Recently, various people have maintained that one must revise either the externalistically-based notion of singular thought or the naïve realism-inspired notion of relational particularity, as respectively applied to some thoughts and to some perceptual experiences. In order to do so, one must either provide a broader notion of singular thought or flank the notion of relational particularity with a broader notion of phenomenal particularity. I want to hold that there is no need of that revision. For the original notions can (...) still play the role for which they were invoked. This requires that (i) both the first and the second notion respectively involve a dependence on and a metaphysical relation to the intentional objects of certain mental states once we are ontologically committed to such objects; (ii) both that object-dependence and that metaphysical relation are interpreted in terms of a substantive individuation of the relevant mental state via the object it is about: that object constitutes the state. (shrink)

I argue that the familiar picture of the rise of analytic philosophy through the early work of G. E. Moore and Bertrand Russell is incomplete and to some degree erroneous. Archival evidence suggests that a considerable influence on Moore, especially evident in his 1899 paper ‘The nature of judgment,’ comes from the literature in nineteenth-century empirical psychology rather than nineteenth-century neo-Hegelianism, as is widely believed. I argue that the conceptual influences of Moore’s paper are more likely to have had their (...) source in the work of two of Moore’s teachers, G. F. Stout and James Ward. What may be called an anti-psychologism about psychology characterizes the work of these and other psychologists of the period. I argue that the anti-psychologism that is the main aim of Moore’s early theory of judgment is an adaptation of this notion, which is significantly dissimilar from the notion defended by Bradley, traditionally thought to have been a key influence on Moore.Keywords: G. E. Moore; Bertrand Russell; Propositions; Anti-psychologism; Early analytic philosophy; G. F. Stout. (shrink)

In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a system (...) treating apparent terms for numbers using these definitions. (shrink)

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...) proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

According to K. McDaniel’s and J. Turner’s Ontological Pluralism, there are many ways of being that are more fundamental than being in general. In this paper, I shall analyze some constraints on this doctrine. Among other, ontological pluralists are committed to the idea that there are no things that have no way of being at all and that it is not legitimate to quantify over ways of being. Later on, I shall introduce a problem for ontological pluralism: if there is (...) a privileged way of being an ontological pluralist, then, given those constraints, ontological pluralists cannot logically express that privileged way. Finally, I shall justify the acceptance of a Half-Meinongian solution to this problem, that is roughly grounded on the acceptance of entities that have no way of being at all. (shrink)

What is the role of measurement in the sociology of culture and how can we sort out the complexities that distinguish qualitative from quantitative approaches to this domain? In this article, we compare the issues and concerns of contemporary scholars who work on matters of culture with the writings of a group of scholars who had prepared papers for a special symposium on scientific measurement held at the annual meeting of the American Association for the Advancement of Science (AAAS) back (...) in 1956. We focus on three issues—the recurring need to reinvent measurement (as illustrated by the career of the psychologist S.S. Stevens), the linkage between qualitative and quantitative methods of analysis (as articulated in the writings of the sociologist Paul Lazarsfeld), and the assertion (by philosophers Ernst Cassirer and Peter Caws) that theorizing necessarily precedes measuring. We review a number of important advances in the way that measurement is theorized and implemented in the sociology of culture and we also point to a number of enduring dilemmas and conundrums that continue to occupy researchers in the field today. (shrink)

This paper develops a (nontrivial) theory of cardinal numbers from a naive set comprehension principle, in a suitable paraconsistent logic. To underwrite cardinal arithmetic, the axiom of choice is proved. A new proof of Cantor’s theorem is provided, as well as a method for demonstrating the existence of large cardinals by way of a reflection theorem.

