In Russell's Problems of Philosophy (PP), acquaintance is the basis of thought and also the basis of empirical knowledge. Thought is based on acquaintance, in that a thinker has to be acquainted with the basic constituents of his thoughts. Empirical knowledge is based on acquaintance, in that acquaintance is involved in perception, and perception is the ultimate source of all empirical knowledge.

In early major works, Cassirer and Schlick differently recast traditional doctrines of the concept and of the relation of concept to intuitive content along the lines of recent epistemological discussions within the exact sciences. In this, they attempted to refashion epistemology by incorporating as its basic principle the notion of functional coordination, the theoretical sciences' own methodological tool for dispensing with the imprecise and unreliable guide of intuitive evidence. Examining their respective reconstructions of the theory of knowledge provides an axis (...) of comparison along which to locate Cassirer's Neo-Kantianism and Schlick's pre-positivist empiricism, and an immediate background of contrast to the subsequent rise of logical empiricism. For in the absence of intuition all our knowledge is without objects and therefore remains entirely empty. (Kant A62/B87) And how awkward is the human mind in diving the nature of things when forsaken by the analogy of what we see and touch directly? (Boltzmann 1895). (shrink)

The standard version of the story of Russell's theory of types gives legitimately precedence to the vicious circle principle, but it fails to appreciate the significance of the doctrine of incomplete symbols and of the ultimate universalist perspective of Russell's logic. It is what the Author tries to do. This enables him to resolve the apparent contradiction which exists in "Principles" between the ontological commitment of the theory itself with respect to individuals, propositions, and functions, and the inventory of the (...) world, according to which there are only individuals and elementary facts. (shrink)

In this article I argue that Russell's multiple-relation theory of judgment is a continuation of the campaign against Frege and Meinong begun in “On Denoting” with the theory of descriptions. More precisely, I hold that the problem of false belief, to which the multiple-relation theory is presented as a solution, emerges quite naturally out of the problem context of “On Denoting” and threatens to give new life to the theories Russell purports to have laid to rest there, and that Russell's (...) solution to the much neglected third puzzle of “On Denoting” contains the gist of the multiple-relation theory. The failure of that theory to solve the problem of false belief thus signifies the failure of the theory of descriptions. (shrink)

In the course of developing a semantics with epistemological intent, Brandom claims that his inferentialism is Hegelian. This paper argues that, even on a charitable reading, Brandom is an anti-Hegelian.

In this paper I argue for a view of groups, things like teams, committees, clubs and courts. I begin by examining features all groups seem to share. I formulate a list of six features of groups that serve as criteria any adequate theory of groups must capture. Next, I examine four of the most prominent views of groups currently on offer—that groups are non-singular pluralities, fusions, aggregates and sets. I argue that each fails to capture one or more of the (...) criteria. Last, I develop a view of groups as realizations of structures. The view has two components. First, groups are entities with structure. Second, since groups are concreta, they exist only when a group structure is realized. A structure is realized when each of its functionally defined nodes or places are occupied. I show how such a view captures the six criteria for groups, which no other view of groups adequately does, while offering a substantive answer to the question, “What are groups?”. (shrink)

A number of papers have argued in favour of the material account of indicative conditionals, but typically they either concentrate on defending the account from the charge that it has counterintuitive consequences, or else focus on some particular positive argument in favour of the theory. In this paper, I survey the various positive arguments that can be given, presenting simple versions where possible and showing the connections between them. I conclude with some methodological considerations.

