After describing the philosophical background of Kerry's work, an account is given of the way Kerry proposed to supplement Bolzano's conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege's work and Kerry's views were then attacked by Frege.The following two issues were central to this controversy: (a) the relation between the content of a concept and the object of a concept; (b) the logical roles of the definite article. Not only (...) did Frege in 1892 offer an unconvincing solution to Kerry's puzzle concerning 'the concept horse' but he also overlooked the many criticisms levelled by Kerry against the notion of an (indefinite) extension on which his own definition of number was based. (shrink)

The existence of complex predicates seems to support an abundant conception of properties. Specifically, the application conditions for complex predicates seem to be explained by the distribution of a sparser base of predicates. This explanatory link might suggest that the existence and distribution of properties expressed by complex predicates are explained by the existence and distribution of a sparser base of properties. Thus, complex predicates seem to legitimize the assumption of a wide array of properties. The additional properties are no (...) explanatory addition to the sparse base. I argue, however, that construing complex predicates as expressing properties undermines the explanatory links between simple and complex predications. The argument explores a variety of accounts of complex predicates currently on offer and develops a number of themes from the work of Herbert Hochberg. (shrink)

This paper considers a problem for dynamic presentism that has received little attention: its apparent inability to accommodate the duration of events (such as conscious experiences). After outlining the problem, I defend presentism from it. This defence proceeds in two stages. First, I argue the objection rests on a faulty assumption: that duration is temporal extension. The paper challenges that assumption on several different ways of conceiving of temporal extension. This is the negative case and forms the bulk of the (...) paper. Second, after diagnosing the error leading to the identification of duration with temporal extension, I outline a new presentist-friendly account of duration that avoids the problem. In particular, a non-reductive account of duration is offered that treats it as a primitive quality which bestows its possessor with a certain modal quality: that the possessor potentially does not change whilst there are changes in its environs. This is the positive case. Together the positive and negative cases provide presentism with an interesting and novel way of overcoming the problem of duration. (shrink)

Much of the recent metaphysical literature on the problem of the relational unity of complexes leaves the impression that Bradley (or some Bradleyan argument) has uncovered a serious problem to be addressed. The problem is thought to be particularly challenging for trope theorists and realists about universals. In truth, there has been little clarity about the nature and import of the original Bradley’s regress arguments. In this paper, I offer a careful analysis and reconstruction of the arguments in Bradley’s Appearance (...) and Reality (1893). The analysis reveals that no less than three regress arguments against relations can be found. I show that none of them are compelling. I argue that, as a result, it is a serious misstep for philosophers today to offer metaphysical theses based on the unchallenged assumption that Bradley has established his regress result. I further analyze the underpinnings of the Bradley problem as it is frequently cast in contemporary literature and show that they rely on certain confusions and biases, which once brought to light, make current Bradley-inspired arguments against relations unconvincing. (shrink)