Since the discovery of incommensurability in ancient Greece, arithmeticism and geometricism constantly switched roles. After ninetieth century arithmeticism Frege eventually returned to the view that mathematics is really entirely geometry. Yet Poincaré, Brouwer, Weyl and Bernays are mathematicians opposed to the explication of the continuum purely in terms of the discrete. At the beginning of the twenty-first century ‘continuum theorists’ in France (Longo, Thom and others) believe that the continuum precedes the discrete. In addition the last 50 years witnessed the (...) revival of infinitesimals (Laugwitz and Robinson—non-standard analysis) and—based upon category theory—the rise of smooth infinitesimal analysis and differential geometry. The spatial whole-parts relation is irreducible (Russell) and correlated with the spatial order of simultaneity. The human imaginative capacities are connected to the characterization of points and lines (Euclid) and to the views of Aristotle (the irreducibility of the continuity of a line to its points), which remained in force until the ninetieth century. Although Bolzano once more launched an attempt to arithmetize continuity, it appears as if Weierstrass, Cantor and Dedekind finally succeeded in bringing this ideal to its completion. Their views are assessed by analyzing the contradiction present in Grünbaum’s attempt to explain the continuum as an aggregate of unextended elements (degenerate intervals). Alternatively a line-stretch is characterized as a one-dimensional spatial subject, given at once in its totality (as a whole) and delimited by two points—but it is neither a breadthless length nor the (shortest) distance between two points. The overall aim of this analysis is to account for the uniqueness of discreteness and continuity by highlighting their mutual interconnections exemplified in the nature of a line as a one-dimensional spatial subject, while acknowledging that points are merely spatial objects which are always dependent upon an extended spatial subject. Instead of attempting to reduce continuity to discreteness or discreteness to continuity, a third alternative is explored: accept the irreducibility of number and space and then proceed by analyzing their unbreakable coherence. The argument may be seen as exploring some implications of the view of John Bell, namely that the “continuous is an autonomous notion, not explicable in terms of the discrete.” Bell points out that initially Brouwer, in his dissertation of 1907, “regards continuity and discreteness as complementary notions, neither of which is reducible to each other.”. (shrink)

Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...) thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

The article considers, in a historical setting, the links between varieties of nominalism—the extreme nominalism of the Quine-Goodman variety and the trope nominalism current today—and types of idealism. In so doing arguments of various twentieth century figures, including Husserl, Bradley, Russell, and Sartre, as well as a contemporary attack on relations by Peter Simons are critically examined. The paper seeks to link the rejection of realism about universals with the rejection of a mind-independent “world”—in short, linking nominalism with idealism.

Philosophers of the modern period are often presented as having made an elementary error: that of confounding the attitude one adopts toward a proposition with its content. By examining the works of Locke and the Port-Royalians, I show that this accusation is ill-founded and that Locke, in particular, has the resources to construct a theory of propositional attitudes.

In this paper, I offer an examination of the two existing criteria of change, one indicated, implicitly, by Aristotle and the other proposed, quite formally, by Russell. Both criteria engender problems. While the Aristotelian criterion is both too narrow and too broad, as it includes bogus changes and excludes subjectless changes, the Russellian criterion avoids the distinction between genuine changes and bogus changes completely. The aim of the paper is to address these problems and to show how these two existing (...) criteria of change can be made to deal with the problems through revision and integration. (shrink)

Claims that necessary and sufficient conditions are not converse relations are discussed, as well as the related claim that If A, then B is not equivalent to A only if B . The analysis of alleged counterexamples has shown, among other things, how necessary and sufficient conditions should be understood, especially in the case of causal conditions, and the importance of distinguishing sufficient-cause conditionals from necessary-cause conditionals. It is concluded that necessary and sufficient conditions, adequately interpreted, are converse relations in (...) all cases. (shrink)

Ned Markosian argues (Australasian Journal of Philosophy 76:213-228, 1998a; Australasian Journal of Philosophy 82:332-340, 2004a, The Monist 87:405-428, 2004b) that simples are ‘maximally continuous’ entities. This leads him to conclude that there could be non-particular ‘stuff’ in addition to things. I first show how an ensuing debate on this issue McDaniel (Australasian Journal of Philosophy 81(2):265-275, 2003); Markosian (Australasian Journal of Philosophy 82:332-340, 2004a) ended in deadlock. I attempt to break the deadlock. Markosian’s view entails stuff-thing coincidence, which I show (...) is just as problematic as the more oft-discussed thing-thing coincidence. Also, the view entails that every particular is only contingently so. If there is a world W like our own, but with ether, then there would be only one object in W. But, since merely adding ether to a world does not destroy the entities in it, then W contains counterparts of all the entities in the actual world—they just are not things. Hence, if simples are maximally continuous, then every actual particular is only contingently so. This in turn entails the following disjunction: (i) identity is contingent or intransitive, or (ii) there are no things at all in the actual world, or (iii) the distinction between stuff and things is one without a difference. I recommend that we reject this stuff-thing dualism. (shrink)

The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.