Between 1903 and 1918 Russell made a number of attempts to understand the unity of the proposition, but his attempts all foundered on his failure clearly to distinguish between different senses in which the relation R might be said to relate a and b in the proposition aRb: he failed to distinguish between the relation as truth-maker and the relation as unifier, and consequently committed himself again and again to the unacceptable consequence that only true propositions are genuinely unified. There (...) is an anticipation of this confusion in the writings of the fourteenth-century philosopher Richard Brinkley. (shrink)

83. It should now be apparent that the familiar problems of reference and modality can be satisfactorily resolved without either abandoning substitutivity of identity in modal contexts or invoking an intensional ontology. It might be argued, however, that the suggested resolution avoids invoking an intensional ontology only because the modal predicates, e.g. Nec and Believes, are left unanalysed. This may well be true but it should be appreciated that the analysis of modal predicates is an issue which is independent of (...) both the problem of reference in modal contexts and the problem of the logical structure of propositions containing such contexts. These problems can be settled, as we have seen, without also settling how the modal predicates are to be analysed. Hence, if an intensional ontology is in the end required, it is required to analyse the modal predicates, not to solve the problems of reference and logical structure. This, we suggest, is an interesting and perhaps unexpected result. (shrink)

In this essay, I discuss some observations by Peirce which suggest he had some idea of the substantive metalogical differences between logics which permit both quantifiers and relations, and those which do not. Peirce thus seems to have had arguments?which even De Morgan and Frege lacked?that show the superior expressiveness of relational logics.

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...) initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception. (shrink)

La constatación de que nuestro universo está constituido de unos y los mismos elementos materiales en cualquier lugar en que podamos observarlo nos lleva directamente a la postulación de un único principio y causa del único proceso universal al que se debe cuanto existe. Y en ese trance parece inevitable preguntar: ¿cómo ha surgido Todo? Todo, aquí, significa cuanto hay; sin excepción alguna. Esta visión puramente física del Universo puede denominarse naturalismo universal, entendiendo el término naturalismo como traducción del término (...) aristotélico physis en su célebre definición. (shrink)

David Chalmers’ two-dimensionalism is an ambitious philosophical program that aims to “ground” or “construct” Fregean meanings and restore “the golden triangle” of apriority, necessity, and meaning that Kripke seemingly broke. This paper aims to examine critically what Chalmers’ theory can in reality achieve. It is argued that the theory faces severe challenges. There are some gaps in the overall arguments, and the reasoning is in some places somewhat circular. Chalmers’ theory is effectively founded on certain strong philosophical assumptions. It is (...) concluded that it is unclear whether the theory can deliver all it promises. (shrink)

In this article, I reconstruct Walter Benjamin's philosophy of language and refine the non-predicational view of meaning often attributed to him. By situating his 1916 essay ‘On Language as Such and on the Language of Man’ within the context of his struggle with Russell's paradox and its implications for phenomenology, I show how Benjamin arrives at his conception of non-conceptual content as an environmentally embedded affordance that is directly apprehended by appropriately situated and capable agents. This affordance-like character of meaning (...) explains Benjamin's account of communication, Adamic naming, and his famous distinction between linguistic and spiritual essences (sprachliche- and geistige Wesen). I conclude by showing why translation is central to his views on expression and communication and how it reinforces his account of language-use. (shrink)

Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an active role in the development of computational science and core mathematics. It is worth exploring some of them in depth, particularly predicative Martin-Löf’s intuitionistic type theory and impredicative Coquand’s calculus of constructions. The logical and philosophical differences and similarities between them will be (...) studied, showing the relationship between these type theories and other fields of logic. (shrink)