Zermelos Zeit in Göttingen (1897?1910) kann als wissenschaftlich fruchtbarste Periode in seiner Karriere angesehen werden. Gleichwohl stehen bisher Untersuchungen aus. die eine Einbettung von Zermelos Werk in den biographischen und sozialen Kontext ermöglichen Die vorliegende Studie will diese Lücke unter Konzentration auf zwei Gegenstandsbereiche teileweise ausfüllen: (1) den historischen Entstehungskontext von Zermelos ersten Arbeiten über die Grundlagen der Mengenlehre; (2) die Vorgeschichte und näheren Umstände des 1907 an Zermelo verliehenen Lehrauftrages für mathematische Logik und verwandte Gegenstände. mit dem ein erster (...) Schritt zur Institutionalisierung dieses Faches als mathematischer Teildisziplin gemacht wurde. Beides wird in enger Verbindung zur ersten Phase des Hilbertschen Programms zur Grundlegung der Mathematik gesehen. Es wird aber auch gezeigt, daß für die Erteilung des Lehrauftrages neben diesen systematischen und forschungspolitischen Motiven auch persönliche und institutspolitische Rücksichten ausschlaggebend waren. Im Anhang werden Teile eines Briefwechsels zwischen Ernst Zermelo und dem Göttinger Philosophen Leonard Nelson ediert sowie die Anträge der Direktoren des Göttinger mathematisch-physikalischen Seminars auf Erteilung des Lehrauftrags und auf Ernennung Zermelos zum außerordentlichen Professor. Zermelo's Göttingen period (1897?1910) can be regarded as the most fruitful period in his scientific career. Nevertheless, up till now there have been no investigations which enable us to embed his work in its biographical and social contexts. This study tries to partially fill the gap, concentrating on two major themes: (I) the historical context of the development of Zermelo's early work on the foundations of set theory; (2) the prehistory and particulars of his lectureship for mathematical logic and related topics, this lectureship, which he was awarded in 1907, being the first step taken in Germany towards the establishment of this subject as a separate mathematical discipline. Both will be seen in close connection with the first phase of Hilbert's programme of founding mathematics. It is shown, however, that this lectureship was not only created to further the aims of Hilbert's research programme but that personal and institutional motives also played a role. In the appendices, parts of a correspondence between Ernst Zermelo and the Göttingen Philosopher Leonard Nelson are edited, as well as the applications of the directors of the Göttingen Mathematisch-physikalisches Seminar for awarding the lectureship to Zermelo in 1907, and for appointing Zermelo to an extraordinary professorship in 1910. (shrink)

This paper gives a survey of David Hilbert's (1862–1943) changing attitudes towards logic. The logical theory of the Göttingen mathematician is presented as intimately linked to his studies on the foundation of mathematics. Hilbert developed his logical theory in three stages: (1) in his early axiomatic programme until 1903 Hilbert proposed to use the traditional theory of logical inferences to prove the consistency of his set of axioms for arithmetic. (2) After the publication of the logical and set-theoretical paradoxes by (...) Gottlob Frege and Bertrand Russell it was due to Hilbert and his closest collaborator Ernst Zermelo that mathematical logic became one of the topics taught in courses for Göttingen mathematics students. The axiomatization of logic and set-theory became part of the axiomatic programme, and they tried to create their own consistent logical calculi as tools for proving consistency of axiomatic systems. (3) In his struggle with intuitionism, represented by L. E. J. Brouwer and his advocate Hermann Weyl, Hilbert, assisted by Paul Bemays, created the distinction between proper mathematics and meta-mathematics, the latter using only finite means. He considerably revised the logical calculus of thePrincipia Mathematica of Alfred North Whitehead and Bertrand Russell by introducing the ε-axiom which should serve for avoiding infinite operations in logic. (shrink)

I present a thought experiment in quantum mechanics and tease out some of its implications for the doctrine of “peaceful coexistence”, which, following Shimony, I take to be the proposition that quantum mechanics does not force us to revise or abandon the relativistic picture of causality. I criticize the standard arguments in favour of peaceful coexistence on the grounds that they are question-begging, and suggest that the breakdown of Lorentz-invariant relativity as a principle theory would be a natural development, given (...) the general trend of physics in this century. (shrink)

I examine and discuss in this paper Orilia’s theory of external, non-symmetrical relations, that is based on ontological roles (O-Roles). I explore several attempts to interpret O-Roles from an ontological viewpoint and I reject them because of two problems concerning the status of asymmetrical relations (to be distinguished from non-symmetrical relations simpliciter) and of exemplification as an external, non-symmetrical relation. Finally, following Heil’s and Lowe’s characterization of modes as particular properties that ontologically depend on their “bearers”, I introduce relational modes (...) in order to define a new solution to the problems of the ontological status of both external, non-symmetrical relations and O-Roles. I also deal with five objections raised by Fraser MacBride against relational modes and O-Roles and I elaborate an analysis of the relations of being to the left of and being to the right of. (shrink)