We must allow that knowledge can be transmitted. But to allow this is to allow that an individual can know a proposition despite lacking any evidence for it and reaching belief by an unreliable means. So some explanation is required as to how knowledge rather than belief is transmitted. This paper considers two non-individualistic explanations: one in terms of knowledge existing autonomously, the other in terms of it existing as a property of communities. And it attempts to decide what is (...) at issue between these explanations. (shrink)

This paper is an attempt to explain why Russell abandoned the ontology of propositions, mind-independent complex entities that are possible objects of judgements. I argue that he did so not because of any decisive argument but because he found it better to endorse the existential account of truth, according to which a judgement is true if and only if there exists (or in his view subsists) a corresponding fact. In order to endorse this account, he had examined various theories of (...) judgement before he adopted the multiple-relation theory of judgement, the most feasible way he then had of espousing it. I also attempt to explain why he preferred the existential account of truth. (shrink)

Russellians can have a no proposition view of empty names. I will defend this theory against the problem of meaningfulness, and show that the theory is in general well motivated. My solution to the problem of meaningfulness is that speakers’ judgements about meaningfulness are tracking grammaticality, and not propositional content.

Building on recent work by Delia Graff Fara and Ora Matushansky on appellative constructions like ‘Mirka called Roger handsome’, I argue that if Millianism about proper names is true, then the quantifier ‘something’ in ‘Mirka called Roger something’ is best understood as a kind of substitutional quantifier. Any adequate semantics for such quantifiers must explain both the logical behavior of ‘Mirka called Roger something’ and the acceptability of ‘so’-anaphora in ‘Mirka called Roger something, and everyone so called is handsome’. Millianism (...) about proper names is inconsistent with such quantifiers being standard non-substitutional second-order quantifiers. But this is not the only option for Millianism: I provide two different propositional semantics for substitutional quantification, each of which is adequate in the sense above, given Millianism. One of these is based on Tobias Rosefeldt’s work on non-nominal quantification, and I identify in what way Rosefeldt’s semantics is substitutional. (shrink)

The identity predicate can be defined using second-order quantification: a=b =df ∀F(Fa↔Fb). Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ϕ≡ψ =df ∀X(Xϕ↔Xψ), where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality? -/- I will argue that reality is not structured in anything like (...) the way that the sentences we use to talk about it are structured. I do so by formulating a higher-order analogue of Russell’s paradox of structured propositions. I then relate this argument to the Frege-Russell correspondence. When confronted with the alleged paradox, Frege agreed that reality was not structured, but maintained that propositions (i.e. thoughts) were structured all the same. Russell replied that his paradox showed Frege’s theory of structured thoughts to be inconsistent, to which Frege replied that Russell’s argument failed to heed the distinction between sense and reference. Most recent commentators have sided with Russell. In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality. I conclude that, if propositions are structured, this is because they correspond not to distinctions in reality, but rather to ways in which those distinctions can be represented. (shrink)

I shall explore in this article the metaphysical possibility of powers’ strongly emerging from relations. After having provided a definition of emergent powers that is also based on the distinction between the possession and the activation of a power, I shall introduce different sorts of Relations that Ground Emergence, both external and internal. Later on, I shall discuss some examples of powers that are grounded on their instantiation. Finally, I shall examine the consequences of accepting such relations within a physicalistic (...) ontology and I shall defend them against two objections based on the notion of bruteness. (shrink)

Network motifs are small patterns of connections, found over‐represented in gene regulatory networks. An example is the negative feedback loop (e.g. factor A represses itself). This opposes its own state so that when ‘on’ it tends towards ‘off’ – and vice versa. Here, we argue that such self‐opposition, if considered dimensionlessly, is analogous to the liar paradox: ‘This statement is false’. When ‘true’ it implies ‘false’ – and vice versa. Such logical constructs have provided philosophical consternation for over 2000 years. (...) Extending the analogy, other network topologies give strikingly varying outputs over different dimensions. For example, the motif ‘A activates B and A. B inhibits A’ can give switches or oscillators with time only, or can lead to Turing‐type patterns with both space and time (spots, stripes or waves). It is argued here that the dimensionless form reduces to a variant of ‘The following statement is true. The preceding statement is false’. Thus, merely having a static topological description of a gene network can lead to a liar paradox. Network diagrams are only snapshots of dynamic biological processes and apparent paradoxes can reveal important biological mechanisms that are far from paradoxical when considered explicitly in time and space. (shrink)

The paper ends with an argument that says: necessarily, if there are finitely spatially extended particulars, then there are monadic universals. Before that, in order to characterize the distinction between particulars and universals, Roman Ingarden’s notions of existential moments and modes (ways) of being are presented, and a new pair of such existential moments is introduced: multiplicity–monadicity. Also, it is argued that there are not only real universals, but instances of universals (tropes) and fictional universals too.