A metafísica de 'Os Princípios da Matemática' de Russell e a controvérsia à respeito da suposta semelhança entre essa metafísica e a ontologia meinongiana Resumo: No presente artigo, objetiva-se apresentar as principais características da metafísica do realismo lógico, desenvolvido por Russell em Os Princípios da Matemática, de 1903, e, principalmente, analisar a controvérsia sobre se os princípios dessa metafísica podem realmente ser interpretados como semelhantes aos princípios da ontologia meinongiana. São comparados os pontos de vista opostos dessa controvérsia à luz (...) dos trechos de Os Princípios da Matemática que supostamente comprometeram Russell de ter elaborado uma gramática filosófica na qual todo e qualquer nome próprio ou descrição definida, ocupando a posição de sujeito lógico nas proposições, referem-se a objetos com alguma categoria de Ser. Ao realizar tal análise, conclui-se que o problema central diz respeito aos nomes próprios vazios e que, portanto, a metafísica de Os Princípios da Matemática expressa uma perspectiva instável da teoria da denotação de Russell. Palavras-chave: Russell; Ser; Existência; Significado. Russell’s The Principles of Mathematics metaphysics and the controversy over the supposed similarity between this metaphysics and the meinongian ontology Abstract: This article aims to present the main characteristics of the metaphysics of logical realism, developed by Russell in The Principles of Mathematics, of 1903, and, mainly, to analyze the controversy about whether the principles of this metaphysics can really be interpreted as similar to the principles of meinongian ontology. The opposing points of view of this controversy are compared in the light of the excerpts from The Principles of Mathematics that supposedly committed Russell to having elaborated a philosophical grammar in which all and any proper names or definite descriptions, occupying the position of logical subject in the propositions, refer to objects with some category of Being. In carrying out such an analysis, it is concluded that the central problem concerns empty proper names and that, therefore, the metaphysics of The Principles of Mathematics expresses an unstable perspective of Russell’s theory of denotation. Keywords: Russell; Being; Existence; Meaning. La metafísica de Los Principios de las Matemáticas de Russell y la controversia sobre la supuesta similitud entre esta metafísica y la ontología meinongiana Resumen: Este artículo tiene como objetivo presentar las principales características de la metafísica del realismo lógico, desarrollada por Russell en Los Principios de las Matemáticas, de 1903, y, principalmente, analizar la controversia sobre si los principios de esta metafísica pueden realmente interpretarse como similares a los principios de la ontología meinongiana. Los puntos de vista opuestos de esta controversia se comparan a la luz de los extractos de Los Principios de las Matemáticas que supuestamente comprometieron Russell a haber elaborado una gramática filosófica en la que todos y cualquier nombre propio o descripción definida, ocupando la posición de sujeto lógico en las proposiciones, se refieren a objetos con alguna categoría de Ser. Al realizar tal análisis, se concluye que el problema central concierne a los nombres propios vacíos y que, por lo tanto, la metafísica de Los Principios de las Matemáticas expresa una perspectiva inestable de la teoría de la denotación de Russell. Palabras clave: Russell; Ser; Existencia; Significado. Data de registro: 10/04/2020 Data de aceite: 08/12/2020. (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.

The Analytic Tradition in Philosophy is an excellent successor to an excellent book : It is a fine an example of the necromantic style in the history of philosophy where the object of the exercise is to resurrect the mighty dead in order to get into an argument with them, either because we think them importantly right or instructively wrong. However what was a pardonable a simplification and a reasonable omission in the earlier book has now metamorphosed into a sin (...) of omission and an oversimplification in its successor—the book lacks is an adequate discussion of the Ramified Theory of Types and Russell’s reasons for adopting it. I conclude with a brief meditation on Open Question Arguments and the threats that they pose to some of the analyses proposed by Russell and Moore themselves. (shrink)

Russell's notion of an incomplete symbol has become a standard against which philosophers compare their views on the relationship between language and the world. But Russell's exact characterization of incomplete symbols and the role they play in his philosophy are still disputed. In this paper, I trace the development of the notion of an incomplete symbol in Russell's philosophy. I suggest – against Kaplan, Evans, and others – that Russell's many characterizations of the notion of an incomplete symbol are compatible. (...) To this end, I examine and reject arguments for the purported incompatibility between declaring an expression to be incomplete and incorporating that symbol into a compositional semantic theory. I then examine how Russell puts the notion of an incomplete symbol to use in metaphysics. (shrink)

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)

This essay argues that the main lesson of Lewis Carroll's Regress is that arguments are constitutively presuppositional.

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)