In early analytic philosophy, one of the most central questions concerned the status of arithmetical objects. Frege argued against the popular conception that we arrive at natural numbers with a psychological process of abstraction. Instead, he wanted to show that arithmetical truths can be derived from the truths of logic, thus eliminating all psychological components. Meanwhile, Dedekind and Peano developed axiomatic systems of arithmetic. The differences between the logicist and axiomatic approaches turned out to be philosophical as well as mathematical. (...) In this paper, I will argue that Dedekind’s approach can be seen as a precursor to modern structuralism and as such, it enjoys many advantages over Frege’s logicism. I also show that from a modern perspective, Frege’s criticism of abstraction and psychologism is one-sided and fails against the psychological processes that modern research suggests to be at the heart of numerical cognition. The approach here is twofold. First, through historical analysis, I will try to build a clear image of what Frege’s and Dedekind’s views on arithmetic were. Then, I will consider those views from the perspective of modern philosophy of mathematics, and in particular, the empirical study of arithmetical cognition. I aim to show that there is nothing to suggest that the axiomatic Dedekind approach could not provide a perfectly adequate basis for philosophy of arithmetic. (shrink)

(2013). Two aspects of propositional unity. Canadian Journal of Philosophy: Vol. 43, Essays on the Nature of Propositions, pp. 518-533.

This paper first discusses how Russell and Hochberg have addressed some phenomena of relatedness, notably relational order, in a similarly ‘positionalist’ way, yet by appealing to different sorts of formal relations: “positions” in Russell's case and “ordering relations” in Hochberg's. After pointing out some shortcomings of both approaches, the paper then proposes an alternative view based on ‘o-roles’, which are, roughly speaking, ontological counterparts of the thematic roles postulated in linguistics. It is argued that o-roles are sort of middle-of-the-road entities (...) in the sense that they have the virtues of positions and those of ordering relations, without having their respective vices. Some tentative ideas on which o-roles should be acknowledged are also put forward. (shrink)

States of affairs involving a non-symmetric relation such as loving are said to have a relational order, something that distinguishes, for instance, Romeo’s loving Juliet from Juliet’s loving Romeo. Relational order can be properly understood by appealing to o-roles, i.e., ontological counterparts of what linguists call thematic roles, e.g., agent, patient, instrument, and the like. This move allows us to meet the appropriate desiderata for a theory of relational order. In contrast, the main theories that try to do without o-roles, (...) proposed by philosophers such as Russell, Hochberg, and Fine, are in trouble with one or another of these desiderata. After discussing some alternatives, it is proposed that o-roles are best viewed as very generic properties characterizable as ways in which objects jointly exemplify a relation. This makes for exemplification relations understood as complex entities having o-roles as building blocks. (shrink)

It is customary in current philosophy of time to distinguish between an A- (or tensed) and a B- (or tenseless) theory of time. It is also customary to distinguish between an old B-theory of time, and a new B-theory of time. We may say that the former holds both semantic atensionalism and ontological atensionalism, whereas the latter gives up semantic atensionalism and retains ontological atensionalism. It is typically assumed that the B-theorists have been induced by advances in the philosophy of (...) language and related A-theorists’ criticisms to acknowledge that semantic atensionalism can hardly stand, but have also maintained that what is essential for the B-theory is ontological atensionalism, which can be independently defended. Here it is argued that the B-theorists have been too quick in abandoning semantic atensionalism: they can still cling to it. (shrink)

This paper defends the view that Newtonian forces are real, symmetrical and non-causal relations. First, I argue that Newtonian forces are real; second, that they are relations; third, that they are symmetrical relations; fourth, that they are not species of causation. The overall picture is anti-Humean to the extent that it defends the existence of forces as external relations irreducible to spatio-temporal ones, but is still compatible with Humean approaches to causation (and others) since it denies that forces are a (...) species of causation. (shrink)

