In the final chapter of their book A Subject With No Object, John Burgess and Gideon Rosen raise the question of the value of the nominalistic reconstructions of mathematics that have been put forward in recent years, asking specifically what this body of work is good for. The authors conclude that these reconstructions are all inferior to current versions of mathematics (or science) and make no advances in science. This paper investigates the reasoning that led to such a negative (...) appraisal, and it produces a rebuttal to this reasoning. I am grateful to the following mathematicians who were kind enough to provide me with their thoughts about nonstandard analysis: Martin Davis, Laura Chihara, Ted Chihara, Steve Galovich, Bonnie Gold, and especially Roger Simons, whose comments about an earlier version of this paper were very helpful. Thanks also go to two referees for their useful suggestions and criticisms of an earlier version of this paper. (shrink)

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.

1. 1. PROGRAM It will be our aim to reconstruct, with precision, certain views which have been traditionally associated with nominalism and to investigate problems arising from these views in the construction of interpreted formal systems. Several such systems are developed in accordance with the demand that the sentences of a system which is acceptable to a nominalist must not imply the existence of any entities other than individuals. Emphasis will be placed on the constructionist method of philosophical analysis. To (...) follow this method is to introduce the central notions of the subject-matter to be investigated into a system governed by exact rules. For example, the constructionist method of investigating the properties of geometric figures may consist in formulating a system of postulates and definitions which, together with the apparatus of formal logic, generates all necessary truths concerning geometric figures. Similarly, a constructionist analysis of the notion of an individual may take the form of an axiomatic theory whose provable assertions are just those which seem essential to the role played by the concept of an individual in system atic contexts. Such axiomatic theories gain in interest if they are supple mented by precise semantical rules specifying the denotation of all terms and the truth conditions of all sentences of the theory. (shrink)

In the last 30 years there has been growing interest in and a greater appreciation of the unique contributions that medieval authors have made to the history of logic. In this thesis, we compare and contrast the modal logics of Robert Kilwardby and John Buridan and explore how their two conceptions of modality relate to and differ from modern notions of modal logic. We develop formal reconstructions of both authors' logics, making use of a number of different formal techniques. In (...) the case of Robert Kilwardby we show that using his distinction between per se and per accidens modalities, he is able to provide a consistent interpretation of the apodictic fragment of Aristotle's modal syllogism and that, by generalising this distinction to hypothetical construction, he can develop an account of connexive logic. In the case of John Buridan we show that his modal logic is a natural extension of the usual Kripke-style possible worlds semantics, and that this modal logic can be shown to be sound and complete relative to a proof-theoretic formalisation of Buridan's treatment of the expository syllogism. (shrink)

It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.

Universals are properties that are shared by multiple objects. In classical South Asia, Brahmanical thinkers from Vyākaraṇa, Nyāya, Vaiśeṣika, and Mīmāṃsā text traditions were realists about universals, while most Buddhists were nominalists. In this paper, my aim is to reconstruct the early Nyāya-Vaiśeṣika theory of universals, with special emphasis on the arguments of the Nyāya philosopher Uddyotakara (6th century CE) against a Buddhist strand of resemblance nominalism. I show that Uddyotakara's contribution to this debate is twofold. First, he is possibly (...) the first Naiyāyika to adopt a sparse theory of universals, a theory according to which it is necessary to posit only those universals which explain how objects resemble each other in the most fundamental or irreducible respects. On the other hand, he offers a few arguments for realism, which are explicitly motivated by a causal constraint on intentionality. (shrink)

The thesis defends the legitimacy of a 'platonistic' metaphysic, according to which there exist non-spatiotemporal 'abstract' objects, against a series of recent nominalist challenges. After distinguishing the nominalism I intend to discuss from a range of distinct views with which it has been historically confused, I take up the core of the nominalist's challenge: the suggestion that abstract objects, if there were such things, would be incapable of causal interaction with us and our surroundings, and hence unknowable. I suggest that (...) every attempt to make this line of thought precise is either internally incoherent or depends upon an implausible conception of rational opinion. There is no a priori case for nominalism grounded in the theory of knowledge. I then take up Hartry Field's case for nominalism, which I take to be grounded in a broadly Quinean conception of philosophical and scientific methodology. And once again it is suggested that there is no way to develop the case in detail against the background of an independently plausible normative epistemology. Finally I take up one strand in the positive case for platonism: the 'Fregean' view that the existence of abstract objects is an analytic consequence of certain independently unproblematic states of affairs. I offer a reconstruction of certain arguments due to Crispin Wright, and tentatively endorse one development of this line of thought. If this is right, nominalism is not simply undermotivated: it is an essentially unstable account of what there is. (shrink)

: From 1902 onward, Peirce viewed esthetics, ethics, and logic as "normative sciences," interconnected spheres of philosophical inquiry that constitute his main work in value theory. The normative sciences provide the basis for a theoretical investigation of questions of value detached from practical interests. Because the normative sciences maintain Peirce's well-known insistence on realism, they set his pragmaticism apart from the more "nominalistic" pragmatism of James and Dewey. The paper aims to clarify Peirce's idea of the normative sciences, to (...) show how his realism applies in the sphere of value, and to explore his views on the proper relation between theory and practice. The concluding section suggests examples of how we might understand Peirce's rich and innovative concept of normative esthetics.Resumo: De 1902 em diante, Peirce considerava a estética, a ética e a lógica como "ciências normativas", esferas interconexas de inquirição filosófica que constituem seu principal trabalho em teoria do valor. As ciências normativas fornecem a base para uma investigação teorética de questões sobre valor independentes de interesses práticos. Porque as ciências normativas mantém a notória insistência de Peirce no realismo, elas colocam seu pragmaticismo à parte do pragmatismo mais "nominalista" de James e Dewey. O artigo almeja esclarecer a idéia de Peirce das ciências normativas, mostrar como seu realismo se aplica à esfera do valor, e explorar suas visões da própria relação entre ciência e prática. A seção concludente sugere exemplos de como podemos entender o rico e inovador conceito peirciano de estética normativa. (shrink)

