We classify the asymptotic densities of the sets according to their level in the Ershov hierarchy. In particular, it is shown that for, a real is the density of an n‐c.e. set if and only if it is a difference of left‐ reals. Further, we show that the densities of the ω‐c.e. sets coincide with the densities of the sets, and there are ω‐c.e. sets whose density is not the density of an n‐c.e. set for any.

We prove uniformly computable versions of the Implicit Function Theorem in its differentiable and non-differentiable forms. We show that the resulting operators are not computable if information about some of the partial derivatives of the implicitly defining function is omitted. Finally, as a corollary, we obtain a uniformly computable Inverse Function Theorem, first proven by M. Ziegler.

Sufficient conditions are given for the computation of an arc that accesses a point on the boundary of an open subset of the plane from a point within the set. The existence of a not-computably-accessible but computable point on a computably compact arc is also demonstrated.

We use the compactness theorem of continuous logic to give a new proof that $$L^r([0,1]; {\mathbb {R}})$$ isometrically embeds into $$L^p([0,1]; {\mathbb {R}})$$ whenever $$1 \le p \le r \le 2$$. We will also give a proof for the complex case. This will involve a new characterization of complex $$L^p$$ spaces based on Banach lattices.

We show that any partial order with a Σ3 enumeration can be effectively embedded into any partial order obtained by imposing a strong reducibility such as ≤tt on the c. e. sets. As a consequence, we obtain that the partial orders that result from imposing a strong reducibility on the sets in a level of the Ershov hiearchy below ω + 1 are co-embeddable.

Let equation image. We show that for many reducibilities, the requirement that a relation be intrinsically reducible to the α-th jump of a countable mode A has a syntactic equivalent. Furthermore, we show that many reducibilities coincide in such a situation.

We study the following classes: Q* (r 1 A 1 ,..., r kA k ) which is defined to be the collection of all sets that can be computed by a Turing machine that on any input makes a total of r i queries to A i for all i ∈ {1,..., k}. Q(r 1A 1 ,...,r kA k ) which is defined like Q* (r 1A 1 ,..., r kA k ) except that queries to A i must be (...) made before queries to A i+1 for all i ∈ {1,..., k - 1}. QC(r 1A 1 ,..., r kA k ) which is defined like Q(r 1A 1 ,..., r kA k ) except that the Turing machine must halt even if given incorrect answers to some of its queries. We show that if A 1 ,..., A k are jumps that are not too close together, then all three of these classes are identical and are not changed if we permute (r 1A 1 ,..., r kA k ). This extends a result of Beigel's [1]. Since the second class is not affected by permutations, we say that these sets commute with each other. We also show that jumps that are too close together may not commute. We also characterize the commutative sequences of sets obtained by iterating the jump operation through an ordinal notation. (shrink)

Call a set A n-correctable if every set Turing reducible to A via a Turing machine that on any input makes at most n queries is Turing reducible to A via a Turing machine that on any input makes at most n-queries and on any input halts no matter what answers are given to its queries. We show that if a c.e. set A is n-correctable for some n ≥ 2, then it is n-correctable for all n. We show that (...) this is the optimal such result by constructing a c.e. set that is 1-correctable but not 2-correctable. The former result is obtained by examining the logical closure properties of c.e. sets that are 2-correctable. (shrink)

The theory of inner functions plays an important role in the study of bounded analytic functions. Inner functions are also useful in applied mathematics. Two foundational results in this theory are Frostman's Theorem and the Factorization Theorem. We prove a uniformly computable version of Frostman's Theorem. We then show that the Factorization Theorem is not uniformly computably true. We then show that for an inner function u with infinitely many zeros, the Blaschke sum of u provides the exact amount of (...) information necessary to compute the factorization of u. Along the way, we prove some uniform computability results for Blaschke products; these results play a key role in the analysis of factorization. We also give some computability results concerning zeros and singularities of analytic functions. We use Type-Two Effectivity as our foundation. (shrink)

Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.