This is the second in a sequence of three essays which axiomatize and apply Edmund Husserl's dependence ontology of parts and wholes as a non-Diodorean, non-Kantian temporal semantics for first-order predicate modal languages. The Ontology of Intentionality I introduced enough of Husserl's dependence-ontology of parts and wholes to formulate his account of order as effected by relating moments of unity, and The Ontology of Intentionality II extends that axiomatic dependence-ontology far enough to enable its semantic application. Formalizing the compatibility [Vereinbarkeit] (...) relation implicated in Husserl's notorious doctrine of impossible meanings, the essay introduces a compatibility restriction on relations to formulate Husserl's distinction between singular [einheitliche] and plural [mehrheitliche] objects, using plural relating moments to define first-order versions of Husserl's notions of relation complexes (i.e. Sachverhalte), abstracta of n-ary relation complexes, categorial relations, abstract eide as unifications of categorial relations, semantic domains as completions of abstract eide, and material regions as semantic domains which are compatibility upper bounds of categorial relations. These concepts will enable the formal dependence-ontological noetic semantics for two-valued, first-order modal languages introduced in the sequel Two-Valued Logics of Intentionality, the third essay in the sequence. (shrink)

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and issues that (...) have arisen. Namely, elements of different structures are different. A structure and its elements ontologically depend on each other. There are no haecceities and each element of a structure must be discernible within the theory. These consequences are not developed piecemeal but rather follow from our definitions of basic structuralist concepts. (shrink)

We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.

This is the introductory essay to a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell’s paper ‘On Denoting’.

A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...) unsupported assumptions concerning existence of physical objects (e.g. that any two actual objects have an actual sum). The theory T Q supports and illustrates a form of naturalistic Platonism, for which claims concerning the existence and properties of universals form part of natural science, and the distinction between accidental generalizations and laws of nature has a basis in the second-order structure of the world. (shrink)

I begin by criticizing an elaboration of an argument in this journal due to Hawley , who argued that, where Leibniz’s Principle of the Identity of Indiscernibles faces counterexamples, invoking relations to save PII fails. I argue that insufficient attention has been paid to a particular distinction. I proceed by demonstrating that in most putative counterexamples to PII , the so-called Discerning Defence trumps the Summing Defence of PII. The general kind of objects that do the discerning in all cases (...) form a category that has received little if any attention in metaphysics. This category of objects lies between indiscernibles and individuals and is called relationals: objects that can be discerned by means of relations only and not by properties. Remarkably, relationals turn out to populate the universe. (shrink)

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (“states” of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a “general syntax of relativized conceptualization” where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified (...) and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie,Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965). (shrink)

After introducing Millianism and touching on two problems raised by genuinely empty names for Millianism (section I), I provide a brief exposition of the Gappy Proposition View (GPV) and of how different versions of this view can reply to the problems in question (section II). In the following sections I develop my reasons against the GPV. First, I will try to argue that apparently promising arguments for the claim that gappy propositions are propositions are not successful (section III). Then, I (...) will develop two arguments against GPs via demonstrating two odd consequences of the GPV: (a) that there can be an atomic proposition which contains other propositions that are not the semantic contents of any part of the .. (shrink)

In the Critique of Pure Reason, Kant conceives of general logic as a set of universal and necessary rules for the possibility of thought, or as a set of minimal necessary conditions for ascribing rationality to an agent . Such a conception, of course, contrasts with contemporary notions of formal, mathematical or symbolic logic. Yet, in so far as Kant seeks to identify those conditions that must hold for the possibility of thought in general, such conditions must hold a fortiori (...) for any specific model of thought, including axiomatic treatments of logic and standard natural deduction models of first-order predicate logic. Kant's general logic seeks to isolate those conditions by thinking through – or better, reflecting on – those conditions that themselves make thought possible. (shrink)