In his book Philosophy of Logic, Putnam (1971) presents a short argument which reads like—and indeed, can be reconstructed as—a formal proof that a nominalistic physics is impossible. The aim of this paper is to examine Putnam’s proof and show that it is not compelling. The precise way in which the proof fails yields insight into the relation that a nominalistic physics should bear to standard physics and into Putnam’s indispensability argument.

Among the various testimonia assembled by Iwakuma and Ebbesen to the twelfth-century school of philosophers known as the Nominales,Iwakuma Yukio and Sten Ebbesen, “Logico -Theological Schools from the Secon d Half of the 12th Century: A List of Sources,” Vivarium XXX (1992):173–210. four record their commitment to the apparently outrageous thesis that nothing grows. My aim in this essay is to explore the reasons the Nominale s had for maintaining this thesis and to investigate the role that the theory which (...) supported it played in the development of late twelfth- and early thirteenth-century debates over the character of the hypostatic union. My investigation concerns onl y one aspect of twelfth-century NominalismSince this group were apparently the first ever to be called ‘nominalists’ I think that we may justifiably capitalize the name of the theory to indicate that we are referring to their version of it. but once this part of their system is understood, we will be better able to characterise the whole and the way in which the views of the Nominales conflicted with those of their opponents. S o long as the testimonia remain few and rather slight such a reconstruction offers our only hope for finding the Nominales and their influence where their name has not been recorded. (shrink)

The ten contributions in this volume range widely over topics in the philosophy of mathematics. The four papers in Part I (entitled "Set Theory, Inconsistency, and Measuring Theories") take up topics ranging from proposed resolutions to the paradoxes of naïve set theory, paraconsistent logics as applied to the early infinitesimal calculus, the notion of "purity of method" in the proof of mathematical results, and a reconstruction of Peano's axiom that no two distinct numbers have the same successor. Papers in (...) the second part ("The Challenge of Nominalism") concern the nominalistic thesis that there are no abstract objects. The two contributions in Part III ("Historical Background") consider the contributions of Mill, Frege, and Descartes to the philosophy of mathematics. (shrink)

Among the various testimonia assembled by Iwakuma and Ebbesen to the twelfth-century school of philosophers known as the Nominales,Iwakuma Yukio and Sten Ebbesen, “Logico -Theological Schools from the Secon d Half of the 12th Century: A List of Sources,” Vivarium XXX (1992):173–210. four record their commitment to the apparently outrageous thesis that nothing grows. My aim in this essay is to explore the reasons the Nominale s had for maintaining this thesis and to investigate the role that the theory which (...) supported it played in the development of late twelfth- and early thirteenth-century debates over the character of the hypostatic union. My investigation concerns onl y one aspect of twelfth-century NominalismSince this group were apparently the first ever to be called ‘nominalists’ I think that we may justifiably capitalize the name of the theory to indicate that we are referring to their version of it. but once this part of their system is understood, we will be better able to characterise the whole and the way in which the views of the Nominales conflicted with those of their opponents. S o long as the testimonia remain few and rather slight such a reconstruction offers our only hope for finding the Nominales and their influence where their name has not been recorded. (shrink)

Charles S. Peirce attempted to develop his semiotic theory of cognitive signs interpretation, which are originated in our basic perceptual operations that quasi-prove the truth of perceptual judgment representing reality. The essential problem was to explain how, by a cognitive interpretation of the sequence of perceptual signs, we can represent external physical reality and reflectively represent our cognitive mind’s operations of signs. With his phaneroscopy introspection, Peirce shows how, without going outside our cognitions, we can represent external reality. Hence Peirce (...) can avoid the Berkeleyian, Humean, and Kantian phenomenologies, as well as the modern analytic philosophy and hermeneutic phenomenology. Peirce showed that with the trio of semiotic interpretation – abductive logic of discovery of hypotheses, deductive logic of necessary inference, and inductive logic of evaluation – we can reach a complete proof of the true representation of reality. This semiotic logic of reasoning is the epistemic logic representing human confrontation in reality, with which we can achieve knowledge and conduct our behavior. However, Peirce did not complete his realistic revolution to eliminate previously accepted nominalistic and idealistic epistemologies of formal logic and pure mathematics. Here, I inquire why Peirce did not complete his historical realist epistemological revolution and following that inquiry I attempt to reconstruct it. (shrink)

At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of .