If a spinning sphere casts a shadow, does the shadow also spin? This riddle is the point of departure for an investigation into the nature of shadow movement. A general theory of motion will encompass all moving things, not just physical objects. Ultimately, I argue that round shadows do indeed spin. Shadows are followers of the objects that cast them. Parts of the shadow correspond to parts of the leader, so motion of the caster's parts accounts for motions of the (...) shadow's parts. I conclude with a discussion of how the dynamic aspects of shadows impose subtle constraints on other puzzles about shadows. (shrink)

This paper is about the Problem of Order, which is basically the problem how to account for both the distinctness of facts like a’s preceding b and b’s preceding a, and the identity of facts like a’s preceding b and b’s succeeding a. It has been shown that the Standard View fails to account for the second part and is therefore to be replaced. One of the contenders is Anti-Positionalism. As has recently been pointed out, however, Anti-Positionalism falls prey to (...) a regress argument which is to prove its failure. In the paper we spell out this worry, show that the worry is a serious one, and distinguish four possible strategies for Anti-Positionalism to deal with it. (shrink)

Along with a well-honoured tradition, we will accept that intentionality is at least a property a thought holds necessarily, i.e., in all possible worlds that contain it; more specifically, a necessary relation, namely the relation of existential dependence of the thought on its intentional object. Yet we will first of all try to show that intentionality is more than that. For we will claim that intentionality is an essential property of the thought, namely a property whose predication to the thought (...) is true in virtue of the identity, or nature, of such a thought. More particularly, for us intentionality will again be a relation, yet a relation of ontological dependence of the thought on its intentional object; specifically, the relation for the thought of being constituted by its object. Moreover, we will try to show that if intentionality is such a constitutive relation for the thought that has it, certain metaphysical consequences ensue. First, an objectual thought, a thought whose content basically consists in its intentional object, is nothing but that object in a certain cogitative modality, or, which is the same, as playing a certain motivational role for the subject entertaining the thought itself (at a certain time). Second, if an objectual thought is nothing but an intentional object in a cogitative modality, such a thought, not only as a type, but also as a token, is an abstract entity. More specifically, an objectual thought-type, an abstract object par excellence, is indeed instantiated by objectual thought-tokens which are again abstract particulars, yet of a specific kind: namely, tropes of a relational sort depending for their existence on their bearers (and possibly also on their temporal location). (shrink)

Despite its importance for early analytic philosophy, Gottlob Frege's account of existence statements, according to which they classify concepts, has been thought to succumb to a number of well-worn criticisms. This article does two things. First, it argues that, by remaining faithful to the letter of Frege's claim that concepts are functions, the Fregean account can be saved from many of the standard criticisms. Second, it examines the problem that Frege's account fails to generalize to cases which involve definite descriptions (...) and proper names. To deal with this the proffered analysis deviates from the letter of Frege's views, while remaining within its spirit. It proposes, in opposition to Frege, that expressions which grammatically look like singular terms should not always be read as referring to objects, but are sometimes best analysed as indicating functions. (shrink)

A. Kenny, Frege, an introduction to the founder of modern analytic philosophy. London:Penguin, 1995. viii-h223pp. £7.99 T. Willamson, Vagueness. London:Routledge, 1994. xiii-f-325 pp. £35.00 TOM BU...

A theory of relations is presented that provides a detailed account of the logical structure of relational complexes. The theory draws a sharp distinction between relational complexes and relational states. A salient difference is that relational complexes belong to exactly one relation, whereas relational states may be shared by different relations. Relational complexes are conceived as structured perspectives on states ‘out there’ in reality. It is argued that only relational complexes have occurrences of objects, and that different complexes of the (...) same relation may correspond to the same state. (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.

