The dual-aspect monist conjecture launched by Pauli and Jung in the mid-20th century will be couched in somewhat formal terms to characterize it more concisely than by verbal description alone. After some background material situating the Pauli–Jung conjecture among other conceptual approaches to the mind–matter problem, the main body of this paper outlines its general framework of a basic psychophysically neutral reality with its derivative mental and physical aspects and the nature of the correlations that connect these aspects. Some related (...) approaches are discussed to identify key similarities to and deviations from the Pauli–Jung framework that may be useful for cross-fertilization. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

This paper argues that the main global critiques of scientism lose their punch because they rely on an uncharitable definition of their target. It focuses on epistemological scientism and divides it into four categories in terms of how strong (science is the only source of knowledge) or weak (science is the best source of knowledge) and how narrow (only natural sciences) or broad (all sciences or at least not only the natural sciences) they are. Two central arguments against scientism, the (...) (false) dilemma and self‐referential incoherence, are analysed. Of the four types of epistemological scientism, three can deal with these counterarguments by utilizing two methodological principles: epistemic evaluability of reliability and epistemic opportunism. One hopes that these considerations will steer the discussion on scientism to more fruitful pastures in the future. For example, there are interesting methodological considerations concerning what evaluability or reliability and epistemic opportunism entail. (shrink)

In this article, we analyze and reject two versions of the content‐argument against animal beliefs, namely, the ontological argument from Davidson and the epistemological argument from Stich. One of the main defects of the strongest version of the argument is that it over‐intellectualizes belief ascriptions in humans and thus sets the comparative bar for belief ascriptions in animals too high. In the second part of the article, we develop a gradualist notion of belief which captures basic beliefs as well as (...) Davidsonian linguistic beliefs, and we specify the conditions under which belief ascriptions to nonlinguistic animals are justified. (shrink)

This essay addresses the collapse/incoherence problem for normative frameworks that contain both fundamental values and rules for promoting those values. The problem is that in some cases, we would bring about more of the fundamental value by violating the framework’s rules than by following them. In such cases, if the framework requires us to follow the rules anyway, then it appears to be incoherent; but if it allows us to make exceptions to the rules, then the framework “collapses” into one (...) that doesn’t make use of rules in the first place. The chapter begins with an examination of happiness and truth as fundamental values in Mill’s work, which lead into parallel versions of the collapse/incoherence problem in ethics and epistemology. It then sets out the collapse problem for rule-consequentialist approaches in ethics, truth-directed accounts of justification in epistemology, and epistemological approaches to argument cogency. The chapter closes with discussion of two potential solutions to the problem. (shrink)

The consequences of Quine's criterion of ontological commitment epitomized in his treatment of the term 'Pegasus' in "On What There Is" are evaluated in terms of Quine's own work, in particular in "The Variable" and "Variables Explained Away". There is a cost to maintaining this criterion with regard to the empirical consequences of some non-existent objects, given considerations prompted by Quine's holism. This cost can be reduced by adopting a noneist position according to which non-existent objects can be values of (...) bound variables as well. (shrink)

Communication and content presents a comprehensive and foundational account of meaning based on new versions of situation theory and game theory. The literal and implied meanings of an utterance are derived from first principles assuming little more than the partial rationality of interacting agents. New analyses of a number of diverse phenomena – a wide notion of ambiguity and content encompassing phonetics, syntax, semantics, pragmatics, and beyond, vagueness, convention and conventional meaning, indeterminacy, universality, the role of truth in communication, semantic (...) change, translation, Frege’s puzzle of informative identities – are developed. Communication, speaker meaning, and reference are defined. Frege’s context and compositional principles are generalized and reconciled in a fixed-point principle, and a detailed critique of Grice, several aspects of Lewis, and some aspects of the Romantic conception of meaning are offered. Connections with other branches of linguistics, especially psycholinguistics, sociolinguistics, historical linguistics, and natural language processing, are explored. -/- The book will be of interest to scholars in philosophy, linguistics, artificial intelligence, and cognitive science. It should also interest readers in related fields like literary and cultural theory and the social sciences. (shrink)