This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision (...) and clarity, and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink)

When I first began to take an interest in the debate over nominalism in philosophy of mathematics, some twenty-odd years ago, the issue had already been under discussion for about a half-century. The terms of the debate had been set: W. V. Quine and others had given “abstract,” “nominalism,” “ontology,” and “Platonism” their modern meanings. Nelson Goodman had launched the project of the nominalistic reconstruction of science, or of the mathematics used in science, in which Quine for a (...) time had joined him before turning against him. William Alston, Rudolf Carnap, and Michael Dummett had raised doubts about what the point of Goodman’s exercise could be, and though they had unfortunately been largely ignored, Quine’s contention that the exercise cannot be successfully completed had gained wide publicity as the so-called “indispensability” argument against nominalism. By contrast, two subtle discussions of Paul Benacerraf had been appropriated by nominalists and turned into the so-called “multiple reductions” and “epistemological” arguments for nominalism. (shrink)

According to the results of medieval studies, modern rationalism depends on late Medieval Age and medieval nominalism. Reconstructing some of Ockham's innovations it is possible to open a new view of the development of modern subjectivity: Ockham's ontological individualism, his thesis that unnecessary individuals are epistemologically prior to universals and that evident knowledge of individuals is possible, his theological nominalism and his expliction of God's omnipotence and his creation, his logic of supposition and the use of his ,,razor" are essential (...) innovations at the end of the Medieval Age. In this way, it can be substantiated, in contrast to the classical prejudicial view of history of philosophy, that the crystallization of modern subjectivity as a postmedieval rationalism was basically influenced by the innovations of Ockham's nominalism. (shrink)

During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard, holding regular private meetings, with Carnap, Tarski, and Quine. Carnap, Tarski, and Quine at Harvard allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap’s notes cover a wide range of topics, but surprisingly, the (...) most prominent question is: If the number of physical items in the universe is finite, what form should scientific discourse take? This question is closely connected to an abiding philosophical problem: What is the relationship between the logico-mathematical realm and the material realm? Carnap, Tarski, and Quine’s attempts to answer this question involve issues central to philosophy today.This book focuses on three such issues: nominalism, the unity of science, and analyticity. In short, the book reconstructs the lines of argument represented in these Harvard discussions, discusses their historical significance (especially Quine’s break from Carnap), and relates them when possible to contemporary treatments of these issues. (shrink)

ABSTRACT: I argue that Sellars’s metaconceptual theory of the categories exemplifies and extends a long line of nominalistic thinking about the nature of the categories from Ockham and Kant to the Tractatus and Carnap, and that this theory is far more central than has generally been realized to each of Sellars’s most famous and enduring philosophical conceptions: the myth of the given, the logical space of reasons, and resolving the ostensible clash between the manifest and scientific images of the (...) human being in the world. Sellars’s distinctive contribution to this longstanding (if currently on the defensive) metaconceptual approach to the nature of ontological categories was to interpret and reconstruct it in terms of his own ‘meaning as use’ or norm-governed inferential role semantics. With these resources Sellars sought to preserve the genuine insights in the ‘realist’ or broadly platonic traditions while simultaneously defending the idea that in the end, as he puts it, “a naturalistic ontology must be a nominalistic ontology” (1980a NAO IV §129). (shrink)

The purpose of this paper is to defend the so-called Ostrich Nominalism against the influential criticism that has been put forward by David M. Armstrong. First, I reconstruct Armstrong’s “One over Many” argument for universals (§§ 1-2), reviewing his main reasons for rejecting the foremost kinds of nominalism (§ 3). I then argue that Ostrich Nominalism has been underrated by Armstrong (§ 4) and that, consequently, his strategy for dealing with it results in misleading and elusive conclusions. I conclude that (...) Ostrich Nominalism represents an arduous challenge to Armstrong’s Realism in that it compels him either to give up his sparse Realism, or to acknowledge that all the solutions to the problem of universals are utterly meaningless (§§ 5-6). (shrink)

In this paper, I develop a new defense of logicism: one that combines logicism and nominalism. First, I defend the logicist approach from recent criticisms; in particular from the charge that a cruciai principie in the logicist reconstruction of arithmetic, Hume's Principle, is not analytic. In order to do that, I argue, it is crucial to understand the overall logicist approach as a nominalist view. I then indicate a way of extending the nominalist logicist approach beyond arithmetic. Finally, I (...) argue that a nominalist can use the resulting approach to provide a nominalization strategy for mathematics. In this way, mathematical structures can be introduced without ontological costs. And so, if this proposal is correct, we can say that ultimately all the nominalist needs is logic (and, rather loosely, ali the logicist needs is nominalism). (shrink)

The purpose of the present paper is to demonstrate a series of connections in terms of concepts and subjects between Ockham and Kant’s philosophical models that may provide a comprehensive framework for their respective insights on Law. Our main thesis postulates the existence of a continuum of certain fundamental assumptions derived from Nominalist theology and enlightened rationality that contribute to the essential unity of so-called “modern thought” and how such continuity is projected in the legal domain. In this sense, we (...) suggest the need to reflect upon the tacit Nominalism underlying Kantian criticism, which, although devoid of all theological premises, reconstructs metaphysics while preserving its basic scheme. In order to do so, our starting point is a very brief reference to the similarities between their respective theories of knowledge. We go on to analyze the structure behind moral actions according to Ockham and Kant’s doctrines. Finally, we point to certain founding principles and elements common to both doctrines in the field of legal-political thought. (shrink)