We develop a reading of Moore’s “Proof of an External World” that emphasizes the connections between this paper and Moore’s earlier concerns and strategies. Our reading has the benefit of explaining why the claims that Moore advances in “Proof of an External World” would have been of interest to him, and avoids attributing to him arguments that are either trivial or wildly unsuccessful. Part of the evidence for our view comes from unpublished drafts which, we believe, contain important clues concerning (...) Moore’s aims and intent. While our approach to PEW may be classified alongside other broadly "metaphysical" readings, we believe that a proper recognition of the continuity in Moore’s philosophical concerns and strategies across his philosophical career shows that the customary distinction between "epistemological" and "metaphysical" interpretative approaches to PEW is at best superficial. (shrink)

While there are reasons to believe that both component forces and a resultant force operate on a body in combined circumstances, the threat of overdetermination largely prevents adoption of this view. Accordingly, a lively debate has arisen over which force actually exists and which force is eliminated in combined circumstances, the components or the resultant. In this article I present a non-reductive model of resultant force which ensures the existence of both the resultant force and the component forces without overdetermination. (...) According to the non-reductive model, the resultant force is the summation of component forces, where summation is interpreted as meaning that the component forces, when temporally and spatially overlapping, form a superposed mixture which is the resultant force, but which is not identical to the conjunction of component forces taken with temporal and spatial independence. (shrink)

Mi objetivo es discutir las principales dificultades que Frank P. Ramsey encontró en Principia Mathematica y la solución que, vía el Tractatus Logico-Philosophicus, propuso al respecto. Sostengo que las principales dificultades que Ramsey encontró en Principia Mathematica están, todas, relacionadas con que Russell y Whitehead desatendieron la forma lógica de las proposiciones matemáticas, las cuales, según Ramsey, deben ser tautológicas.

We put together several observations on constructive negation. First, Russell anticipated intuitionistic logic by clearly distinguishing propositional principles implying the law of the excluded middle from remaining valid principles. He stated what was later called Peirce’s law. This is important in connection with the method used later by Heyting for developing his axiomatization of intuitionistic logic. Second, a work by Dragalin and his students provides easy embeddings of classical arithmetic and analysis into intuitionistic negationless systems. In the last section, we (...) present in some detail a stepwise construction of negation which essentially concluded the formation of the logical base of the Russian constructivist school. Markov’s own proof of Markov’s principle (different from later proofs by Friedman and Dragalin) is described. (shrink)

Between April and November 1912, Bertrand Russell and Ludwig Wittgenstein were engaged in a joint philosophical program. Wittgenstein‘s meeting with Gottlob Frege in December 1912 led, however, to its dissolution – the joint program was abandoned. Section 2 of this paper outlines the key points of that program, identifying what Russell and Wittgenstein each contributed to it. The third section determines precisely those features of their collaborative work that Frege criticized. Finally, building upon the evidence developed in the preceding two (...) sections, section 4 recasts along previously undeveloped lines Wittgenstein‘s logical–philosophical discoveries in the two years following his encounter with Frege in 1912. The paper concludes, in section 5, with an overview of the dramatic consequences the Frege-Wittgenstein critique had for Russell‘s philosophical development. (shrink)

There is a core to the referential/attributive distinction that reveals a propositional ambiguity that is scope-related and rooted in syntax.

This paper is concerned with what I call the ‘problem of unity’ . This is the puzzle of how Armstrong‐like states of affairs are unified. The general approach is ‘relational internalism’: the unifier of such a state of affairs is a relation of some sort in it. A view commonly associated with relational internalism is that if such a relation satisfies a certain ‘naive’ expectation to a relation – that it is related to its relata – then Bradley's regress results. (...) As I argue, for one very natural species of relational internalism, this is indeed the case. Influential writers on the topic have therefore maintained that this relation is not related to its relata. But, as we shall see, while this ‘classic’ relational internalism obviously avoids Bradley's regress, intuitively, it fails completely to solve the problem of unity. I argue, however, that given the rejection of a natural, but unfounded, assumption of conventional relational internalism, a unique relation can unify states of affairs without leading to Bradley's regress. I consequently propose a novel version of relational internalism on which states of affairs are unified by such an entity. (shrink)