We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric structure. As the truth value of a sentence of continuous logic may be any real in [0, 1], we introduce two kinds of diagrams at each level: the closed diagram, which encapsulates weak inequalities of the form $$\phi ^\mathcal {M}\le r$$, and the open diagram, which encapsulates strict inequalities of the form $$\phi ^\mathcal {M}< r$$. We show (...) that the closed and open $$\Sigma _N$$ diagrams are $$\Pi ^0_{N+1}$$ and $$\Sigma ^0_N$$ respectively, and that the closed and open $$\Pi _N$$ diagrams are $$\Pi ^0_N$$ and $$\Sigma ^0_{N + 1}$$ respectively. We then introduce effective infinitary formulas of continuous logic and extend our results to the hyperarithmetical hierarchy. Finally, we demonstrate that our results are optimal. (shrink)

Suppose \ is a computable real. We extend previous work of Clanin, Stull, and McNicholl by determining the degrees of categoricity of the separable \ spaces whose underlying measure spaces are atomic but not purely atomic. In addition, we ascertain the complexity of associated projection maps.

We examine the reverse mathematics and computability theory of a form of Ramsey's theorem in which the linear n-tuples of a binary tree are colored.

BackgroundIt is commonly reported by editors that it has become harder to recruit reviewers for peer review and that this is because individuals are being asked to review too often and are experiencing reviewer fatigue. However, evidence supporting these arguments is largely anecdotal.Main bodyWe examine responses of individuals to review invitations for six journals in ecology and evolution. The proportion of invitations that lead to a submitted review has been decreasing steadily over 13 years (2003–2015) for four of the six (...) journals examined, with a cumulative effect that has been quite substantial (average decline from 56% of review invitations generating a review in 2003 to just 37% in 2015). The likelihood that an invitee agrees to review declines significantly with the number of invitations they receive in a year. However, the average number of invitations being sent to prospective reviewers and the proportion of individuals being invited more than once per year has not changed much over these 13 years, despite substantial increases in the total number of review invitations being sent by these journals—the reviewer base has expanded concomitant with this growth in review requests.ConclusionsThe proportion of review invitations that lead to a review being submitted has been declining steadily for four of the six journals examined here, but reviewer fatigue is not likely the primary explanation for this decline. (shrink)

Comparative philosophy is dependent upon translation, often translations that will help preserve some fundamental commitments: to linguistic mastery, to the recovery or preservation of an original, and to the protection of an authenticity that will ground these commitments. Such a view can sometimes obscure a nostalgia for questionable causes. Comparative philosophy, especially with continental affinities, often relies on two moves: first, a boundary must be found (or produced) between philosophy itself and other forms of writing (literature or fiction, say), to (...) ensure proper grounding. Second, it must be understood that this boundary depends upon an underlying philosophy of language: language speaks us, it speaks Being; to dwell in a different language is to dwell in a different house of being (Martin Heidegger). But how might this project – its historiography of return and grounding, and its mythologizing of linguistic and ontological recovery – be challenged by the very practice of translation itself? Perhaps this challenge is one of translation’s philosophical benefits. (shrink)

BackgroundThere is concern in the academic publishing community that it is becoming more difficult to secure reviews for peer-reviewed manuscripts, but much of this concern stems from anecdotal and rhetorical evidence.MethodsWe examined the proportion of review requests that led to a completed review over a 6-year period (2009–2015) in a mid-tier biology journal (Molecular Ecology). We also re-analyzed previously published data from four other mid-tier ecology journals (Functional Ecology, Journal of Ecology, Journal of Animal Ecology, and Journal of Applied Ecology), (...) looking at the same proportion over the period 2003 to 2010.ResultsThe data from Molecular Ecology showed no significant decrease through time in the proportion of requests that led to a review (proportion in 2009 = 0.47 (95 % CI = 0.43 to 0.52), proportion in 2015 = 0.44 (95 % CI = 0.40 to 0.48)). This proportion did decrease for three of the other ecology journals (changes in proportions from 2003 to 2010 = −0.10, −0.18, and −0.09), while the proportion for the fourth (Functional Ecology) stayed roughly constant (change in proportion = −0.04).ConclusionsOverall, our data suggest that reviewer agreement rates have probably declined slightly but not to the extent suggested by the anecdotal and rhetorical evidence. (shrink)