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)

Since its publication in 1967, van Heijenoort’s paper, “Logic as Calculus and Logic as Language” has become a classic in the historiography of modern logic. According to van Heijenoort, the contrast between the two conceptions of logic provides the key to many philosophical issues underlying the entire classical period of modern logic, the period from Frege’s Begriffsschrift (1879) to the work of Herbrand, Gödel and Tarski in the late 1920s and early 1930s. The present paper is a critical reflection on (...) some aspects of van Heijenoort’s thesis. I concentrate on the case of Frege and Russell and the claim that their philosophies of logic are marked through and through by acceptance of the universalist conception of logic, which is an integral part of the view of logic as language. Using the so-called “Logocentric Predicament” (Henry M. Sheffer) as an illustration, I shall argue that the universalist conception does not have the consequences drawn from it by the van Heijenoort tradition. The crucial element here is that we draw a distinction between logic as a universal science and logic as a theory. According to both Frege and Russell, logic is first and foremost a universal science, which is concerned with the principles governing inferential transitions between propositions; but this in no way excludes the possibility of studying logic also as a theory, i.e., as an explicit formulation of (some) of these principles. Some aspects of this distinction will be discussed. (shrink)

After presenting the ordinary and the Fregean formulations of the ancestral, I raise the question of what is their relationship, the natural candidate being that the Fregean version is an analysans intended to improve upon, and replace, the common notion of ancestral (the analysandum). Next, two types of circles that arise in connection with the Fregean ancestral are presented, and it is claimed that one of the circles makes it impossible to maintain the just described (“replacement”) interpretation. A reference is (...) made to Kerry, who was the first to point out a circularity in Frege’s ancestral. Some of Frege’s remarks are examined in order to tentatively sketch, an answer to the issue of the relationship between ordinary and Fregean ancestral; the latter, if not as an analysans replacing the common notion, can still be seen as a profound enrichment of the former. (shrink)

Russell's involuted path in the development of his theory of logical types from 1903 to 1910-13 is examined and explained in terms of the development in his early philosophy of the notion of a logical subject vis-a-vis the problem of the one and many; i.e., the problem for russell, first, of a class-as-one as a logical subject as opposed to a class as many, and, secondly, of a propositional function as a single and separate logical subject as opposed to existing (...) only in the many propositions that are its values. (shrink)

The view that plural reference is reference to a set is examined in light of George Boolos's treatment of second-order quantification as plural quantification in English. I argue that monadic second-order logic does not, in Boolos's treatment, reflect the behavior of plural quantifiers under negation and claim that any sentence that properly translates a second-order formula, in accordance with his treatment, has a first-order formulation. Support for this turns on the use of certain partitive constructions to assign values to variables (...) in a way that makes Boolos's reading of second-order variables available for a first-order language and, with it, the possibility of interpreting quantification in an unrestricted domain.A first-order theory, T(D), is developed on the basis of Boolos's treatment of simple plural definite descriptions extended to Richard Sharvy's general theory of definite plural and mass descriptions. I introduce a primitive predicate, o, for the relation of the referent of a singular description to that of its plural. If o is simply added to T(D), is definable in T(D), and the result is inconsistent. If o is added to a theory with axioms for the fragment of T(D) I call D-mereology, the result is a natural basis for the development of a pluralized Zermelo set theory. This theory, however, is inconsistent in an unrestricted domain, unless it is recast as a second-order theory of sets interpreted in Boolos's way. (shrink)

Plural Logic is an extension of First-Order Logic with plural terms and quantifiers. When its plural terms are interpreted as denoting more than one object at once, Plural Logic is usually taken to be ontologically innocent: plural quantifiers do not require a domain of their own, but range plurally over the first-order domain of quantification. Given that Plural Logic is equi-interpretable with Monadic Second-Order Logic, it gives us its expressive power at the low ontological cost of a first-order language. This (...) makes it a valuable tool in various areas of philosophy. Some authors believe that Plural Logic can be extended into an even more expressive logic, Higher-Level Plural Logic, by adding higher-level plural terms and quantifiers to it. The basic idea is that second-level plurals stand to plurals like plurals stand to singulars. Allegedly, Higher-Level Plural Logic enjoys the expressive power of type theory while, again, committing us only to the austere ontology of a first-order language. Were this really the case, Higher-Level Plural Logic would be a very useful tool, extending and strengthening some of the applications of Plural Logic. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with scepticism. The main objection raised against them is that higher-level plural reference is unintelligible. This has been argued, among others, on the grounds that there are no higher-level plurals in natural language and that, if there were any, they could be eliminated. In this thesis, after introducing the debate on plurals in Chapters 1 and 2, I turn to defending the legitimacy of the notion of higher-level plural reference. To this end, in Chapter 3, I present and elucidate the notion. Next, in Chapter 4, I show that some natural languages clearly contain these expressions and that they do so in an ineliminable manner. Finally, in Chapters 5 and 6, I develop a semantics for higher-level plurals that employs only devices previously well-understood by English speakers. To finish, in Chapter 7, I describe an application of Higher-level Plural Logic: a strengthening of the neo-Fregean programme. After describing my proposal, I turn to the issue of the logical status of this formalism and defend an optimistic take on the matter. (shrink)