Fictionalist approaches to ontology have been an accepted part of philosophical methodology for some time now. On a fictionalist view, engaging in discourse that involves apparent reference to a realm of problematic entities is best viewed as engaging in a pretense. Although in reality, the problematic entities do not exist, according to the pretense we engage in when using the discourse, they do exist. In the vocabulary of Burgess and Rosen (1997, p. 6), a nominalist construal of a given discourse (...) is revolutionary just in case it involves a “reconstruction or revision” of the original discourse. Revolutionary approaches are therefore prescriptive. In contrast, a nominalist construal of a given discourse is hermeneutic just in case it is a nominalist construal of a discourse that is put forth as a hypothesis about how the discourse is in fact used; that is, hermeneutic approaches are descriptive. I will adopt Burgess and Rosen’s terminology to describe the two different spirits in which a fictionalist hypothesis in ontology might be advanced. Revolutionary fictionalism would involve admitting that while the problematic discourse does in fact involve literal reference to nonexistent entities, we ought to use the discourse in such a way that the reference is simply within the pretense. The hermeneutic fictionalist, in contrast, reads fictionalism into our actual use of the problematic discourse. According to her, normal use of the problematic discourse involves a pretense. According to the pretense, and only according to the pretense, there exist the objects to which the discourse would commit its users, were no pretense involved. My purpose in this paper is to argue that hermeneutic fictionalism is not a viable strategy in ontology. My argument proceeds in two steps. First, I discuss in detail several problematic consequences of any interesting application of hermeneutic fictionalism. Of course, if there is good evidence that hermeneutic fictionalism is correct in some cases, then some of these drastic consequences would have to be accepted.. (shrink)

This paper seeks to reconstruct an important controversy between leibniz and malebranche over innate ideas. It is argued that this controversy is in some ways more illuminating than the better-Known debate between leibniz and locke, For malebranche's objections to innate ideas raise fundamental questions concerning the status of dispositions and the relationship between logic and psychology. The paper shows that in order to meet malebranche's objections, Leibniz adopts a strategy which is doubly reductionist: ideas are reduced to dispositions to think (...) in certain ways, And these dispositions are in turn reduced to unconscious perceptions. It is suggested that malebranche's platonist commitment to the existence of abstract entities forces leibniz to reveal the extent of his nominalism. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) (...) is not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)

This paper contains a reconstruction and discussion of some central subjects in Nelson Goodman's philosophical work. Goodman's creative symbol-constructional philosophy concerns fundamental aspects of human cognition and practice. It is argued that this provides us with the intellectual tools for constructing a genuine relationship between logic, knowledge, art, and understanding. This is shown by focusing on subjects ranging from the projectibility of predicates and nominalistic mereology to constructive relativity, ways of worldmaking and a general theory of symbols.

In the twentieth century, we often think of Nietzsche, nihilism, and the death of God as inextricably connected. But, in this pathbreaking work, Michael Gillespie argues that Nietzsche, in fact, misunderstood nihilism, and that his misunderstanding has misled nearly all succeeding thought about the subject. Reconstructing nihilism's intellectual and spiritual origins before it was given its determinitive definition by Nietzsche, Gillespie focuses on the crucial turning points in the development of nihilism, from Ockham and the nominalist revolution to Descartes, Fichte, (...) the German Romantics, the Russian nihilists and Nietzsche himself. His analysis shows that nihilism is not the result of the death of God, as Nietzsche believed but the consequence of a new idea of God as a God of will who overturns all eternal standards of truth and justice. To understand nihilism, one has to understand how this notion of God came to inform a new notion of man and nature, one that puts will in place of reason, and freedom in place of necessity and order. (shrink)

In this chapter, we offer a reconstruction of the evolution of Leibniz’s thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability, and syncategorematicity, and the closely related question of the possibility of infinitesimal quantities, both in physics and in mathematics.Some scholars have argued that syncategorematicity is a mature acquisition, to which Leibniz resorts to solve the question of his infinitesimals – namely the idea that infinitesimals are just signs for Archimedean exhaustions, and their (...) unassignability is a nominalist maneuver. On the contrary, we show that syncategorematicity, as a traditional idea of classical scholasticism, is a feature of young Leibniz’s thinking, from which he moves away in order to solve the same problem, as he gains mathematical knowledge.We have divided Leibniz’s path toward his mature view of infinitesimals into five phases, which are especially significant for reconstructing the entire evolution. In our reconstruction, an important role is played by Leibniz’s text De Quadratura Arithmetica. Based on this and other texts, we dispute the thesis that fictionality coincides with syncategorematicity, and that unassignability can be bypassed. (In this chapter, we employ “syncategorematic” as a shorthand for “eventually identifiable with a procedure of exhaustion” and, as a consequence, “involving only assignable quantities.” We also identify syncategorematicity with potentiality, as suggested by some part of the scholastics, and in Sect. 2.2, we show that the two characterizations are equivalent, provided that “potentiality” is intended in the correct way: namely as in the unending iterative procedures of Greek mathematics.) On the contrary, we maintain that unassignability, as incompatible with the principle of harmony, is the ultimate reason for the fictionality of infinitesimals. (shrink)

Excerpt from Erkennen und Wissen nach Gregor von Rimini: Ein Beitrag zur Geschichte der Erkenntnistheorie des Nominalismus Krebs engelbert, Theologie und Wissenschaft nach der Lehre der Hoch scholastik (beitrage XI, 3 Munchen 1912. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the (...) aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.". (shrink)

Are there any universal entities? Or is the world populated only by particular things? The problem of universals is one of the most fascinating and enduring topics in the history of metaphysics, with roots in ancient and medieval philosophy. This collection of new essays provides an innovative overview of the contemporary debate on universals. Rather than focusing exclusively on the traditional opposition between realism and nominalism, the contributors explore the complexity of the debate and illustrate a broad range of positions (...) within both the realist and the nominalist camps. Realism is viewed through the lens of the distinction between constituent and relational ontologies, while nominalism is reconstructed in light of the controversy over the notion of trope. The result is a fresh picture of contemporary metaphysics, in which traditional strategies of dealing with the problem of universals are both reaffirmed and called into question. (shrink)

