Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of (...) mathematical instrumentalism are defeated by Gödel’s theorem, not all are. By considering inductive reasons in mathematics, we show that some mathematical instrumentalisms survive the theorem. (shrink)

In this paper we devise some technical tools for dealing with problems connected with the philosophical view usually called mathematical instrumentalism. These tools are interesting in their own right, independently of their philosophical consequences. For example, we show that even though the fragment of Peano's Arithmetic known as IΣ₁ is a conservative extension of the equational theory of Primitive Recursive Arithmetic (PRA). IΣ₁ has a super-exponential speed-up over PRA. On the other hand, theories studied in the Program of (...) Reverse Mathematics that formalize powerful mathematical principles have only polynomial speed-up over IΣ₁. (shrink)

Scientific realists often appeal to some version of the conjunction objection to argue that scientific instrumentalism fails to do justice to the full empirical import of scientific theories. Whereas the conjunction objection provides a powerful critique of scientific instrumentalism, I will show that mathematical instnrunentalism escapes the conjunction objection unscathed.

An Essay on Mathematical Instrumentalism M. Detlefsen. THE PHILOSOPHICAL FUNDAMENTALS OF HILBERT'S PROGRAM 1. INTRODUCTION In this chapter I shall attempt to set out Hilbert's Program in a way that is more revealing than ...

The main thesis of this paper is that, Contrary to general belief, George berkeley did in fact express a coherent philosophy of mathematics in his major published works. He treated arithmetic and geometry separately and differently, And this paper focuses on his philosophy of arithmetic, Which is shown to be strikingly similar to the 19th and 20th century philosophies of mathematics known as 'formalism' and 'instrumentalism'. A major portion of the paper is devoted to showing how this philosophy of (...) mathematics follows directly from berkeley 's theory of signs and his philosophy of language, And from his discovery of an alternative to the correspondence theory of truth used by most of his predecessors. (shrink)

In this paper I examine Field’s account of the applicability of mathematics from a measurementtheoretic perspective. Within this context, I object to Field’s instrumentalism, arguing that it depends on an incomplete analysis of applicability. I show in particular that, once the missing piece of analysis is provided, the role played by numerical entities in basic empirical theories must be revised: such revision implies that instrumentalism should be rejected and mathematical entities be regarded not merely as useful tools (...) but also as conceptual schemata by means of which we can articulate our understanding of experience. (shrink)

The delicate point in the formalistic position is to explain how the non-intuitionistic classical mathematics is significant, after having initially agreed with the intuitionists that its theorems lack a real meaning in terms of which they are true (S. C. Kleene, 1952).

The roles of classical realism, logical positivism, and pragmatic instrumentalism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War II developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the “schism” in twentieth (...) century physics created by the Bohr-Einstein “disagreements” on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of “truth” in general, or its conventionalistic version in post-World War II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's “positivism” with Einstein's “realism” by emphasizing the existence of an underlying quantum reality, in which they both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by developing the conceptual and mathematical tools that are most appropriate for such a use. (shrink)

The Quine-Putnam Indispensability argument is the argument for treating mathematical entities on a par with other theoretical entities of our best scientific theories. This argument is usually taken to be an argument for mathematical realism. In this chapter I will argue that the proper way to understand this argument is as putting pressure on the viability of the marriage of scientific realism and mathematical nominalism. Although such a marriage is a popular option amongst philosophers of science and (...) mathematics, in light of the indispensability argument, the marriage is seen to be very unstable. Unless one is careful about how the Quine-Putnam argument is disarmed, one can be forced to either mathematical realism or, alternatively, scientific instrumentalism. I will explore the various options: (i) finding a way to reconcile the two partners in the marriage by disarming the indispensability argument (Jody Azzouni [2], Hartry Field [13, 14], Alan Musgrave [18, 19], David Papineau [21]); (ii) embracing mathematical realism (W.V.O. Quine [23], Michael Resnik [25], J.J.C. Smart [27]); and (iii) embracing some form of scientific instrumentalism (Ot´ avio Bueno [7, 8], Bas van Fraassen [30]). Elsewhere [11], I have argued for option (ii) and I won’t repeat those arguments here. Instead, I will consider the difficulties for each of the three options just mentioned, with special attention to option (i). In relation to the latter, I will discuss an argument due to Alan Musgrave [19] for why option (i) is a plausible and promising approach. From the discussion of Musgrave’s argument, it will emerge that the issue of holist versus separatist theories of confirmation plays a curious role in the realism–antirealism debate in the philosophy of mathematics. I will argue that if you take confirmation to be an holistic matter—it’s whole theories (or significant parts thereof) that are confirmed in any experiment—then there’s an inclination to opt for (ii) in order to resolve the marital tension outlined above.. (shrink)