We draw a distinction between the Aharonov–Bohm phase shift and the Aharonov–Bohm effect. Although the Aharonov–Bohm phase shift occurring when an electron beam passes around a magnetic solenoid is well-verified experimentally, it is not clear whether this phase shift occurs because of classical forces or because of a topological effect occurring in the absence of classical forces as claimed by Aharonov and Bohm. The mathematics of the Schroedinger equation itself does not reveal the physical basis for the effect. However, the (...) experimentally observed Aharonov–Bohm phase shift is of the same form as the shift observed due to electrostatic forces for which the consensus view accepts the role of the classical forces. The Aharonov–Bohm phase shift may well arise from classical electromagnetic forces which are simply more subtle in the magnetic case since they involve relativistic effects of the order v 2 /c 2 . Here we first review the experimentally observable differences between phenomena arising from classical forces and phenomena arising from the quantum topological effect suggested by Aharonov and Bohm. Second we point out that most discussions of the classical electromagnetic forces involved when a charged particle passes a solenoid are inaccurate because they omit the Faraday induction terms. The subtleties of the relativisitic v 2 /c 2 classical electromagnetic forces between a point charge and a solenoid have been explored by Coleman and Van Vleck in their analysis of the Shockley–James paradox; indeed, we point out that an analysis exactly parallel to that of Coleman and Van Vleck suggests that the Aharonov–Bohm phase shift is actually due to classical electromagnetic forces. Finally we note that electromagnetic velocity fields penetrate even excellent conductors in a form which is unfamiliar to many physicists. An ohmic conductor surrounding a solenoid does not screen out the magnetic field of the passing charge, but rather the time-integral of the magnetic field is an invariant; this time integral is precisely what is involved in the classical explanation of the Aharonov–Bohm phase shift. Thus the persistence of the Aharonov–Bohm phase shift when the solenoid is surrounded by a conductor does not exclude a classical force-based explanation for the phase shift. At present there is no experimental evidence for the Aharonov–Bohm effect. (shrink)

Although there is good experimental evidence for the Aharonov–Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v 2 /c 2 analogous to those discussed by Coleman and Van Vleck in their treatment of the Shockley–James paradox. In this article we show that a treatment (...) exactly analogous to that given by Coleman and Van Vleck predicts classical electromagnetic forces which provide the basis for the Aharonov–Bohm phase shift. The magnetic force on the solenoid due to the passing charge leads to a displacement of the solenoid center of energy which must be balanced by the displacement of the passing charge. This classical displacement of the passing charge is exactly what is required to account for the Aharonov–Bohm phase shift. Also, we discuss a magnetic moment model which appears frequently in the literature and note that although the model provides conservation of linear momentum, it does not satisfy the general requirements for relativistic theories. We give an example suggesting that the new equation of motion for a magnetic moment proposed by Aharonov, Pearle, and Vaidman based upon the hidden momentum of the magnetic moment is completely inappropriate. Finally, we emphasize that the Aharonov–Casher phase shift is also explained by classical electromagnetic forces exactly parallel to those explaining the Aharonov–Bohm phase shift. (shrink)

There is substantial controversy about the nature of both particulars and properties. Some philosophers think that the categories of particular and property are fundamental, that at least some of the things in both are in no way derived from or dependent on things in another category. These philosophers are Realists about both particulars and properties. Nominalists think of particulars as fundamental and of properties as non‐fundamental, with the latter being derived from the former. This chapter explores why someone might go (...) in for Realism about properties. If one insists that universals are just properties that could be exemplified by more than one thing, Class and Resemblance Nominalism turn out to be committed to universals. Ostrich Nominalism is much larger qualitatively, since UP‐Realism has only two fundamental kinds, whereas Ostrich Nominalism has n fundamental kinds. Ostrich Nominalists must posit a very large number of metaphysically fundamental sorts of things: spheres, cubes, blue things, red things, etc. (shrink)

At present classical physics contains two contradictory groups of derivations of the equilibrium spectrum of random classical electromagnetic radiation. One group of derivations finds Planck's spectrum based upon the use of classical electromagnetic zero-point radiation and fundamental ideas of thermodynamics. The other group of derivations finds the Rayleigh-Jeans spectrum from scattering equilibrium for non-linear mechanical systems in the limit of small charge coupling to radiation. Here we examine the scaling symmetries of classical thermal radiation. We find that, in general, classical (...) mechanical systems do not share the scaling symmetries of thermal radiation. In particular, this is true for the mechanical scattering systems used in the derivations of the Rayleigh-Jeans law. Indeed, relativistic hydrogenlike systems with Coulomb potentials of fixed charge are the only mechanical potential systems which do share the scaling symmetries of thermal radiation. We propose that only these last mechanical systems are allowed in a classical electromagnetic description of nature. (shrink)

Classical electromagnetic forces can account for the experimentally observed phase shifts seen in an electron interference pattern when a line of electric dipoles or a line of magnetic dipoles (a solenoid) is placed between the electron beams forming the interference pattern.