During the past several decades, linguists have developed and applied widely techniques which enable them, to a considerable extent, to determine and state the structure of natural languages without semantic reference. It is of interest to inquire seriously into the formality of linguistic method and the adequacy of whatever part of it can be made purely formal, and to examine the possibilities of applying it, as has occasionally been suggested,s to a wider range of problems. In order to pursue these (...) aims it is first necessary to reconstruct carefully the set of procedures by which the linguist derives the statements of a linguistic grammar from the behaviour of language users, distinguishing clearly between formal and experimental in such a way that grammatical notions, appearing as definienda in a constructional system, wM be formally derivable for any language from a fixed sample of linguistic material upon which the primitives of the system are experimentally defined. The present paper will be an attempt to formalize a certain parts of the linguist's generalized syntax language. From another point of view, this paper is an attempt to develop an adequate notion of syntactic category within an inscriptional nominalistic framework. The inscriptional approach seems natural for linguistics, particularly in view of the fact that an adequate extension of the results of this paper will have to deal with the problem of homonymity, i.e., with a statement of the conditions under which tokens of the same type must be assigned to different syntactic classes. It will appear below that the calculus of individuals can often supply quite simple solutions to constructional.. (shrink)

Invoking a form of quantifier variance promises to let us explain mathematicians’ freedom to introduce new kinds of mathematical objects in a way that avoids some problems for standard platonist and nominalist views. In this paper I’ll note that, despite traditional associations between quantifier variance and Carnapian rejection of metaphysics, Siderian realists about metaphysics can naturally be quantifier variantists. Unfortunately a variant on the Quinean indispensability argument concerning grounding seems to pose a problem for philosophers who accept this hybrid. However (...) I will charitably reconstruct this problem and then argue for optimism about solving it. (shrink)

Ever since Charles Darwin's On the Origin of Species was published, the received view has been that Darwin literally thought of species as not extra-mentally real. In 1969 Michael Ghiselin upset the received view by interpreting Darwin to mean that species taxa are indeed real but not the species category. In 1985 John Beatty took Ghiselin's thesis a step further by providing a strategy theory to explain why Darwin would say one thing (his repeated nominalistic definition of species) and (...) do another (hold that species taxa are real). In the present paper I attempt to take this line of interpretation to a new level. Guided by the principle of charity, I provide and analyze a considerable amount of evidence from Darwin's mature writings (both private and published) to show that (contra Ghiselin and Beatty) Darwin did not simply accept the species delimitations of his fellow naturalists but actually employed, repeatedly and consistently, a species concept in a thoroughly modern sense, albeit with an implicit definition, a concept uniquely his own and fully in accord with his theory of evolution by natural selection. This implicit concept and definition is carefully reconstructed in the present paper. A new strategy theory is then provided to account for why Darwin would define species (both taxa and category) nominalistically on the one hand but delimit species realistically on the other. (shrink)

This paper investigates the reason why, in the tradition of Western philosophy, a logic of relations was developed only in the second half of the nineteenth century. To this end, it moves along two different but interconnected paths: on the one hand, it attempts to reconstruct the main views concerning the ontology of relations during the middle ages; on the other, it focuses on the treatment of so-called oblique terms in the logical works of some preeminent authors belonging to the (...) scholastic and late-scholastic tradition. From the ontological point of view, realists and nominalist both denied that polyadic expressions of the language signify polyadic properties in the world extra. Some authors, such as Peter Auriol, claimed that polyadic expressions signify something merely mental, thus recognizing, even though in a limited ontological domain, the existence of full-fledged relations, that is, of ‘things’ simultaneousl... (shrink)

This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language – and specifically, the ability to institute conventions for the truth conditions of sentences. This philosophical stance leads to an alternative way of practicing mathematics: instead of “building” objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory. Semantic (...) conventionalism is justified first through criticism of Cantorian set theory, intuitionism, logicism, and predicativism; then on its own terms; and finally, exemplified by a detailed reconstruction of arithmetic and real analysis. Also included is a simple solution to the liar paradox and the other paradoxes that have traditionally been recognized as semantic. And since it is argued that mathematics is semantics, this solution also applies to Russell’s paradox and the other mathematical paradoxes of self-reference. In addition to philosophers who care about the metaphysics and epistemology of mathematics or the paradoxes of self-reference, this book should appeal to mathematicians interested in alternative approaches. (shrink)

`Proto-idea' was a central concept in the thinking of the Polish microbiologist and philosopher of science Ludwik Fleck (1896–1961). Based on studies of the origin of the modern concept of syphilis, Fleck claimed that many established scientific facts are best understood as interpretations of pre scientific, somewhat hazy `proto-ideas' in the framework of a certain `thought-style'. As an example,Fleck saw the modern knowledge of infection as an interpretation of the ancient proto-idea of diseases as caused by minute `animalcules'. However, the (...) epistemological aspects of the concept of proto-ideas have only been sparsely developed and discussed by Fleck and his critics. This paper attempts to bridge the gap. Firstly, I reconstruct the concept of proto-ideasin the context of Fleck's constructivist theory of knowledge. Secondly, I illustrate the relation between Fleck's concept of proto-ideas and his nominalist view on medical taxonomy. Finally, I discuss four philosophical problems implied by Fleck's concept of proto-ideas: (a) the problem of combining two conflicting perspectives on the history of science (b) the problem of accounting for the notion of` continuity' within a non realist theory of knowledge (c) the problem of ascribing no truth-content to proto-ideas, and (d) the problem concerning the non-neutrality of the analyst's viewpoint. (shrink)