The philosophical investigation of perceptual illusions can generate fruitful insights in the study of subjective time consciousness. However, the way illusions are interpreted is often controversial. Recently, proponents of the so-called dynamic snapshot theory have appealed to the Waterfall Illusion, a kind of motion aftereffect, to support a particular view of temporal consciousness according to which experience is structured as a series of instantaneous snapshots with dynamic qualities. This dynamism is meant to account for familiar features of the phenomenology of (...) time, such as succession, continuity, and change. Previous theories have typically appealed to a subjective present occupying an interval of time; that is, a “specious present.” I argue, through analysis of motion aftereffect illusions and the rare condition of akinetopsia, i.e. motion-blindness, that the Waterfall Illusion fails to support the dynamic snapshot theory as intended. Furthermore, I suggest that future theories of subjective time should see temporal phenomenology as the result of non-localised processes closely tied to the mechanism underlying consciousness generally. (shrink)

An account of validity that makes what is invalid conditional on how many individuals there are is what I call a conditional account of validity. Here I defend conditional accounts against a criticism derived from Etchemendy’s well-known criticism of the model-theoretic analysis of validity. The criticism is essentially that knowledge of the size of the universe is non-logical and so by making knowledge of the extension of validity depend on knowledge of how many individuals there are, conditional accounts fail to (...) reflect that the former knowledge is basic, i.e., independent of knowledge derived from other sciences. Appealing to Russell’s pre-Principia logic, I defend conditional accounts against this criticism by sketching a rationale for thinking that there are infinitely many logical objects. (shrink)

This paper presents an account of the manner in which a proposition’s immediate structural features are related to its core truth-conditional features. The leading idea is that for a proposition to have a certain immediate structure is just for certain entities to play certain roles in the correct theory of the brute facts regarding that proposition’s truth conditions. The paper explains how this account addresses certain worries and questions recently raised by Jeffery King and Scott Soames.

Richmond Campbell and Thomas Vinci have recently presented a Bayesian theory of confirmation by novel evidence (Campbell and Vinci [1983]). I shall review their theory as briefly as possible and present three objections to it.

Van Bendegem has recently offered an argument to the effect that, if time is discrete, then there should exist a correspondence between the motions of massive bodies and a discrete geometry. On this basis, he concludes that, even if space is continuous, it should nonetheless appear discrete. This paper examines the two possible ways of making sense of that correspondence, and shows that in neither case van Bendegem’s conclusion logically follows.

To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable (...) as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined. (shrink)

This paper defends a realist account of the composition of Newtonian forces, dubbed ‘residualism’. According to residualism, the resultant force acting on a body is identical to the component forces acting on it that do not prevent each other from bringing about its acceleration. Several reasons to favor residualism over alternative accounts of the composition of forces are advanced. (i) Residualism reconciles realism about component forces with realism about resultant forces while avoiding any threat of causal overdetermination. (ii) Residualism provides (...) a systematic semantics for the term ‘force’ within Newtonian mechanics. (iii) Residualism allows us to precisely apportion the causal responsibility of each component force in the ensuing acceleration. (iv) Residualism handles special cases such as null forces, single forces, and antagonistic forces in a natural way. (v) Residualism provides a neat picture of the causal powers of forces: each force essentially has two causal powers⎯the power to bring about accelerations (sometimes together with other co-directionnal forces) and the power to prevent other forces from doing so⎯exactly one of which is manifested at a time. (vi) Residualism avoids commitment to unobservable effects of forces: forces cause either stresses (tensile or compressive) or accelerations. (shrink)

