The paper is concerned with the way in which “ontology” and “realism” are to be interpreted and applied so as to give us a deeper philosophical understanding of mathematical theories and practice. Rather than argue for or against some particular realistic position, I shall be concerned with possible coherent positions, their strengths and weaknesses. I shall also discuss related but different aspects of these problems. The terms in the title are the common thread that connects the various sections.

This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of (...) contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together well-known scholars and younger researchers, the essays in this collection – prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat) – show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to long-standing philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics – FilMat. (shrink)

Universalism (the thesis that distinct objects always compose a further object) has come under much scrutiny in recent years. What has been largely ignored is its role in the metaphysics of classes. Not only does universalism provide ways to deal with classes in a metaphysically pleasing fashion, its success on these grounds has been offered as a motivation for believing it. This paper argues that such treatments of classes can be achieved without universalism, examining theories from Goodman and Quine, Armstrong (...) and Lewis. In the case of each theory, universalism is drafted in to ensure that there are enough material objects to play a particular role. I argue that, for each theory, there's a better theory that ditches universalism and instead uses an alternative principle of composition demanding that the unrestricted composition of entities other than material objects (respectively: regions, states of affairs and singletons) play that role instead. I conclude that (1) non-universalists can consider accepting such theories of classes and (2) we should ignore any alleged motivation for universalism on the basis of dealing with classes. (shrink)

This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...) along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts. (shrink)

Non-Relational Realism is a popular solution to the Bradleyan regress of facts or truths. It denies that there is a relational universal of exemplification; for an object a to exemplify a universal F-ness, on this view, is not for a relation to subsist between a and F-ness. An influential objection to Non-Relational Realism is that it is unacceptably obscure. The author argues that Non-Relational Realism can be understood as a selective application of satisfaction semantics to predicates like ‘exemplify’, and that (...) so understood, it is not obscure. This kind of selective use of satisfaction semantics may be feasible in other contexts as a means of making theories more parsimonious. (shrink)

Carnap’s seminal ‘Empiricism, Semantics and Ontology’ makes important use of the notion of a framework and the related distinction between internal and external questions. But what exactly is a framework? And what role does the internal/external distinction play in Carnap’s metaontology? In an influential series of papers, Matti Eklund has recently defended a bracingly straightforward interpretation: A Carnapian framework, Eklund says, is just a natural language. To ask an internal question, then, is just to ask a question in, say, English. (...) To try to ask an external question is to try, absurdly, to ask a question in no language at all. Finding that so trivial an I/e distinction can’t help to explain Carnap’s deflationary metaontology, Eklund is led to attribute to Carnap a view he calls ontological pluralism. In this paper, I show that Eklund misreads Carnap, and I argue that this misreading obscures fundamental features of Carnap’s philosophy. I then defend an account of frameworks as what Carnap called semantical systems, and I place this account in the context of Carnap’s philosophical program of explication. Finally, I discuss the role that frameworks and the I/e distinction play in ESO, showing that ESO provides no reason to attribute the doctrine of ontological pluralism to Carnap. (shrink)

The view, in Quine, that all there are are pure sets is presented and endorsed.

As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing (...) the development of his views in the forties have recently begun to be published, as well as careful philosophical studies of, for instance, the evolution of his key doctrine that mathematical and logical truth are continuous with, not divorced from, the truths of natural science. But one central text has remained unexplored: Quine's Portuguese-language book on logic, his 'farewell for now' to the discipline as he embarked on an assignment in the Navy in WWII. Anglophone philosophers have neglected this book because they could not read it. Jointly with colleagues, I have completed the first full English translation of this book. In this accompanying paper I draw out the main philosophical contributions Quine made in the book, placing them in their historical context and relating them to Quine's overall philosophical development during the period. Besides significant developments in the evolution of Quine's views on meaning and analyticity, I argue, this book is also driven by Quine's indebtedness to Russell and Whitehead, Tarski, and Frege, and contains crucial developments in his thinking on philosophy of logic and ontology. This includes early versions of some arguments from 'On What There Is', four-dimensionalism, and virtual set theory. (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 problem that motivates me arises from a constellation of factors pulling in different, sometimes opposing directions. Simplifying, they are: (1) The complexity of the world; (2) Humans’ ambitious project of theoretical knowledge of the world; (3) The severe limitations of humans’ cognitive capacities; (4) The considerable intricacy of humans’ cognitive capacities . Given these circumstances, the question arises whether a serious notion of truth is applicable to human theories of the world. In particular, I am interested in the questions: (...) (a) Is a substantive standard of truth for human theories of the world possible? (b) What kind of standard would that be? (shrink)