Up to the introduction of the term and concept of incommensurability by T. S. Kuhn and P. K. Feyerabend in the early 1960s, scientific texts were supposed to pose no problem as regards their translation, unlike literature, which was thought very difficult to translate. After the introduction of the term, translation of scientific language became equally problematic because, due to conceptual and perceptual incommensurability, there was no common observation basis to ground linguistic equivalences between languages of incommensurable paradigms. This article (...) highlights the presuppositions that link incommensurability to dramatic consequences (impossibility of communication, translation, and comparative evaluation of paradigms) and tries to sketch an alternative way of understanding incommensurability and translation drawing on Kuhn’s work. From this perspective, translation is not an all-or-nothing affair for either science or literature and becomes a problem to be solved for each particular set of circumstances. (shrink)

This article highlights the long accomplishments of Claude Sumner, S.J. in the field of African philosophy. During his lifetime he published over 33 books and 184 articles. He lived and worked in Ethiopia for 44 years. He translated into English and analysed several key historical works in Ethiopian philosophy, written originally in Ge’ez. He argued that modern rationalist philosophy began in Africa with Zera Yacob at the same time that it began in France with Descartes. He then set to work (...) recording and analyzing oral philosophical sources found in proverbs and songs. He theorized on the definitions of philosophy and the methods to explore philosophy found in different sources. (shrink)

Quine's views on ontology and naturalism are well-known but rarely considered in tandem. According to my interpretation the connection between them is vital. I read Quine as a global epistemic structuralist. Quine thought we only ever know objects qua solutions to puzzles about significant intersections in observations. Objects are always accessed descriptively, via their roles in our best theory. Quine's Kant lectures contain an early version of epistemic structuralism with uncharacteristic remarks about the mental. Here Quine embraces mitigated anomalous monism, (...) allowing introspection and the availability in principle of full physical descriptions of the perceptual states which get science off the ground. Later versions abandon these ideas. My epistemic-structural interpretation explains why. I argue first-personal introspective access to mental states is incompatible with global epistemic structuralism. (shrink)

The culture-economy dialectic (CED) – the opposition of the concepts and phenomena of culture and economy – is one of the most important ideas in the modern history of ideas. Both disciplinary boundaries and much theoretical thought in social science are strongly influenced or even determined by the CED. For that reason, a thorough analysis and evaluation of the CED is needed to improve understanding of the history of ideas in social science and the currently fashionable research on the cultural (...) influences on economic differences between countries and regions. This thesis is an attempt to do just that. The concepts of “culture” and “economy” (and related concepts) and the (assumed) relations therebetween are compared and analyzed. Empirical results from earlier studies are summarized and some new test are presented. These new tests are partly based on a measurement of Dutch regional culture. However, most theories of the CED are (nearly) impossible to verify (empirically). There appears to be some influence of wealth on specific cultural phenomena (such as individualism and post-materialism), but the often assumed influence of culture on entrepreneurship and economic growth remains unconfirmed. Moreover, from an analysis of the theories themselves, it appears that most of these cannot be falsified and are, therefore, hardly 'scientific'. Many of the theories of the CED and, in fact, many theories of social science in general are of a conceptual rather than a causal nature. These theories cannot be falsified (or verified) by empirical means alone, but must be studied by means of conceptual analysis. In the final conclusions, this thesis, therefore, argues for conceptual analysis in – and a more anarchist approach to – social science. (shrink)

In his “Wissenschaftslogik: The Role of Logic in the Philosophy of Science,” Michael Friedman argues that Carnap’s philosophy of science “is fundamentally anti-metaphysical—he aims to use the tools of mathematical logic to dissolve rather [than] solve traditional philosophical problems—and it is precisely this point that is missed by his logically-minded contemporaries such as Hempel and Quine”. In this paper, I take issue with this claim, arguing that Quine, too, is a part of this anti-metaphysical tradition. I begin in section I (...) with Russell’s account of scientific philosophy, focusing on its critique of metaphysics and its reliance on logical constructions. I then argue that each of Carnap and Quine take up this call to scientific philosophizing but that they both find Russell’s account of logic wanting. In section II, I first provide an account of Carnap’s critique of metaphysics and its reliance on developments in logic. This is followed by a discussion of his appeal to the analytic/synthetic distinction so as to improve upon Russell’s account of logic. Section III follows this same structure but focuses on Quine. In the end, though, Quine turns not to the analytic/synthetic distinction but to holism to provide an account of logic suitable to scientific philosophy. Carnap had claimed to be “more Russellian than Russell,” and in this final move by Quine I argue that he is “being more Carnapian than Carnap.” I conclude by showing how, contrary to Friedman’s view, Quine’s rejection of the analytic/synthetic distinction does not yield a return to the kind metaphysics that he, Carnap, and Russell all objected to. (shrink)