The aim of my dissertation is to investigate how universal concepts are formed according to the later medieval Franciscan theologian Peter Auriol (d. 1322). Specifically, in the dissertation I inquiry into the relation between Auriol's ontology - according to which only individuals, and not universals, have real, extra-mental existence - and his philosophical psychology, a study of how extra-mental particulars can give rise to universal concepts, according to Auriol's view. In the past academic year I refined the topic of my (...) PhD thesis in two ways : first, I have delineated the definitive table of content ; second, I have wrote down the results of my research. The thesis comprises two volumes. The second one contains a collation of Peter Auriol's,Reportatio II, d. 9, qq. 2 - 3. The text has been obtained by confronting two manuscripts, considered as the exemplars of the two main families that convey his Second Book of the Sentences: ms. Firenze, Biblioteca nazionale centrale, ms. conv. soppr. A.3.120 (Fb); (iii) il ms. Padova, Biblioteca Antoniana, ms. 161 scaff. IX (Pg). The first volume, instead, has been divided into five chapters: the first two offer a historical introduction, while the remaining three are dedicated to the study of Auriol's doctrine, starting from the analysis of the text proposed in the collation, then extending the investigation to all the documentary heritage available relating to the Franciscan master. The first chapter provides a survey of the main theories of the universals of the early fourteenth century, taking into account in particular the opinions of those thinkers who, like Duns Scotus, in addition to marking a philosophical era, have been significant for Auriol's developing of his theory of universals. These are: John Duns Scotus, Henry of Harclay, Walter Bulery and Hervaeus Natalis. In order to properly understand the philosophical proposal of the Doctor facundus, it is necessary to know how it fits into a debate that in the academic debate of the fourteenth century. The second chapter is mainly aimed at the identification of the sources of Rep. II, d. 9, qq. 2 - 3. In the quaestio secunda, Auriol deals with the foundation of the universals. In a.1, he discusses the opinion of multiwho he labels as 'platonic'. We tried, therefore, to detect the targets of his criticism. Burley, Wylton, Bacon, Duns Scotus have been identified as possible addresses. In a. 2 of the same question, Auriol analyzes the position of Duns Scotus on the common nature. It has been then hypothesized that the two articles - aa. 1-2 - has to be considered as a general presentation and specific case of it; as a thesis common to several forms of realism and the realism of one of its most important interpreters. The third chapter focuses Auriol's criticism of the different forms of realism reported in a. 1 and of Duns Scotus's theory, as it is found in a. 2. In both cases, Auriol reproaches the realists for breaking the unity of substance, into a multiplicity of formalitatesreally occurring in reand corresponding to the concepts of genus and difference. On the contrary, Auriol maintains that universal concepts have no unity in the extra-mental reality. Only individuals really exist and numerical unity the only fully existing unity. As a consequence, the unity of the universal concept is just similitudinaria,that is only given a concept. Successively, the criticisms that Auriol makes to the principle of individuation are considered. Generally speaking, everything that exists, insofar as it exists, is singular, according to him. It is a primitive fact and it is not, therefore, necessary to search for the causes of its individuation. Thus, mirroring the structure of the quaestio secunda, in q. 3, Auriol discusses, in the first place, Duns Scotus's position and secondly a group of theories, arisen during the scholastic debate between the end of the thirteenth and the beginning of the fourteenth century. Interestingly, to reconstruct this set of doctrines, Auriol follows almost literally the reconstruction that Scotus himself makes of the same theories in his Ordinatio. Now, relying on the assumption that everything that exists is individual, Auriol gives shape to the notions of individuality and singularity and their mutual difference. This is one of the hubs of the dissertation. According to Auriol, a singularity is an entity that does not admit the existence of other realities that can be considered as similar with it. In this sense, God is the only authentic singularity. Ordinary reality, on the other hand, is made up of individualities. An individuality is an entity that, being finite, does not exhaust in itself the totality of the species to which it belongs (as far as the species as such exists only in virtue of an act of the intellect), admits the existence of other realities conceivable as similar with it. Thus, inasmuch as reality is made up of individuals or individualities, the mind is able to form the corresponding universal concepts. Being finite, for Auriol, is the condition of the validity of universals. In this respect, the relation between the concept of individuality and that of singularity is taken into account. Subsequently, we analyze the function of the category of Quantity, as it is related to individuality. According to Auriol, Quantity has no individuating capacity. At most, in bodily substances, it functions as principle of distinction. Being, in fact, discrete realities, a material substance spatially ends where another one begins. The fourth chapter is a kind of juncture between the third one, in which the structure of the concrete individual is analyzed, and the fifth one, in which the cognitive side of the process of concept formation is discussed. What is discussed here are the rationes. According to Auriol, the rationesare the basic units that constitute the quiddity of each individual and serve to direct our thought to form certain concepts. Each concept is the concept of a ratio,indeed. In this respect, Auriol claims that, say, Socrates has the rationes substance, corporeality, sensitivity, rationality. Additionally, rationes of the same type occurring in different objects are "maximally similar" (simillimae). For example, the rationesof Socrates are utterly similar with those of Plato (Cf. Scriptum, d. 2, q. 1, a. 4). Therefore, although these rationes are non-universal characteristics - inasmuch as a ratio belongs to one and only one individual - due to their maximal similarity they do count as the extramental ground for our general concepts (Cf.II Sent., d. 9, q. 3, a. 1). According to these premises, Auriol can hold that different singulars can be mutually highly similar, without participating in the same common nature (Cf. II Sent., d. 9, q. 3, a. 3).At the same time, it is relevant to note these rationesdo not compromise the unity of an existing particular. Rather each ratiocoagulates into each other giving birth to the individual's ultimate ratio. This final ratiois an indivisible ratio (ratio atoma), which cannot be further specified or divided (II Sent., d. 9, q. 3). According to Auriol, then, the rationesqua rationesdo not exist in extra-mental reality. Rather, the exist as such only in virtue of an act of the intellect. This means that they have an ambiguous being. On the one hand, they indicate a nature that cannot be altered by the intellect. On the other, the need the mind's activity to exist as rationes. According to Auriol, therefore, the rationesare independent of any cognitive act, with regard to the content they express, while they depend on mind's activity with regard to their unity and their existence. Now, the opaqueness concerning the ontological consistency of rationesdirectly depends on Auriol's understanding of cognition. Chapter five mainly deals with the different stages of the process of formation of the universal concept. In this respect, the notion of impressiois what is firstly analyzed. The impressionescan be considered, for Auriol, as the rationesthat are 'deposited' in the intellect and constitute, in cooperation with the cognitive faculty, what the Franciscan theologian calls the actus intellectus. The intellectual act, according to Auriol, is an entity composed of the impressed similarity of the object and the intellectual power, in fact. Moreover, in his view, it is really identical to the intelligible species. Now, the identity that the Franciscan theologian establishes between these two noetic tools, which were traditionally considered as distinct, imposes a reinterpretation of the notion of species. Coinciding with the act, the species can no longer be considered as an entity juxtaposed to it, deputed to the activation of the cognitive process performed by the intellect. Indeed, all those theories of universal concepts that add other noetic tools to the act, be they a species, a quality, or something else, would necessarily compromise intellection, preventing it from having acquaintance with extra-mental reality. According to Auriol, considering intellectual cognition as a connotation allows us to avoid such inconveniences. According to this view, the intellectual cognition must be regarded as an activity that poses nothing but to allow something to appear to the cognizer. In this respect, the concept, for Auriol, is nothing but the real object qua appearingto the intellect, fully identical with the intellectual act in recto,while denominatively distinct in obliquo. In this perspective, the definition of intellection that the Franciscan theologian proposes is analyzed, trying, in particular, to determine the ontological status of the concept and its epistemological function. In conclusion, with this study we have tried to give an account of Auriol's philosophical attitude, of the scope of his theory of universals, focusing on the relationship between ontology and philosophical psychology. Using Auriol's texts and specifically the collation of Rep. II, d. 9, qq. 2 - 3, the answers to these questions were searched for in the words of the Franciscan theologian himself. The picture emerged is that of an autonomous, critical thinker, but perfectly inserted in the historical context in which he lives. A thinker who places himself, so to speak, halfway between Duns Scotus's realism and Ockham's nominalism, nevertheless succeeding, albeit with some opacity, in balancing an ontology in which the metaphysical priority is granted only to the individual and the universal concepts have a solid foundation and validity. (shrink)