The two-point correlation functions of classical electromagnetic zero-point radiation fields are evaluated in four-vector notation. The manifestly Lorentz-covariant expressions are then shown to be invariant under scale transformations and under the conformal transformations of Bateman and Cunningham. As a preliminary to the electromagnetic work, analogous results are obtained for a scalar Gaussian random classical field with a Lorentz-invariant spectrum.

Recent experiments undertaken by Caprez, Barwick, and Batelaan should clarify the connections between classical and quantum theories in connection with the Aharonov–Bohm phase shift. It is pointed out that resistive aspects for the solenoid current carriers play a role in the classical but not the quantum analysis for the phase shift. The observed absence of a classical lag effect for a macroscopic solenoid does not yet rule out the possibility of a lag explanation of the observed phase shift for a (...) microscopic solenoid. (shrink)

This chapter focuses on two clusters of questions concerning existence. The first cluster concerns the scope of existence, examining how wide the domain of existing things is and whether it encompass absolutely everything. The second cluster concerns vagueness and indeterminacy, explaining whether vague things and vague categories of things are there or all vagueness is a matter of referring indifferently to a large number of absolutely precise things and showing the ultimate source of vagueness. There are two theories of vagueness, (...) epistemic and metaphysical. The chapter focuses on Meinongian definitions of 'existence' and examines four arguments in favor of Anti‐Actualism. The first and second respectively appeals to common sense and the need for intentional objects, that is, objects of certain mental attitudes. The third appeals to the need for fictional and illusory entities. And the fourth appeals to the need for non‐existent things as constituents of certain merely possible situations. (shrink)

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell’s equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation (...) and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics. (shrink)

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. (...) Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example. (shrink)

Most Chinese religious practice and belief in times past, and even throughout much of the Chinese world today, falls into the still current category of superstition. Assessing the ethical notions that tend to obtain within this vast area of religious life is not easy, but it needs to be done for practical reasons, not least because the legal consequences of moral actions arising from the body of beliefs concerned are starting to come before courts outside China itself. Once the assumptions (...) of a very different worldview affirming the existence of an unseen spirit world are taken into account, the deeds of believers in this worldview can be discussed from the point of view of ethics. Philosophers might do well to pay more attention to this topic. (shrink)

One might think that the best metaphysical theory of the world includes the existence of other minds and of the physical world, while denying that we can know or be certain that this theory is true. This chapter considers Solipsism as a theory about reality. It examines the Veil of Perception, and then considers a series of direct arguments against the Solipsistic Veil, Phenomenalism, and Solipsism itself. The chapter looks at two obviously inadequate arguments for the Veil, namely, Berkeley's inconceivability (...) argument and the argument from causal mediation. Then, the chapter looks at two much more interesting and important arguments, namely, the argument from hallucination and illusion and the argument from color and other secondary qualities. Besides the Veil of Perception, arguments for Idealism and Solipsism depend on an appeal to Ockham's Razor. These arguments can be taken either as providing additional support for Perceptual Realism or as a defense of Inferred Anti‐Idealism. (shrink)

Fred Dretske, David M. Armstrong, and Michael Tooley have all proposed that the truths about the laws of nature are metaphysically fundamental, consisting in a primitive, unanalyzable relation of 'necessitation' holding between two or more properties or universals. According to Strong Nomism, the laws of nature determine which counterfactual conditionals are true, and they also determine which powers and tendencies particular things have. This chapter treats Nomism as committed to the Dretske‐Armstrong‐Tooley (DAT) theory. Nomism provides a metaphysical explanation of the (...) difference between lawful and accidental generalization. The chapter focuses on the Neo‐Humeist or Ramsey/Lewis Theory of the laws of nature. The Neo‐Humeist program proceeds in the following way. First, give a reductionist account of the laws of nature, and then use the laws to ground the truths of attributions of power and of counterfactual conditionals. (shrink)