I defend the view that linguistic meaning is a relation borne by an expression to a type of speech act, and that this relation holds in virtue of our overlapping communicative dispositions, and not in virtue of linguistic conventions. I argue that this theory gives the right account of the semantics–pragmatics interface and the best-available semantics for non-declarative clauses, and show that it allows for the construction of a rigorous compositional semantic theory with greater explanatory power than both truth-conditional and (...) dynamic semantics. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

What is the role of the environment, and of the information it provides, in cognition? More specifically, may there be a role for certain artefacts to play in this context? These are questions that motivate "4E" theories of cognition (as being embodied, embedded, extended, enactive). In his take on that family of views, Hajo Greif first defends and refines a concept of information as primarily natural, environmentally embedded in character, which had been eclipsed by information-processing views of cognition. He continues (...) with an inquiry into the cognitive bearing of some artefacts that are sometimes referred to as 'intelligent environments'. Without necessarily having much to do with Artificial Intelligence, such artefacts may ultimately modify our informational environments. -/- With respect to human cognition, the most notable effect of digital computers is not that they might be able, or become able, to think but that they alter the way we perceive, think and act. (shrink)

Contemporary analytic philosophy is dominated by metaphilosophical naturalism, the view that philosophy ought to be continuous with science. This naturalistic turn is for a significant part due to the work of W. V. Quine. Yet, the development and the reception of Quine’s naturalism have never been systematically studied. In this paper, I examine Quine’s evolving naturalism as well as the reception of his views. Scrutinizing a large set of unpublished notes, correspondence, drafts, papers, and lectures as well as published responses (...) to Quine’s work, I show how both internal tensions and external criticisms forced him to continuously develop, rebrand, and refine his metaphilosophy before he explicitly decided to label his view ‘naturalism’ in the late 1960s. (shrink)

During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...) follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. -/- This book offers a comprehensive study of Quine’s naturalism. Building on Quine’s published corpus as well as thousands of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, this book aims to reconstruct both the nature (chapters 2-4) and the development (chapter 5-7) of his naturalism. As such, this book aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. (shrink)

RESUMEN: Si remitimos la dialéctica a su punto de partida socrático, es decir, a un método puramente interrogativo, hemos de comprender la aporia en un sentido radical: lejos de deberse a factores subjetivos o existenciales tales como la ignorancia de la respuesta, la aporia propiamente dicha es una cuestión que objetivamente no se puede decidir, pero que sin embargo, paradójicamente, no puede ser superada sino a través de una decisión. Se pone de manifiesto aquí que la cuestión del sentido de (...) ser, básico en la metafísica desde Aristóteles, presenta este carácter de manera ejemplar. ABSTRACT: If we bring dialectics back to its socratic origin, i.e. to a purely interrogative method, we are at the same time led to take aporia in a radical far from being due to such subjective or existential factors as the ignorance of the answer, aporia is, strictly speaking, a question that objectively cannot be settled in one sens more than in another- to the effect that, paradoxically, it is a question upon which one has necessarily and only to decide. The point here is that the question, basic to metaphysics from Aristotle onwards, «What does mean being?» presents this character in a paradigmatic way. (shrink)

ABSTRACT Historical structuralist views have been ontological. They either deny that there are any mathematical objects or they maintain that mathematical objects are structures or positions in them. Non-ontological structuralism offers no account of the nature of mathematical objects. My own structuralism has evolved from an early sui generis version to a non-ontological version that embraces Quine’s doctrine of ontological relativity. In this paper I further develop and explain this view.