Odo of Tournai, the Phoenix, and the Problem of Universals IRVEN M. RESNICK OVER THE PAST SEVERAL YEARS a good deal of attention has been focused on the philosophical literature of the late eleventh and early twelfth centuries in an attempt to locate the origins of nominalism? As part of this effort, several scholars have attempted to come to a new and better appreciation of one of the most vilified figures of the late eleventh century, namely Roscelin of Com- pi~gne, (...) whose logical doctrine, sometimes described as "proto-nominalism" or "vocalism, ''2 represents an early stage in the development of twelfth-century logical thought. Some have attempted simply to reconstruct, on the basis of the little material available to us that describes Roscelin's views, a less polemical and more coherent account of his theory of universals.3 Others have attempted to identify additional writings -- both published and unpublished -- that may prop- erly shed light on Roscelin's philosophy.4 All, however, would agree on Roscelin's significance for the history of philosophy at the beginning of the twelfth-century renaissance. Roscelin's importance does not necessarily presuppose his originality. Evi- ' This effort has resulted in the dedication of an entire number of Vivarium to the origin and meaning of twelfth-century nominalism. Cf. Vivarium 3o/1 . For a discussion of various doctrines on universals that emerged before Abelard, see Augustine Thompson, "The Debate.. (shrink)

The Question of Truth in Pedro da Fonseca: the Problem of the simplex apprehensio and the Foundation of Logical Identities. This article deals with the theory of truth in Pedro da Fonseca (1528-1599) as it is presented in his commentary on Aristotle’s Metaphysics (1577-1612). The first part of the paper is dedicated to Fonseca’s definition of intellective truth within the doctrinal topography of the Aristotelian tradition. The Author especially points out Fonseca’s attempt to justify the notion of a “simple” truth (...) of the “simple apprehension”, based on a specific use of Cajetan’s distinction between “signified act” and “exercised act” as well as on a (partially) nominalist account of the relationship between “simple” and “enunciative” concepts. The second part deals instead with Fonseca’s definition of transcendental truth, understood as the conformity between the intellect and the esse realis of the res, and as the conformity of the latter with exemplars in God’s mind. Here the Author also reconstructs Fonseca’s theory of divine ideas and his theory of logical identities. (shrink)