Propositional contingentism is the view that what propositions there are is a contingent matter—certain propositions ontologically depend on objects which themselves only contingently exist. Possible worlds are, loosely, complete ways the world could have been. That is to say, the ways in which everything in its totality could have been. Propositional contingentists make use of possible worlds frequently. However, a neglected, but important, question concerns whether there are any notions of worlds which are both theoretically adequate and consistent with propositional (...) contingentism. Some notion of a possible world is adequate if the systematic connection between, at least, possibility and truth at some possible world holds. Here, I argue that no adequate notion of a possible world is available to at least those who subscribe to one natural formulation of propositional contingentism. I also show that this result contrasts with a simple and adequate definition of a possible world available to the necessitist—those who hold that necessarily everything necessarily exists. (shrink)

Absolutism about mass claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Dasgupta, Oxford studies in metaphysics, Oxford University Press, Oxford, 2013) argues for comparativism about mass, in the context of Newtonian Gravity. Such an argument requires proving that comparativism is empirically adequate. Dasgupta equates this to showing that absolute masses are undetectable, and attempts to do so. This paper develops an argument by Baker to the contrary: absolute masses are in fact empirically meaningful, that is (...) detectable. Additionally, it is argued that the requirement of empirical adequacy should not be cashed out in terms of undetectability in the first place. The paper closes by sketching the possible strategies that remain for the comparativist. Along the way a framework is developed that is useful for thinking about these issues: Ozma games—how could one explain to an alien civilisation what an absolute mass is? (shrink)

A common adage runs that, given a theory manifesting symmetries, the syntax of that theory should be modified in order to construct a new theory, from which symmetry-variant structure of the original theory has been excised. Call this strategy for explicating the underlying ontology of symmetry-related models reduction. Recently, Dewar has proposed an alternative to reduction as a means of articulating the ontology of symmetry-related models—what he calls sophistication, in which the semantics of the original theory is modified, and symmetry-related (...) models of that theory are treated as if they are isomorphic. In this paper, we undertake a critical evaluation of sophistication about symmetries—we find the programme underdeveloped in a number of regards. In addition, we clarify the interplay between sophistication about symmetries, and a separate debate to which Dewar has contributed—viz., that between interpretational versus motivational approaches to symmetry transformations. (shrink)

Since the early part of this century there has been a considerable amount of discussion of the question 'Does time pass?'. A useful way of approaching the debate over the passage of time is to consider the following thesis: The space-time thesis (SPT): Time is similar to the dimensions of space in at least this one respect: there is no set of properties such that (i) these properties are possessed by time, (ii) these properties are not possessed by any dimension (...) of space, and (iii) in virtue of time's possession of these properties it is true to say that time passes. Those who say that time does not pass generally want to affirm something like SPT. But those, on the other hand, who say that time does pass generally want to deny SPT. Of course, SPT is, as it stands, a mere skeleton of a thesis. It needs to be fleshed out. What could the relevant properties be? Why exactly would it be that in virtue of time's possession of these properties it is true to say that time passes? What exactly would it mean to say that time passes? These are all matters that require considerable discussion. The aim of this paper, however, is to take up some linguistic issues that have been considered central to the debate over the passage of time. There are two main reasons why I think it is appropriate to discuss these linguistic issues independently of the relevant metaphysical issues. The first reason is historical: many of the writers who have taken up the issue of whether or not time passes have begun their discussions by focusing on linguistic.. (shrink)

Absolutism about mass within Newtonian gravity claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Defenders of comparativism promise to recover all the empirical and theoretical virtues of absolutism, but at a lower ‘metaphysical cost’. This article develops a Machian form of comparativism about mass in Newtonian gravity, obtained by replacing Newton’s constant in the law of universal gravitation by another constant divided by the sum over all masses. Although this form of comparativism is indeed empirically (...) equivalent to the absolutist version of Newtonian gravity—thereby meeting the challenge posed by the comparativist’s bucket argument—it is argued that the explanatory power and metaphysical parsimony of comparativism are highly questionable. (shrink)

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into 5 (...) sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory. (shrink)