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem using (...) an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. (...) I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

When we examine the history of astronomy up to the end of the seventeenth century by considering the relation between mathematical astronomy and natural philosophy, it has been argued that there were two groups of philosophers and astronomers: instrumentalists and realists. However, this classification is deficient when we consider attitudes toward the explanatory power of mathematics in determining astronomical theories. I offer the solution of dividing realists into two subcategories—mathematical realists and physical realists. Mathematical realists include those (...) who thought mathematics could provide the real motions of celestial bodies. The physical realists, who include Ibn Rushd (Averroës), believed mathematics could not provide us with the real structure of the heavens. To avoid contradictions between the physical and mathematical models, the physical realists held that a mathematical model of the heavens should be designed by considering physics. I argue, in this article, that Francis Bacon can be considered a physical realist. (shrink)

This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. (...) I argue for two claims intended to advance our understanding of singular thought about mathematical abstracta. First, that the conditions for possession of a file for an abstract mathematical object are the same as the conditions for possessing a file for an object perceived in the past—namely, that the agent retains information about the object. Thus insofar as we are able to have memory-based files for objects perceived in the past, we ought to be able to have files for abstract mathematical objects too. Second, at least one recently articulated condition on a file’s being a device for singular thought—that it be capable of surviving a certain kind of change in the information it contains—can be satisfied by files for abstract mathematical objects. (shrink)

For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and (...) updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

Adapated from talks at the UCLA Logic Center and the Pitt Philosophy of Science Series. Exposition of material from Fixing Frege, Chapter 2 (on predicative versions of Frege’s system) and from “Protocol Sentences for Lite Logicism” (on a form of mathematical instrumentalism), suggesting a connection. Provisional version: references remain to be added. To appear in Mathematics, Modality, and Models: Selected Philosophical Papers, coming from Cambridge University Press.

Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly "meaningless" signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions (Weyl (1949); Kitcher (1976)). The paper traces the history and context of Hilbert's reasoning about (...) signs, which illuminates Hilbert's account of mathematical objectivity, axiomatics, idealization, and consistency. (shrink)

The motivating question of this paper is: ‘How are our beliefs in the theorems of mathematics justified?’ This is distinguished from the question ‘How are our mathematical beliefs reliably true?’ We examine an influential answer, outlined by Russell, championed by Gödel, and developed by those searching for new axioms to settle undecidables, that our mathematical beliefs are justified by ‘intuitions’, as our scientific beliefs are justified by observations. On this view, axioms are analogous to laws of nature. They (...) are postulated to best systematize the data to be explained. We argue that there is a decisive difference between the cases. There is agreement on the data to be systematized in the scientific case that has no analog in the mathematical one. There is virtual consensus over observations, but conspicuous dispute over intuitions. In this respect, mathematics more closely resembles stereotypical philosophy. We conclude by distinguishing two ideas that have long been associated -- realism (the idea that there is an independent reality) and objectivity (the idea that in a disagreement, only one of us can be right). We argue that, while realism is true of mathematics and philosophy, these domains fail to be objective. One upshot of the discussion is that even questions of fundamental physics may fail to be objective in roughly the sense that the question, ‘Is the Parallel Postulate is true?’, understood as one of pure mathematics, fails to be. Another is a kind of pragmatism. Factual questions in mathematics, modality, logic, and evaluative areas go proxy for non-factual practical ones. -/- . (shrink)