Formal ontology as a main branch of metaphysics investigates categories of being. In the formal ontological approach to metaphysics, these ontological categories are analysed by ontological forms. This analysis, which we illustrate by some category systems, provides a tool to assess the clarity, exactness and intelligibility of different category systems or formal ontologies. We discuss critically different accounts of ontological form in the literature. Of ontological form, we propose a character- neutral relational account. In this metatheory, ontological forms of entities (...) are their standings in internal relations whose holding is neutral on the character of their relata. These relations are “formal ontological relations”. Entities belong to ontological categories because they stand in the same formal ontological relations. We hold a nominalist relationalism about ontological categories and forms. We conclude by showing that our metatheory is useful for understanding categorial fundamentality/non- fundamentality, different formal ontologies, and for unifying metaphysical questions. (shrink)

Similarity has long been excluded from reality in both the analytical and continental traditions. Because it exists in the aesthetic realm, and because aesthetics is thought to be divorced from objective reality, similarity has been confined to the prison of the subject. In The Being of Analogy, Noah Roderick unleashes similarity onto the world of objects. Inspired by object-oriented theories of causality, Roderick argues that similarity is ever present at the birth of new objects. This includes the emergent similarity of (...) new mental objects, such as categories—a phenomenon we recognize as analogy. Analogy, Roderick contends, is at the very heart of cognition and communication, and it is through analogy that we can begin dismantling the impossible wall between knowing and being. (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)

This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options (...) available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments. (shrink)

This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of mathematics. It belongs (...) to anti-realism, but can meet those challenges and can perhaps convince some realists, at least those who are also naturalists. (shrink)

Philosophers have tried to explain how science finds the truth by using new developments in logic to study scientific language and inference. R. G. Collingwood argued that only a logic of problems could take context into account. He was ignored, but the need to reconcile secure meanings with changes in context and meanings was seen by Karl Popper, W. v. O. Quine, and Mario Bunge. Jagdish Hattiangadi uses problems to reconcile the need for security with that for growth. But he (...) mistakenly insists that all problems are mere contradictions and artificially separates rigid from flexible aspects of meanings. In order to resolve the conflict we must (1) replace the quest for rigid terms with techniques for improvement, (2) use plausible arguments to uncover confused meanings, (3) use frameworks to choose problems and to regulate meanings, and (4) employ a bootstrap approach that uses frameworks to improve meanings and refined meanings to improve frameworks. (shrink)

This article examines how Quine and Sellars develop informatively contrasting responses to a fundamental tension in Carnap’s semantics ca. 1950. Quine’s philosophy could well be styled ‘Essays in Radical Empiricism’; his assay of radical empiricism is invaluable for what it reveals about the inherent limits of empiricism. Careful examination shows that Quine’s criticism of Carnap’s semantics in ‘Two Dogmas of Empiricism’ fails, that at its core Quine’s semantics is for two key reasons incoherent and that his hallmark Thesis of Extensionalism (...) is untenable. The tension in Carnap’s semantics together with Quine’s exposure of the severe limits of radical empiricism illuminate central features of Sellars’s philosophy: the fully general form of the myth of givenness, together with Sellars’s alternative Kantian characterisation of understanding; the full significance of Carnap’s distinction between conceptual analysis and conceptual explication, and its important methodological implications; the specifically pragmatic character of Sellars’s realism; and Sellars’s methodological reasons for holding that philosophy must be systematic and that systematic philosophy must be deeply historically and textually informed. This paper thus re-examines this recent episode of philosophical history for its philosophical benefits and systematic insights. (shrink)

Don Marquis’s “future-like-ours” argument against the moral permissibility of abortion is widely considered the strongest anti-abortion argument in the philosophical literature. In this paper, I address the issue of whether the argument relies upon controversial metaphysical premises. It is widely thought that future-like-ours argument indeed relies upon controversial metaphysics, in that it must reject the psychological theory of personal identity. I argue that that thought is mistaken—the future-like-ours argument does not depend upon the rejection of such a theory. I suggest, (...) however, that given a widely-accepted view about contraception and abstinence, the argument is committed to contentious metaphysics after all, as it relies upon a highly controversial assumption about mereology. This commitment is not only relevant for those who are inclined to endorse the argument but reject the mereological view in question, but in addition entails dialectical and epistemological liabilities for the argument, which on some views will be fatal to the argument’s overall success. (shrink)