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v 2 /c 2 , does reveal a connection between (...) the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c 4 and hence is negligible in a 1/c 2 analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c 2 , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems. (shrink)

This chapter focuses on question of the relation of properties to particulars. It considers three theories of facts: as tropes, as states of affairs, and as nexuses between particulars and universals, noting that in each case, facts turn out to be particulars of a kind. The chapter investigates the question of substances, considering two accounts about the relationship between substances and properties, namely, Relational and Constituent Ontology. Substances would have a surprising degree of metaphysical complexity. According to Constituent Ontology, properties (...) are literally parts of substances they characterize. According to Relational Ontology, in contrast, properties are separate things, extrinsically related to their instances. The chapter examines two versions of Constituent Ontology, Bundle Theory and Substrate Theory. Classical Bundle Theory purports to reduce substances to bundles of universals. The chapter also examines Nuclear Bundle Theory that faces an especially virulent form of the problem of Individuation. (shrink)

One popular approach to the metaphysics of dispositional properties takes them to involve ascribing a conditional property, a property corresponding to a conditional statement. This chapter looks at some recent work on the semantics and logic of conditionals, followed by a consideration of Hypotheticalism, Nomism, Neo‐Humeism, and Powerism. It examines directly the question whether Hypotheticalism or Anti‐Hypotheticalism (categoricalism) is correct, and shows how to evaluate counterfactual conditionals. The evaluation of conditionals seems to turn on two sorts of facts about the (...) actual world: the laws of nature, and the true propositions that are co‐tenable with the conditional's antecedent. Strong Hypotheticalists hold that the truths of counterfactual conditionals are fundamental, and that truths about the laws of nature and of powers and dispositions are reducible to them. (shrink)

This chapter focuses mainly on how possible worlds relate to the truth and falsity of modal claims (or propositions), and therefore to whether claims are necessarily true, necessarily false, possibly true, possibly false, and so on. This issue is that of modality de dicto, modality concerning propositions. But there is another type of modality, namely modality de re. This has to do with the modal status of relations between things and their properties, with whether things possess properties necessarily, contingently or (...) not even possibly. This chapter introduces the distinction between de dicto and de re necessity, and then explores different ways of making sense of de re necessity‐necessities involving particular individuals. It talks about Strong Transworld Identity, and explores how Abstractionists respond to the Leibniz's Law argument. Some metaphysicians go farther and identify what is possible with what is conceivable, or perhaps with what we are justified in believing to be possible. (shrink)

The first way that a discussion of truth gets one going in metaphysics is via its connection to propositions. Philosophers have taken a number of views about the true nature of propositions. The early part of the twentieth century saw a strong reaction against holism, led prominently by Bertrand Russell and Ludwig Wittgenstein. This chapter considers why we should believe in Classical Truthmaker Theory in the first place, as well as a fundamental challenge to the very foundation of truthmaker theory: (...) the deflationary theory of truth. The simplest, most natural understanding of Truthmaker Theory is the view that every truth has a truthmaker. This is 'Truthmaker Maximalism'. One of the fundamental motivations for truthmaker theory of any form is, as we have seen, the Correspondence Theory of Truth. Importantly, deflationists are anti‐realists only about one thing: the existence of a real property of truth. (shrink)

This chapter examines questions having to do with whether and how things persist through change and how things do so If they do persist. Next, assuming that intrinsic change does take place, the chapter examines two principal views about how things persist through change of intrinsic properties, Substratism and Replacementism. It focuses on the specific but very important case of motion, or change of location. There are three major theories: Intrinsic Motion; Bertrand Russell's At/At Theory, and an Aristotelian theory (Motion (...) Intervalism). The chapter also considers the problem of the persistence of composite objects, including objects that can gain or lose parts. Replacementists might consider taking on board a metaphysically fundamental genidentity relation. Substratists have an explanation for the reflexivity, symmetry, and transitivity of genidentity, something that Classical Genidentity Theorists have to posit as a brute metaphysical necessity. This provides the Substatists with an advantage in terms of Ockham's Razor. (shrink)

