particulars possess whenever they satisfy the same predicate and belong to the same class, however artificial. I call them “L-properties” (for “Liberal”). Some liberals also admit that some few L-properties are natural, while most of them are artificial (the same applies to the corresponding classes). Others (mostly but not only realists) commit to a more discriminating use of the category: properties are sparse, they make for the (...) objective similarities among particulars, and more importantly, they allow to analyze “objective similarity” and “class naturalness” in terms of property-possessing and sharing. They give particulars their “true nature”, and I call them “A-properties” (for “Analytical”). This article provides a defense of this second type of properties, in the particular case of sortals. To that end, a new fact is put forward: that sorts are classes which are natural not as a primitive feature, but in virtue of what the particulars which belong to them are, and which makes them _naturally belong_ to them. I then argue that this fact entails the existence of the desired type of properties, “sortal A-properties”, although leaving open the question of how they should be construed. (shrink)

This article analyses the different connotations of “normality” and “being natural,” bringing together the theoretical discussion from both human medicine and veterinary medicine. We show how the interpretations of the concepts in the different areas could be mutually fruitful. It appears that the conceptions of “natural” are more elaborate in veterinary medicine, and can be of value to human medicine. In particular they can nuance and correct conceptions of nature in human medicine that may be too idealistic. Correspondingly, the wide (...) ranging conceptions of “normal” in human medicine may enrich conceptions in veterinary medicine, where the discussions seem to be sparse. We do not argue that conceptions from veterinary medicine should be used in human medicine and vice versa, but only that it could be done and that it may well be fruitful. Moreover, there are overlaps between some notions of normal and natural, and further conceptual analysis on this overlap is needed. (shrink)

The conduct of hostilities is very bad for the environment, yet relatively little attention has been focused on environmental military ethics by just war theorists and revisionist philosophers of war. Contemporary ecological concerns pose significant challenges to jus in bello. I begin by briefly surveying existing literature on environmental justice during wartime. While these jus in bello environmental issues have been addressed only sparsely by just war theorists, environmental jus ad bellum has rarely been tackled within JWT or the morality (...) of war. In line with the theme of this special issue, I focus my discussion of war and the natural environment primarily on the jus ad bellum level. I set out with the presumption against the use of force, and its possible exceptions. The principal question raised is whether environmental harm can trigger a new justification for war. Beyond just cause, I consider what might be a proportionate response to “environmental aggression,” or negligent harm to nature. The use of force is clearly justified in response to military attacks, against the natural environment or otherwise. Where harm to nature or its inhabitants are not caused by military aggression, just war theory criteria point in favor of responding via measures short of war. Finally, I suggest that responding by means that are not themselves harmful to nature serves to fulfill the further jus ad bellum criterion of “right intention.”. (shrink)

For all of his failures to secure patronage, John Dee was successful compared with his contemporaries. We know more about his patronage relations than those of any other natural philosopher in Tudor England. Only by comparing him with other English client practitioners can we understand how unusual and even productive were Dee’s relations with his patrons. This article makes those comparisons and offers an overview of Dee’s patronage, but in the main it explores three of the unusual aspects.The first is (...) Dee’s good relationship with female patrons and patronage brokers, notably Queen Elizabeth. The second is the kind of office that Dee sought. His greatest efforts were aimed at securing the headship of a collegiate institution such as Eton College or the Hospital of St Cross. Not only did they fit his aspiration to set up a research institute, but all were offices in the Queen’s direct gift, and so played to Dee’s strengths. Nevertheless, Dee was frustrated at nearly every turn. It is suggested that a major cause was the young Dee’s links with both Sir John Cheke’s network of Protestant humanists, who became Marian exiles, and with ‘Louvainist’ Catholic exiles opposed to Edward VI and Elizabeth. We see how Dee was consistently passed over in favour of other members of these circles. Notwithstanding this, it is concluded that Dee was relatively successful, given the English court’s refusal to patronise speculative natural philosophy, even that offered by Thomas Digges, William Gilbert or Francis Bacon. Finally, some of Dee’s supposed failings as a client, such as the sparseness of printed works, are shown to have been systemic. (shrink)

Many human languages have complex grammatical machinery devoted to temporality, but very little is known about how this came about. This paper investigates how people convey temporal information when they cannot use any conventional languages they know. In a laboratory experiment, adult participants were asked to convey information about simple events taking place at a given time, in spoken language and in silent gesture. It was shown that in spoken language, participants formed utterances according to the rules of their native (...) language, but in silent gesture, the temporal information was presented initially, and structurally separately, from the other information in the utterance. The experimental results are consistent with findings from natural systems emerging in situations of communicative stress: unsupervised adult second language learning and homesign. This confirms that presenting temporal information separately and initially is a robust strategy to talk about past and future when only sparse communicative means are available. (shrink)

The authors explicate Aquinas's conception of mathematics. They show that in his work the Aristotelian conception is prevalent, according to which this discipline is—together with physics and metaphysics—a theoretical science, whose subject is the study of real quantity and its necessary properties. But, alongside this dominant and prevalent conception, Aquinas's work contains a number of indications that cast doubt. These sparse and rather marginal reflections lead the authors to conclude that Aquinas's texts contain a "constructivist" conception of mathematics in rudimentary (...) form. According to this approach, mathematics is not a theoretical science examining real quantity but, rather, a special kind of "art" by means of which mathematical objects are "created." From a constructivist point of view the authors then attempt to formulate a conception of mathematics that would accord with the basic Aristotelian assumptions of Aquinas's thought. (shrink)