This article critically assesses the empirical research that leads Quine, in his posthumously published work, to abandon his empiricist principle that humans do not have any innate concepts, or knowledge. It is the same empirical research that Penelope Maddy capitalizes on to develop her own contributions to naturalized epistemology, and it has been pioneered by developmental psychologist Elisabeth Spelke. Spelke employs the method of habituation and preferential looking to argue that human infants have innate concepts, and that they have some (...) knowledge about what can and cannot happen to physical objects. Taking into account empirical studies as well as methodological considerations, this article examines whether this research can support these strong philosophical conclusions drawn from it, finding that it likely cannot provide such support. (shrink)

In this article I dispute the claim, made by several contemporary scholars, that Spinoza was a naturalist. ‘Naturalism’ here refers to two distinct but related positions in contemporary philosophy. The first, ontological naturalism, is the view that everything that exists possesses a certain character permitting it to be defined as natural and prohibiting it from being defined as supernatural. I argue that the only definition of ontological naturalism that could be legitimately applied to Spinoza's philosophy is so unrestrictive as to (...) tell us nothing about the content of his ideas. The second, methodological naturalism, is the view that the natural sciences are the best means of finding out substantial truths about the concrete world. I present some historical research showing that Spinoza's way of positioning himself with respect to other philosophers in the Dutch Republic casts very serious doubt on the claim that he was a methodological naturalist. This adds further weight to arguments that have already been made against the naturalist reading of Spinoza. (shrink)

According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, (...) I outline a different approach, which circumvents these problems by dispensing with the priority or dependence relation altogether. Along the way, I show how this approach enables the mathematical structuralist to defuse an objection recently raised against her view. (shrink)

This note describes Saunders Mac Lane as a philosopher, and indeed as a paragon naturalist philosopher. He approaches philosophy as a mathematician. But, more than that, he learned philosophy from David Hilbert’s lectures on it, and by discussing it with Hermann Weyl, as much as he did by studying it with the mathematically informed Göttingen Philosophy professor Moritz Geiger.

This paper considers Maddy’s strategy for naturalising mathematics in the context of Quine’s scientific naturalism. The aim of this proposal is to account for the acceptability of mathematics on scientific grounds without committing to revisionism about mathematical practice entailed by the Quine-Putnam indispensability argument. It has been argued that Maddy’s mathematical naturalism makes inconsistent assumptions on the role of mathematics in scientific explanations to the effect that it cannot distinguish mathematics from pseudo-science. I shall clarify Maddy’s arguments and show that (...) the objection can be overcome. I shall then reformulate a novel version of the objection and consider a possible answer, and I shall conclude that mathematical naturalism does not ultimately provide a viable strategy for accommodating an anti-revisionary stance on mathematics within a Quinean naturalist framework. (shrink)

According to the editors, Alfred Tarski: Early work in Poland – Geometry and Teaching has three main goals. First, to publish translations so that all of Alfred Tarski's work will be accessi...

In spite of the relevance of a scientific representation of the world for naturalism, it is surprising that philosophy of science is less involved in the debate on naturalism than expected. Had the viewpoint of philosophy of science been duly considered, naturalism could not have overlooked the established lesson, according to which there is no well-defined recipe for what science must or must not be. In the present paper I address some implications of this lesson for naturalism, arguing that a (...) radically naturalistic outlook fails to pay sufficient attention to some of the main lessons that philosophy of science has taught us concerning the nature of scientific theories. One of these lessons is that real scientific theories are far more normative than ordinary scientific naturalism is ready to accept, a circumstance that at a minimum is bound to force most naturalization strategies to re-define their significance. (shrink)

In this paper we isolate a notion that we call “formalism freeness” from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability. We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic in the (...) 20th century. (shrink)

In this paper, I critically discuss recent work on the role that the principle of tolerance plays in Rudolf Carnap's philosophy. Specifically, I consider how two prominent interpretations of Carnap's principle of tolerance can be used to argue for Carnap's anti-metaphysical views. I then argue that there are serious problems with these arguments, and I diagnose those problems as resulting, in part, from a tension between competing goals of Carnap's philosophical project.

This review essay attempts to present a coherent and reasonably unitary picture of the contemporary ‘speculative turn’ in continental philosophy as charted in Levi Bryant, Nick Srnicek and Graham Harman, eds, The Speculative Turn: Continental Realism and Materialism (2011). Avoiding a more objective yet more anodyne chapter by chapter summary, I paint an intentionally synoptic view by selecting some common concerns of the authors involved, and group them under five ‘core themes’. Throughout, I try to keep open the comparative channel (...) with the realist tenets of critical realism, and conclude vouching for the necessity for more bridge-building works to appear in the future. (shrink)

In this paper I will take into examination the relevance of the main indispensability arguments for the comprehension of the applicability of mathematics. I will conclude not only that none of these indispensability arguments are of any help for understanding mathematical applicability, but also that these arguments rather require a preliminary analysis of the problems raised by the applicability of mathematics in order to avoid some tricky difficulties in their formulations. As a consequence, we cannot any longer consider the applicability (...) problems as subordinate to ontological ones: no ontological stance on mathematical entities can offer an easy road to the comprehension of the applicability of mathematics. (shrink)

Published in 1891, Edmund Husserl’s first book, Philosophie der Arithmetik, aimed to “prepare the scientific foundations for a future construction of that discipline.” His goals should seem reasonable to contemporary philosophers of mathematics: . . . through patient investigation of details, to seek foundations, and to test noteworthy theories through painstaking criticism, separating the correct from the erroneous, in order, thus informed, to set in their place new ones which are, if possible, more adequately secured. [7, p. 5]2 But the (...) ensuing strategy for grounding mathematical knowledge sounds strange to the modern ear. For Husserl cast his work as a sequence of “psychological and logical investigations,” providing a psychological analysis.. (shrink)

11We thank Rohan French for a detailed discussion of this review. We also wish to reciprocally thank Shawn Standefer for detailed discussions about the book.Logical pluralism is the view according...