An appeal to ontological parsimony or economy plays an important, perhaps indispensable, role in evaluating metaphysical theories. This chapter focuses primarily on the first conception of grounding, grounding as metaphysical explanation. It briefly discusses the relation of ontological dependency and its connections with grounding as explanation. Debates about grounding are a recurring theme in the history of Western philosophy. Much of Aristotle's metaphysical method also presupposes the existence of a grounding relation. The chapter investigates both conceptual and ontological grounding and (...) explores the relationship between grounding and truthmaking. The chapter considers various alternatives or competitors to grounding theory. It examines the connection between grounding, fundamentally, and Ockham's Razor and also relation between grounding and ontological dependence. The chapter shows how grounding is different from causal explanation and discusses connections between grounding and entailment. (shrink)

This chapter examines the problem of unity and considers how it is possible for one thing to exist in and through a plurality of parts or phases. It begins with a general discussion of the existence of composite things. The chapter considers the view that composite entities are always an 'ontological free lunch', things that can be freely posited without incurring any cost in relation to ontological economy or Ockham's Razor. It looks at the issue of causal redundancy, a consideration (...) which suggests that positing composite entities as fundamental things is in fact quite costly, something to be undertaken only with strong reasons. The chapter examines three candidates for fundamental composite entities: heaps, artifacts, and organisms. It considers question of which sorts of composite things exist at all, whether fundamentally or derivatively. This involves a search for an intelligible principle of composition. (shrink)

Laws of nature are merely expressions of the powers possessed by various kinds of things, and counterfactual conditionals are grounded in the powers and tendencies of the entities involved in the counterfactual supposition together with their counterfactual surroundings. There are two versions of Strong Powerism. One takes the truthmakers for causal laws to be universals (a 'Realist' version). The second takes the truthmakers for causal laws to be the particulars that fall under the laws (a 'Nominalist' version). This chapter focuses (...) on how Powerism compares to other views about the laws. Neo‐Humeism has the leanest metaphysical theory, since its class of fundamental truths includes no conditionals, laws of nature or attributions of power. Metaphysically, Nomism is burdened with a large number of brute necessities, linking laws with actual patterns of particular fact. The chapter talks about the causal theory of properties: causal structuralism. (shrink)

This chapter considers various views about the precise nature of possible worlds, but each view is compatible with this initial characterization. It considers modality, particularly focusing on metaphysical possibility, necessity, and impossibility, that broadest kind of modality. The chapter offers an example of why one might care about this issue, an example of why the study of modality matters to philosophy more generally. It is plausible that modality is importantly connected to understanding. The chapter focuses on two contrasting views about (...) the nature of possible worlds, Concretism and Abstractionism. The fundamental difference between Concretism and Abstractionism is whether possible worlds are concrete or abstract. Concretism is the view that possible worlds are like parallel universes. Concretism requires Modal Indexicalism and denies Modal Anti‐Indexicalism. The chapter describes the ways that the Concretism carries out its reduction of possibility and actuality. (shrink)

This chapter considers the possibility of Nihilism, that nothing exists, and its alternative, Aliquidism, that something exists. This will lead us into an investigation of the point of positing existing things. The chapter looks at the debate between Monists, who believe in only one thing, and Pluralists, who believe in many. It also considers both radical and more moderate forms of both Nihilism and Monism, including, for example, Priority Monism. The chapter examines four arguments for Monism: those of Parmenides, Spinoza, (...) Bradley, and Jonathan Schaffer. Parmenides of Elea authored a single work, a poem traditionally titled On Nature. In the first part of this poem, Parmenides seems to be arguing for Monism. Baruch Spinoza offered a set of metaphysical arguments that could be interpreted as attempting to show that only one thing exists. The chapter considers the import of Bradley's Regress for Constituent Realism, UPRealism combined with Constituent Ontology. (shrink)

This chapter covers number of Abstractionist views of modality. It considers three ways that Abstractionists might account for how possible worlds represent possibilities, rather than in terms of the categorial nature of worlds. First, there is Magical Abstractionism, according to which that question has no informative answer. Second, there is Linguistic Abstractionism, according to which possible worlds represent in the way that languages do. And finally, there is Pictorial Abstractionism, according to which possible worlds represent in the way that pictures (...) do. Pictorial Abstractionists might respond by trying to identify a feature that Concretist worlds have that their worlds don't, or vice versa. One way for something to be possible is for actual things to have the power to make it so. Since the notion of power is central to Aristotelian Modality, we get sub‐varieties of the view depending on one's metaphysical account of powers. (shrink)