W. V. Quine’s first philosophical monograph, Word and Object, is widely recognized as one of the most influential books of twentieth century philosophy. Notes, letters, and draft manuscripts at the Quine Archives, however, reveal that Quine was already working on a philosophical book in the early 1940s; a project entitled Sign and Object. In this paper, I examine these and other unpublished documents and show that Sign and Object sheds new light on the evolution of Quine’s ideas. Where “Two Dogmas (...) of Empiricism” is usually considered to be a turning point in Quine’s development, this paper redefines the place of ‘Two Dogmas’ in his oeuvre. Not only does Quine’s book project reveal that his views were already fairly naturalistic in the early 1940s ; Sign and Object also unearths the steps Quine had to take in maturing his perspective; steps that will be traced in the second half of this paper. (shrink)

Quine is routinely perceived as saving metaphysics from Carnapian positivism. Where Carnap rejects metaphysical existence claims as meaningless, Quine is taken to restore their intelligibility by dismantling the former’s internal–external distinction. The problem with this picture, however, is that it does not sit well with the fact that Quine, on many occasions, has argued that metaphysical existence claims ought to be dismissed. Setting aside the hypothesis that Quine’s metaphysical position is incoherent, one has to conclude that his views on metaphysics (...) are subtler than is often presupposed; both the received view that Quine saved metaphysics and the opposite view that Carnap and Quine are on the same anti-metaphysical team seem too one-sided if we take seriously Quine’s own pronouncements on the issue. In this paper, I offer a detailed reconstruction of Quine’s perspective on metaphysical existence claims. Scrutinizing his published work as well as unpublished papers, letters, and notebooks, I show how Quine is able to both blur the boundary between scientific sense and metaphysical nonsense and to argue that we cannot ask what reality is really like in a distinctively philosophical way. I argue that although Quine’s position is much closer to Carnap’s than the received view suggests, it still differs in two crucial respects. (shrink)

W. V. Quine is arguably the intellectual father of contemporary naturalism, the idea that there is no distinctively philosophical perspective on reality. Yet, even though Quine has always been a science-minded philosopher, he did not adopt a fully naturalistic perspective until the early 1950s. In this paper, I reconstruct the genesis of Quine’s ideas on the relation between science and philosophy. Scrutinizing his unpublished papers and notebooks, I examine Quine’s development in the first decades of his career. After identifying three (...) commitments supporting his naturalism—viz. empiricism, holism, and realism—I piece together the evolution of Quine’s position by examining the origins of these commitments one by one, showing how his early views gradually evolved into the mature naturalistic position that would have such an enormous impact on post-war analytic philosophy. (shrink)

Discussion of atomistic and monistic theses about abstract reality.

When does a human being begin to exist? We argue that it is possible, through a combination of biological fact and philosophical analysis, to provide a definitive answer to this question. We lay down a set of conditions for being a human being, and we determine when, in the course of normal fetal development, these conditions are first satisfied. Issues dealt with along the way include: modes of substance-formation, twinning, the nature of the intra-uterine environment, and the nature of the (...) relation between fetus and mother (connection, parthood, dependence). (shrink)

According to a growing consensus in the secondary literature on Quine, the judgment Quine makes in favor of the nominalism outlined in “Steps Toward a Constructive Nominalism” is in tension with the naturalism he later adopts. In this paper, I show the consensus view is mistaken by showing that Quine’s judgment is rooted in a naturalistic standard of clarity. Moreover, I argue that Quine late in his career is committed to accepting one plausible reading of his judgment in 1947. In (...) making these arguments, I draw attention to a version of naturalism that misreadings of Quine have prevented philosophers from appreciating, and thereby articulate and clarify a version of naturalism I recommend philosophers investigate today. (shrink)

W.V. Quine is a well-known proponent of naturalism, the view on which reality is described only in science. He is also well-known for arguing that our current scientific theories commit us to the existence of abstract objects. It is tempting to believe that the naturalistic philosopher should think scientists outside of philosophy are in the best position to assess the merits of revising our current commitment to abstract objects. But Quine rejects this deferential view. On the reading of Quine’s philosophical (...) methodology that I defend in this paper, the naturalistic philosopher not only may assess the merits of revising the commitments of our scientific theories, but also will recommend we make such revisions if doing so simplifies and clarifies our science. To develop my reading, I will examine John Burgess and Gideon Rosen’s naturalism in ontology that includes the deferential view Quine rejects. By explaining how Quine’s naturalism differs from the anti-revisionist, deferential naturalism in philosophy of mathematics that Burgess and Rosen advance, I seek to clarify and advance contemporary debates on naturalism. (shrink)

A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.