The At-At Account of motion is the extremely popular view that, necessarily, something moves if and only if it’s at one place at one time, and at a distinct place at a distinct time. This, many believe, is all that motion consists in. However, I will present a case in which, intuitively, motion does not occur, though the At-At Account of motion entails that it does. I will then turn to the only tenable response that avoids revising the At-At Account: (...) denying the possibility of my case. I will argue that the response is both contentious and fails to defend the spirit of the At-At Account qua reduction of motion (rather than mere listing of necessary and sufficient conditions for motion’s occurring). (shrink)

Traditionally one main emphasis of the quantum mechanical measurement theory is on the question how the pure state of the compound system 'measured system + measuring apparatus' is transformed into the 'mixture' of all possible results of that measurement, weighted with their probability: the so-called “disappearance of the interference terms”. It is argued in this note that in reality there is no such transformation, so that there is no need to account for such a transformation theoretically. _German_ Gewöhnlich liegt ein (...) Hauptgewicht der quantenmechanischen Messtheorie auf der Frage des Übergangs vom,reinen Fall' des Gesamtsystems,gemessenes System + Messgerät' in das,Gemenge' aus allen möglichen Messergebnissen, gewichtet mit ihren Wahrscheinlichkeiten: Das sog.,,Verschwinden der Interferenzterme“. In dieser Notiz wird die Meinung vertreten, dass es einen solchen Übergang faktisch nicht gibt, so dass es nicht notwendig ist, eine theoretische Erklärung für den Übergang zu geben. (shrink)

Russell's version of the multiple-relation theory from the "Theory of Knowledge" manuscript is presented and defended against some objections. A new problem, related to defining truth via correspondence, is reconstructed from Russell's remarks and what we know of Wittgenstein's objection to Russell's theory. In the end, understanding this objection in terms of correspondence helps to link Russell's multiple-relation theory to his later views on propositions.

I argue that three main interpretations of the aim of Russell’s early logicism in The Principles of Mathematics (1903) are mistaken, and propose a new interpretation. According to this new interpretation, the aim of Russell’s logicism is to show, in opposition to Kant, that mathematical propositions have a certain sort of complete generality which entails that their truth is independent of space and time. I argue that on this interpretation two often-heard objections to Russell’s logicism, deriving from Gödel’s incompleteness theorem (...) and from the non-logical character of some of the axioms of Principia Mathematica respectively, can be seen to be inconclusive. I then proceed to identify two challenges that Russell’s logicism, as presently construed, faces, but argue that these challenges do not appear unanswerable. (shrink)

Never shall this be proved, that things that are not are. ParmenidesTo say that something does not exist, or that there is something which is not, is clearly a contradiction in terms; hence “ ” must be true. Moreover, we should certainly expect leave to put any primitive name of our language for the “x” of any matrix “ … x … ”, and to infer the resulting singular statement from “ ”; it is difficult to contemplate any alternative logical (...) rule for reasoning with names. (shrink)

Professor Weinberg, in his recention, Relation, and Induction, has critically discussed the nominalistic tradition stemming from Ockham and continuing in the work of Berkeley and Hume. In this tradition there is one fundamental principle, which however divides into two parts. The first is Whatever is distinguishable is distinct, and conversely. The second is Whatever is distinct is separable, and conversely. Weinberg argues that both and are mistaken.In this paper I propose to explore the case against nominalism. I shall suggest that (...) Weinberg's argument against, though not defective in the way some recent critics believe, depends upon a hidden premiss. I shall also suggest that the argument against, when the needed premiss is added, is but a special case of a more general argument. The latter in no way depends upon considerations concerning relational predicates, though Weinberg does in his discussion specifically introduce such considerations. Nor is that unreasonable on his part. (shrink)