The object of this article is the scholastic inspirations found in the metaphysical disputation De principio individui by Gottfried Wilhelm Leibniz. The purpose ofthis study was, on one hand, a reconstruction of Leibniz’s theory concerning the principle of individuation, and on the other hand, a presentation of some texts by medieval scholastic authors (Henry of Ghent, Peter of Falco, Thomas Aquinas, Aegidius of Rome, Robert Kilwardby, William of Ockham) to whose ideas Leibniz refers in the named work, even though (...) he had, for the most part, only second-hand information concerning them. In his juvenile treatise, Leibniz states that the individuating principle has to be universal, which means relevant to all kinds of being; it has to be metaphysical in character and not merely epistemological. He regards individuality as synonymous with unity combined with difference. He resolutely takes sides with nominalism and rejects the reality of all kinds of universal beings and beings whose unity is weaker than numerical unity. As a consequence of this assumption, he rejects the conceptions in which the principle of individuation is formed by: double negation, existence or the haecceity. By contrast, he embraces the solution (close to the tradition originated by Ockham and also related to Suarez), according to which the whole entity (tota entitas) of an individual thing is the principle of individuation. In effect, for Leibniz, any real thing is simply singular, which comes down to the thesis that a thing is singular owing to its own metaphysical subcomponents, which are singular by themselves. (shrink)

Tianyi Zhang offers in this study an innovative philosophical reconstruction of Shihāb al-Dīn al-Suhrawardī's (d. 1191) Illuminationism. Commonly portrayed as either a theosophist or an Avicennian in disguise, Suhrawardīappears here as an original and hardheaded philosopher who adopts mysticism only as a tool of philosophical inquiry. Zhang makes use of Plato's cave allegory to explain Suhrawardī's Illuminationist project. Focusing on three areas-the theory of presential knowledge, the ontological discussion of mental considerations, and Light Metaphysics-Zhang convincingly reveals the Nominalist and (...) Existential nature of Illuminationism, and thereby proposes a new way of understanding how Suhrawardī's central philosophical ideas cohere. (shrink)

It is argued that, of the three distinct approaches usually adhered to in discussions of this controversy, none will produce an adequate reconstruction of the episode. The philosophical-methodological type of approach leads to a glossing over of the intricacies of deductive and inductive procedures inhering in the writings of both antagonists (§ 1). The metaphysical approach leads to oversimplification as to the thinking of either scientist on the problem of the continuous or discontinuous character of Nature(§ 2). The epistemological (...) (theory of knowledge) type of approach, finally, leads authors to posit a Linnaean realism vs. a Buffonian nominalism, whereas the true position was much more complex than what transpires(§ 3). The paper proceeds, therefore, to provide a novel reconstruction of this wellknown controversy (§ 4-5), concentrating on the differing choices made by the two naturalists in their work of botanical or zoological classification : thus seeking to show that the clash came about because Buffon rejected the rigid principle of character subordination put forward by Linnaeus, and, on a more general level, because the two protagonists were proceeding from deeply diverging views of what natural history, and what the naturalist's function, should be. (shrink)

I defend a reading of David Hume’s nominalism that he comes close to Keith Campbell's contemporary trope theory in the specific case of spatial properties. I argue that Hume's view should be construed as classifying spatial properties as Campbellian tropes (particular properties): abstract, particular, determinate and qualitatively simple properties. This has implications for reconstructing Hume's answer to the problem of universals. I argue that Hume’s account of objects resembling each other in respect of spatial properties is grounded in the resemblance (...) of tropes rather than in the resemblance of objects. (shrink)

A straightforward ontological account would be one which acknowledges relations as real beings, and that means, according to the scholastic tradition, as universals. The realist move in this sense which has been re-established within contemporary analytical ontology at least since Russell's early theory, is, however, not the only possible way to take relations seriously. In my paper I shall argue that there is much room for the ontological reconstruction of relations, even if one does not accept universals. The background (...) for this argument is a particularist and realist theory, based on tropes ("trope" being the short name for "property instance" or "individual quality"). One way of reconstruction is that relations themselves are particulars. They are supposed to be relational or polyadic tropes (J. Bacon, D. Mertz). The other way is to hold that relations are internal or formal, and therefore do not require a category sai generis (K. Mulligan, P. Simons). I shall discuss these alternatives and finally opt for the second, i.e., the reconstruction of relations as internal to their relata. Moreover, I offer an argument for why basic relations such as existential dependence should be granted a transcategorial status within trope ontology. Hence, the gist of my paper is to take relations seriously without falling prey either to stubborn nominalism or to strict realism. What I intend to explore is a middle avenue thereby choosing the best of both sides in order to explicate a moderate view on the realism of relations. (shrink)

This paper is an attempt to explicate, using the method of conceptual reconstruction rather than historical, text-oriented analysis, the plurality of meanings of two connected terms that play an important role in scholastic thought: “confusio” and “praecisio”. These terms are used in a plurality of meanings by the scholastics, and sometimes even in one and the same context. The aim of this paper is to disentangle these various meanings from each other, offer their precise definitions and explore not only (...) their interrelations, but also their role and impact in such crucial matters as theory of abstraction, realism-nominalism dispute, theory of science, or theory of analogy. (shrink)

G. E. Moore’s early essay, “The Nature of Judgment,” makes common cause with F. H. Bradley’s Principles of Logic against British empiricism’s characteristic view of judgment. But primarily it attacks positions Bradley and the empiricists share. I develop a fuller analysis of both aspects of “The Nature of Judgment” than has appeared. Bradley’s rejection of empiricist nominalism, I argue, enables him to develop what Moore considers a superior account of judgment to empiricism’s. But positions carried over from empiricism require Bradley (...) to seek all judgments’ truth conditions in existing circumstances, a result intolerable to Moore, who views mathematical and ethical judgments as being true independently of the world. Moore abandons Bradley’s vestigal empiricism, arguing that it leads invariably to self-contradiction. I reconstruct this argument, and draw out of it an unrecognized tension between the anti-empiricist and the anti-idealist themes of Moore’s early writings. (shrink)