It is known that the Restricted Predicate Calculus can be embedded in an elementary theory, the signature of which consists of exactly two equivalences. Some special models for the mentioned theory were constructed to prove this fact. Besides formal adequacy of these models, a question may be posed concerning their conceptual simplicity, "transparency" of interpretations they assigned to the two stated equivalences. In works known to us these interpretations are rather complex, and can be called "technical", serving only the purpose (...) of embedding. We propose a conversion method, which transforms an arbitrary model of RPC into some model of the elementary theory TR, which includes three equivalences. RPC is embeddable in TR, and it appears possible to assign some "natural" interpretations to three equivalences using the "Track of Relation " concept. (shrink)

The paper seeks to answer two new questions about truth and scientific change: What lessons does the phenomenon of scientific change teach us about the nature of truth? What light do recent developments in the theory of truth, incorporating these lessons, throw on problems arising from the prevalence of scientific change, specifically, the problem of pessimistic meta-induction?

For almost twenty years, Penelope Maddy has been one of the most consistent expositors and advocates of naturalism in philosophy, with a special focus on the philosophy of mathematics, set theory in particular. Over that period, however, the term ‘naturalism’ has come to mean many things. Although some take it to be a rejection of the possibility of a priori knowledge, there are philosophers calling themselves ‘naturalists’ who willingly embrace and practice an a priori methodology, not a whole lot different (...) from traditional conceptual analysis. Along a different line, some take naturalism to involve the rejection of abstract objects—a sort of physicalism—while other naturalists not only allow the existence of abstracta; they take this existence to be all but obvious.For present purposes, we can begin with W.V.O. Quine, who once characterized naturalism as ‘the abandonment of the goal of first philosophy’ and ‘the recognition that it is within science itself …that reality is to be identified and described’. For Quine, the ‘naturalistic philosopher begins his reasoning within the inherited world theory as a going concern …[The] inherited world theory is primarily a scientific one, the current product of the scientific enterprise’ [Quine, 1981, p. 72]. This characterizes at least the bulk of contemporary philosophers who call themselves ‘naturalists’, and it characterizes the targets of many who oppose what they call ‘naturalism’. But as Maddy notes at the start, ‘the term has come to mark little more than a vague science-friendliness’.An attempt to define naturalism more fully would surely require a characterization of science—at least so that the reader can see when someone sins against that naturalism by being unscientific. But, as Maddy notes, one ‘lesson won through decades of study in the philosophy of science [is that] there is no …. (shrink)

A central metaphilosophical project seeks to evaluate the reliability of the types of evidence that figure in philosophical arguments and, relatedly, the justificatory status of relying on those types of evidence. Traditionally, metaphilosophers have approached this project via an analysis of intuition. This article argues that the category picked out by “intuition” is both too broad and too heterogeneous to serve as the appropriate target for metaphilosophical inquiry. Intuition is a gerrymandered and disjunctive kind, undeserving of the widespread attention it (...) receives in the literature. Instead, metaphilosophers should examine more finely grained mental states. Three promising strategies for parsing intuitions more finely are proposed: by their causal origins, by their context of employment, and by the exoticism of their content. This more narrow focus may significantly alter the dialectic in three prominent metaphilosophical arguments: the argument from calibration, the argument from self-defeat, and the argument from intuitional sensitivity. (shrink)

In response to comments on my book, Being Realistic about Reasons, by Justin Clarke-Doane, David Enoch and Tristram McPherson, and Gideon Rosen, I try to clarify my domain-based view of ontology, my understanding of the epistemology of normative judgments, and my interpretation of the phenomenon of supervenience.

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.