Penelope Maddy's latest book, devoted to Wittgenstein's early and late philosophy of logic, can be seen as an extension of Maddy 2007, in which the thoughts of Descartes, Kant (and Car...

In comparing classical and non-classical solutions to the semantic paradoxes arguments relying on strength have been influential. In this paper I argue that non-classical solutions should preserve the proof-theoretic strength of classical solutions. Leitgeb’s logic of HYPE is then presented as an interesting possibility to strengthen FDE with a suitable conditional. It is shown that HYPE allows for a non-classical Kripkean theory of truth, called KFL, that is strong enough for the relevant purposes and has additional attractive properties.

This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...) the concepts of science through the construction and use of suitably robust meta-logical languages. My primary interpretive claim is that Carnap's understanding of logic and mathematics as a set of formal auxiliaries is premised upon this prior analysis of the character of logico-mathematical knowledge, his understanding of its role in the language of science, and the methods used by practicing mathematicians. Thus the Principle of Tolerance, and so Carnap's logical pluralism, is licensed and justified by these methodological insights. This interpretation of Carnap's program contrasts with the popular Deflationary reading as proposed in Goldfarb & Ricketts. The leading idea they attribute to Carnap is a Logocentrism: That philosophical assertions are always made relative to some particular language, and that our choice of syntactical rules for a language are constitutive of its inferential structure and methods of possible justification. Consequently Tolerance is considered the foundation of Carnap's entire program. My third chapter argues that this reading makes Carnap's program philosophically inert, and I present significant evidence that such a reading is misguided. The final chapter attempts to extend the methodological ideals of Carnap's program to the analysis of the ongoing debate between category- and set-theoretic foundations for mathematics. Recent criticism of category theory as a foundation charges that it is neither autonomous from set theory, nor offers a suitable ontological grounding for mathematics. I argue that an analysis of concepts can be foundationally informative without requiring the construction of those concepts from first principles, and that ontological worries can be seen as methodologically unfruitful. (shrink)

This paper defends the Quine-Putnam mathematical indispensability argument against two objections raised by Penelope Maddy. The objections concern scientific practices regarding the development of the atomic theory and the role of applied mathematics in the continuum and infinity. I present two alternative accounts by Stephen Brush and Alan Chalmers on the atomic theory. I argue that these two theories are consistent with Quine’s theory of scientific confirmation. I advance some novel versions of the indispensability argument. I argue that these new (...) versions accommodate Maddy’s history of the atomic theory. Counter-examples are provided regarding the role of the mathematical continuum and mathematical infinity in science. (shrink)

The traditional formulation of the indispensability argument for the existence of mathematical entities (IA) has been criticised due to its reliance on confirmational holism. Recently a formulation of IA that works without appeal to confirmational holism has been defended. This recent formulation is meant to be superior to the traditional formulation in virtue of it not being subject to the kind of criticism that pertains to confirmational holism. I shall argue that a proponent of the version of IA that works (...) without appeal to confirmational holism will struggle to answer a challenge readily answered by proponents of a version of IA that does appeal to confirmational holism. This challenge is to explain why mathematics applied in falsified scientific theories is not considered to be falsified along with the rest of the theory. In cases where mathematics seemingly ought to be falsified it is saved from falsification, by a so called 'Euclidean rescue'. I consider a range of possible answers to this challenge and conclude that each answer fails. (shrink)

Traditional philosophy has been under attack from several quarters in recent years. The traditional philosopher views philosophy as an armchair discipline relying, for the most part, on reason and reflection. Some philosophers doubt the legitimacy of this type of inquiry. Their arguments usually occur along two dimensions. Some argue that the primary data source for the armchair philosopher--intuition--does not provide evidence for philosophical theories. Others argue that conceptual analysis, which is the preferred method of inquiry for armchair philosophers, can't yield (...) the results the philosopher is looking for, since concepts like 'knowledge' or 'free-will' vary from culture to culture or even between persons within a culture. Finally, some philosophers argue that we should abandon the armchair program because philosophy should be an empirical enterprise continuous with the sciences. I argue that attempts to undermine intuition fail and that one can justify the evidential status of intuition in a non-question begging way. I then argue that attacks on the belief in shared concepts do not succeed because they often conflate the nature of scientific objects with those of interest to the philosopher. However, if concepts do vary from culture to culture, I show that the philosopher need not abandon the armchair. She can still do conceptual analysis but it will be only the entry point into the philosophical dialogue. I apply this approach to epistemology arguing that the central epistemic questions ought to be the existential and the normative. This approach helps to vindicate epistemic internalism. (shrink)