This chapter takes up issues to do with Peter van Inwagen's (1990a) general composition question: what is it for one thing to be a part of another? The chapter begins with some background to do with formal mereology, the study of parts and wholes. In discussing the metaphysics of parts and wholes, it is helpful to have some specialized vocabulary, as well as a well thought‐out mathematical model of a very broad, inclusive theory. The theory of mereology, proposed by the (...) logician Stanislaw Lesniewski and introduced to the widerworld by Goodman and Leonard in an article in the Journal of Symbolic Logic, provides that vocabulary and such a model. These mereologists proposed some basic axioms for the part‐whole relation. Alternatively, the Composition as Identity (CAI) theorist could try to build transitivity into their definition of the part‐whole relation. Finally, the chapter provides some answers to the General Composition Question and considers whether those answers can supply a ground for the correct principles of mereology. (shrink)

The nature of causation has been one of the central questions of metaphysics since ancient times. This chapter looks at the arguments for Causal Anti‐Realism. Causation requires necessary connections between separate existences. David Hume argued that the ordinary conception of causation involves the separateness of the cause and effect. Hume had a further, closely related argument against the reality of causation. Authors' idea of causation is merely a confusion of several distinct concepts, namely, the concepts of regular succession and contiguity (...) among events, and the concept of a felt propensity on their own part to infer one thing from another. There are four objections to Universal Causation, one assuming Mereological Universalism, a second employing a pluralized version of Universal Causation, a third involving a chain principle, and a fourth including an argument against infinite causal regresses. (shrink)

Causal connectionists need to provide an account of causal linkage and of causal direction. This chapter distinguishes between two kinds of causal connection, namely, discrete and continuous. Causal connectionists have a number of options for explaining the linkage between causes and effects in the case of discrete causation. The chapter provides some popular options. If some causation is discrete, and the exercise of causal powers provides a direction to discrete causation, then the causal direction of processes can be derived from (...) the causal direction of discrete interaction. David Hume famously made the claim about the knowledge of causation in his Enquiry Concerning Human Understanding. Hume offers, in defense of his principle, a set of thought‐experiments that seem to show that we can always imagine any event's having a different result from the one we in fact observe. Causal processes like locomotion may provide counterexamples to Hume's Epistemic Principle. (shrink)

There are a number of different versions of Reductive Nominalism, versions distinguished by the way in which each accounts for facts about having and sharing properties. This chapter discusses three broad varieties of Reductive Nominalism: Predicate Nominalism, Class Nominalism, and Resemblance Nominalism. Class Nominalism identifies properties with classes or sets. Resemblance Nominalists come in two sub‐varieties, depending on whether they take the resemblance relation to hold between particular properties (called 'tropes') or particular things that have properties (ordinary particulars). Trope Theory (...) comes in two varieties depending on whether one plumps for universals. It should not be difficult to see that Extreme Resemblance Nominalism is faced with Class Nominalism's extensionality problems, both the problem of contingent predication and the co‐extensive property problem. Resemblance Nominalists can reply by insisting on a distinction between a priori or conceptual equivalence and metaphysical equivalence. The chapter focuses on the extensionality problems for Class Nominalism. (shrink)

The primary thesis of this article is that the rights and powers of corporations--to collect, recombine, and resell personal data--have accrued in such a way as to fundamentally circumvent traditional and conventional conceptions of privacy, especially with respect to the sphere of informational privacy. In so doing, informational capitalism has also altered in fundamental ways the public and social sphere itself, the sphere through which one might expect these corporate forces and uses of technology to be controlled.

This chapter looks at six arguments against Tensism. They are, equivalently, arguments for Anti‐Tensism. The arguments are of three basic kinds: those that argue that Tensism is incoherent or mysterious, those that argue that it is in irresolvable conflict with modern science, and those that fault Tensism for its unexplainable or brute necessities. The chapter considers the objection that Tensism cannot sensibly account for the rate of the flow of time. It shows in which a variety of objections based on (...) Truthmaker Theory are lodged against various versions of Tensism. The chapter looks at science, especially Einstein's theory of relativity, as the basis for an argument against Tensism. It concerns additional philosophical objections to Tensism and then considers epistemological problems for Tensism; and McTaggart's argument that Tensism is self‐contradictory. The chapter explores the number of brute necessities for which Tensism can provide no simple explanation. (shrink)