Las teorías que usamos para representar el mundo pueden ser extremadamente complejas. Abordan temas tales como electrones, campos cuánticos, estrellas de neutrones, materia oscura, redes neuronales, mercados económicos, la atmósfera y muchas otras entidades que suponemos existen en el universo. Al formular nuestras teorías, recurrimos a lenguajes exactos que nos permiten minimizar la vaguedad y expresarnos lo más precisa y cuantitativamente posible. Recurrimos a la matemática. Cuando formulamos nuestras teorías fácticas en lenguaje matemático, estas se refieren no solamente a objetos (...) que nosotros interpretamos como materiales, tales como partículas o personas, sino también a entidades más raras de un mundo abstracto: conjuntos, números, funciones, espacios algebraicos, variedades, topologías, y otras entidades similares. Estos objetos no son materiales en el sentido en que nosotros decimos que una manzana es material. Ellos no existen en el espacio-tiempo, no interactúan, no cambian o evolucionan. Sin embargo, allí están, profundamente arraigados en nuestras teorías más apreciadas acerca del mundo. (shrink)

Syntactic Reductionism, as understood here, is the view that the ‘logical forms’ of sentences in which reference to abstract objects appears to be made are misleading so that, on analysis, we can see that no expressions which even purport to refer to abstract objects are present in such sentences. After exploring the motivation for such a view, and arguing that no previous argument against it succeeds, sentences involving generalized quantifiers, such as ‘most’, are examined. It is then argued, on this (...) basis, that Syntactic Reductionism is untenable. (shrink)

This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)

In order to reconnect Quine's views to the current debate on scientific realism, I reframe Quine's scientific realism into a semantic, a metaphysical, and an epistemological dimension. With this conceptual background, I review the historical development of Quine's scientific realism from the late 1940s until his death in 2000. I challenge Soames's view that Quine is a phenomenalist at the time of “Two Dogmas of Empiricism” (1951) and show that he remains agnostic between a realist and an anti‐realist conceptual scheme (...) instead. I also argue that Quine's early views on regimentation are incompatible with a strong formulation of semantic realism. I proceed in reconstructing how he becomes a metaphysical and epistemological realist in the mid‐1950s and argue against the view of Keskinen and Fogelin that interprets Quine as being a metaphysical anti‐realist. Contrary to Davidson, I defend the view that he never gave up normative epistemology and really is a proper epistemological realist. Finally, I discuss how he tries to reconcile his realism with his thesis of ontological relativity and how this necessitates the switch to a stronger form of semantic realism. (shrink)

William Tait's standing in the philosophy of mathematics hardly needs to be argued for; for this reason the appearance of this collection is especially welcome. As noted in his Preface, the essays in this book ‘span the years 1981–2002’. The years given are evidently those of publication. One essay was not previously published in its present form, but it is a reworking of papers published during that period. The Introduction, one appendix, and some notes are new. Many of the essays (...) will be familiar to the readers of this journal; indeed two first appeared here.It should be no surprise to those who know Tait's work that this is a very rich collection, with contributions on a wide variety of issues, both systematic and historical. That poses a problem for a reviewer, because a serious discussion of even all the major issues would be beyond the scope of a review.Before the essays in this collection, Tait's publications were almost all in mathematical logic, especially proof theory. He was a leading actor in the work on the revised Hilbert program stimulated after the war by Georg Kreisel, Kurt Schütte, and Gaisi Takeuti. Tait thus has an experience in mathematical research that is rare among those whose careers have been institutionally in philosophy. In the 1970s Tait became disillusioned with the proof-theoretic program on which he had worked. However, he draws on that background in several of these essays, and he has continued to work on mathematical questions. In particular, the set-theoretic project reflected in essay 6 is as much mathematical as philosophical.It is not easy to characterize Tait's philosophical viewpoint briefly. Both the title of the book and some of its content mark him as a rationalist. His hero in the earlier history …. (shrink)

In this paper I revisit R. M. Martin’s logic of belief. As with much of Martin’s work, his formal studies into belief and belief reports have gone largely unnoticed. However, in my article I suggest reasons for thinking that these studies warrant revisiting. One reason is that Martin adopted an account of the notion of belief which was more comprehensive than that employed by most rival theorists. Another reason is that Martin couched his theory in a formal pragmatics which utilised (...) a pragmatical meta-language. This method resulted in a rather novel approach which may turn out to be more enlightening than many popular alternative accounts. Martin was a constructivistic nominalist whose approach to philosophical analysis was characterised by a commitment to first-order extensional systems. Yet in the statement of his theory of belief he employed a platonistic syntax simply for the reason that this kind of syntax is a little easier to implement than one which is nominalistic. However Martin also supposed that a fully nominalised version of his theory could be developed. In my article I investigate whether it can. I do this by sketching an inscriptional pragmatics, where this pragmatical system presupposes an inscriptional semantics of the kind developed by Martin himself. While further work is required, I think that a nominalisation of Martin’s logic of belief may be developed. (shrink)