It is often held to be definitive of consciousness that there is something it is like to be in a conscious state. A consensus has arisen that ‘is like’ in relevant ‘what it is like’ locutions does not mean ‘resembles’. This paper argues that the consensus is mistaken. It is argued that a recently proposed ‘affective’ analysis of these locutions fails, but that a purported rival of the resemblance analysis, the property account, is in fact compatible with it. Some of (...) the implications of this argument are briefly explored: it is suggested that the meaning of ‘what it’s like’ does not, in itself, have any special bearing on consciousness, and that the implications for the so-called ‘hard problem’ of consciousness are deflationary. (shrink)

In this paper, I discuss Quine’s views on language sharing and linguistic communities. It is sometimes explicitly and often implicitly taken for granted that Quine believes that speakers can form communities in which they share a language. The aim of the paper is to show that this is a misinterpretation and, on the contrary, Quine is closer to linguistic individualism – the view according to which there is no guarantee that speakers within a community share a language and the notion (...) of idiolect is more fundamental than the notion of shared language. (shrink)

The purpose of this paper is to argue that however impressive and useful its results, neuroscience alone does not provide a complete theory of mind. We specifically enlist John Dewey to help dispel the notion that the mind is the brain. In doing so, we explore functionalism to clarify Dewey’s modified functionalist stance and argue for avoiding “the mereological fallacy.” Mereology is the study of part-whole relations. The mereological fallacy arises from confusing the properties of a necessary subfunction with the (...) properties that derive from the unity of the whole functional coordination. We conclude that the mind is a complex distributed biologicalsociocultural function that is not simply located anywhere and, therefore, is not completely in the possession of any one : it occurs wherever it has consequences. (shrink)

Evolutionary reliabilism is the view that natural selection likely favoured reliable cognitive faculties in humans. While ER enjoys some plausibility, Stephen Stich and Alvin Plantinga have presented well-known challenges to the view. Their arguments rely on a common premiss; namely, that natural selection is indifferent to truth. This article shows that this premiss is both imprecise and too weak to support their conclusions and, therefore, that their challenges to ER fail.

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...) abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

Logic is often conceived as a science of propositions, or of relations between propositions. There is an alternative view, however, defended by Meinong, Pfänder, Reinach and others, which sees logic as a science of “Sachverhalte” or states of affairs. A consideration of this view, which was defended especially by thinkers within the tradition of Brentano, throws new light on the problems of intentionality and of mental content. It throws light also on the development of logic in Poland. Here the influence (...) of Brentano’s student Kasimir Twardowski is especially important, and the paper concludes with a new interpretation of Tarski’s work on truth against the background of Twardowski’s thinking. (shrink)

The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. (...) In what follows we show that the supervaluationist approach to singular reference, when wedded to the truthmaker idea, yields a framework of surprising power, which offers a uniform set of solutions to a range of problems regarding identity, reference and knowledge, problems which have hitherto been dealt with on an ad hoc basis. (shrink)

Thanks to David Kaplan, we all know how to handle indexicals like ‘I’. ‘I’ doesn’t refer to an object simpliciter; rather, it refers to an object only relative to a context. In particular, relative to a context C, ‘I’ refers to the agent of C. Since different contexts can have different agents, ‘I’ can refer to different objects relative to different contexts. For example, relative to a context c whose agent is Gottlob Frege, ‘I’ refers to Frege; relative to a (...) context c* whose agent is Alexius Meinong, ‘I’ refers to Meinong. (shrink)

The modalities come into the world by being projections or objectivizations of our epistemic constitution. Thus this paper is a statement of Humean projectivism. In fact, it goes beyond Simon Blackburn’s version. It is also designed as a comprehensive counter-program to David Lewis’ program of Humean supervenience. In detail, the paper explains: Already the basic fact that the world is a world of states of affairs is due to the nature of our epistemic states. Objects, which figure in states of (...) affairs and which embody metaphysical modality, are constitutable by their essential properties and in fact constituted by us according to our ontological policies. What the facts are, to which the correspondence notion of truth refers, is determined by applying an epistemic or pragmatic notion of truth to the world. Causation is a specific objectivization of our conditional beliefs. Nomicity is a ‘habit of belief’, a specific way of generalizing epistemic attitudes. This covers the basic metaphysical and natural modalities. The paper attempts to convey that talking of projection or objectivization is not just imagery, but a constructively realizable program. (shrink)

I consider two competing approaches to metasemantics: productivism, whereby endowment with semantic significance emerges directly from conditions surrounding the production or employment of the items semantically endowed; and interpretationism, whereby endowment with semantic significance emerges directly from conditions surrounding the interpretive consumption of such items. Focusing on the version of interpretationism developed by Lewis and his followers, I present a novel argument to the conclusion that such an approach cannot secure determinacy for singular reference. I then draw a larger moral (...) for metasemantics and its relation to truth-conditional semantics. (shrink)

This essay argues that deflationism is incompatible with the phenomenon of referential indeterminacy. This puts the deflationist in the difficult position of having to deny the possibility of what otherwise seems like a manifest and theoretically important phenomenon. Section 1 provides background on deflationism. Section 2 considers an intuitive argument by Stephen Leeds to the effect that deflationism precludes RI; the essay argues that this argument does not succeed. The rest of the essay presents its own, distinct argument for the (...) incompatibility of deflationism and RI. Section 3 argues that direct RI—RI that is not simply a derivative of some other, nonreferential instance of indeterminacy—is strictly incompatible with deflationism. Section 4 considers a couple of different ways the deflationist might try to achieve indirect RI—via indeterminate identity and indeterminate synonymy—and argues that each is unsatisfactory. (shrink)

This volume - the joint effort of the research groups on practical philosophy and the history of political thought of the Institute of Philosophy of the Research Centre for the Humanities of the Hungarian Academy of Sciences - brings together scholarly essays that attempt to face the challenges of the contemporary situation. The authors come from rather divergent disciplinary backgrounds, including philosophy, law, history, literature and the social sciences, from different cultural and political contexts, including Central, Eastern and Western Europe, (...) and belong to different generations. But they all share an interest to bravely answer the large topical issues concerning universal morality, here and now. (shrink)

Paul Horwich is aware of the fact that his theory as stated in his works is directly applicable only to a language in which a word, understood as a syntactic type, is connected with exactly one literal meaning. Yet he claims that the theory is expandable to include homonymy and indexicality and thus may be considered as applicable to natural language. My concern in this paper is with yet another kind of ambiguity—systematic polysemy—that assigns multiple meanings to one linguistic type. (...) I want to combine the characteristics of systematic polysemy with the Kaplanian insight that meanings of expressions may be defined by semantic rules which assign content in context and to ask the question if minimalism about truth and meaning is compatible with such rule-based systematic polysemy. I will first explain why the expressions that exhibit rule-based systematic polysemy are difficult to combine with a truth theory that is based on a use theory of meaning before proceeding to argue that indexicals and proper names are such expressions. (shrink)

In this note I present a solution to Kripkenstein’s paradox, based on a very simple argument: (1) natural language and rule-following are empirical phenomena; (2) no case has been described, in real life, of a person who behaves as Wittgenstein’s or Kripke’s fictional character; (3) therefore, the discussion of such a case is completely devoid of interest. I lay out the example of a ‘Kripkensteinian apple’, which has a normal weight on even days and is weightless on odd days, in (...) order to highlight the contrast between a genuinely empirical perspective, such as that of physics, and the logical-analytical perspective, under which Kripkenstein’s paradox has attracted so much attention. (shrink)

Much recent work in metaontology challenges the so-called ‘Quinean tradition’ in metaphysics. Especially prominently, Amie Thomasson argues for a highly permissive ontology over ontologies which eliminate many entities. I am concerned with disputing not her ontological claim, but the methodology behind her rejection of eliminativism – I focus on ordinary objects. Thomasson thinks that by endorsing the Quinean criterion of ontological commitment eliminativism goes wrong; a theory eschewing quantification over a kind may nonetheless be committed to its existence. I argue (...) that, contrary to Thomasson's claims, we should retain the Quinean criterion. Her arguments show that many eliminativist positions are flawed, but their flaws lie elsewhere: the Quinean criterion is innocent. Showing why reveals the importance of pragmatism in ontology. In §1 I compare Thomasson's account and the eliminativist views to which it stands in opposition. In §2 I re-construct Thomasson's reasons for rejecting the Quinean criterion. In §3 I defend the Quinean criterion, showing that the eliminativists’ flaws are not consequences of applying the Quinean criterion, before explaining the criterion's importance when properly understood. I conclude that Thomasson, though right to criticise the methodology of ordinary-object eliminativists, is wrong to identify the Quinean criterion as the source of their mistake. (shrink)

Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, to undermine Ishiguro’s (...) interpretation. Leibniz frequently writes that his infinitesimals are useful fictions, and we agree, but we show that it is best not to understand them as logical fictions; instead, they are better understood as pure fictions. (shrink)

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)