The article deals with the position of Lutheran theologian Andreas Osiander sen. in the history of philosophy, history of science and philosophy of science. It works on humanistic foundation of Osiander’s thought and his elaboration of the tradition of the antient wisdom and Christian cabbala of Giovanni Pico della Mirandola in particular in the biblical exegesis. The article deals with Osiander’s edition of Nicolaus Copernicus’ book De revolutionibus orbium caelestium as well and with his edition of the mathematical work (...) of Girolamo Cardano. In the context of philosophy of science Osiander’s foreword to Copernicus is analyzed and its role in the controversy between instrumentalism and realism is assessed. Osiander’s instrumentalism is viewed as an anachronism. Finally, the influence of Neoplatonism and Paracelsism in Osiander’s theology is analyzed and judged as too general. (shrink)

Mathematical Astronomy as the most developed branch of ancient exact sciences has been widely discussed - especially epistemological issues e.g. concerning astronomy as a prime example of the distinction between instrumentalist and realist understanding of theories. In contrast to these the very methodology of ancient astronomy has received little attention. Following the work of Jaakko Hintikka and Unto Remes Aristarchus' method of determining the distance of the Sun is sketched and Ptolemy's solar model is discussed in detail.

The empirical-transcendental debate in philosophy of technology, as debates go, took a turn toward the counterposing of the two perspectives, ‘empirical’-pragmatic-pragmatist versus ‘transcendental’-critical. Postphenomenology aligns itself with the former standpoint, and it is in this spirit that commentators have criticized it for its too-instrumentalist stance and lack of overarching, i.e., transcendental orientation. But the positions may have become too starkly delineated in order for the debate to reach any breakthrough: a seemingly unbridgeable gap yawns between the stances of ‘technology with (...) a small “t”’ and ‘Technology with a capital “T.”' Is there any way to reorient the debate? In this paper I propose to do so by considering whether there would be some way of arriving from one end of the spectrum to the other—crossing the gap. Exploring the purported wasteland in between “technology” and “Technology” by way of object-oriented ontology (OOO)—Harman, Morton—we can find it actually filled with countless gaps, adhering to every thing. Following the radical insights of OOO, we’d have to attest to a ‘thing-transcendentality.’ The ‘gap,’ then, that seemed so threatening and all-encompassing, becomes smeared out, levelled down to a multiplicity of perspectives. And this casts the debate, with its purported strict tension between ‘empirical’ and ‘transcendental’ positions, in fresh terms, opening up new ways for studying how the two interrelate. (shrink)

Introduction. The book is a study in Adam Smith's system of ideas; its aim is to reconstruct the peculiar framework that Adam Smith’s work provided for the shaping of a semi-autonomous new discipline, political economy; the approach adopted lies somewhere in-between the history of ideas and the history of economic analysis. My two claims are: i) The Wealth of Nations has a twofold structure, including a `natural history' of opulence and an `imaginary machine' of wealth. The imaginary machine is a (...) kind of Newtonian theory, whose connecting links are principles; provided either by `partial' characteristics of human nature or by analoga of physical mechanisms transferred to the social world; ii) a domain of the economic, understood as a self-standing social sub-system, was discovered first by Adam Smith. His `discovery' of the new continent of the economic was an `unintended result' of a deviation in his voyage to the never-found archipelago of natural jurisprudence. -/- 1. Imaginary machines and invisible chains: natural philosophy and method. The first chapter reconstructs Smith's views on the method in natural philosophy, presented primarily in the History of Astronomy (HA). The peculiar kind of semi-sceptical Newtonianism which permeates the essay is highlighted. Its reconstruction of the history of one natural science is shown to be based on the assumptions of Hume’s epistemology, and to lead to a self-aware deadlock. Smith's dilemma is between an essentialist realism and sceptical instrumentalism; the Cartesian presuppositions he shares with Hume and with the 18th century as a whole make it impossible for him to overcome his dilemma. The following chapters will show how, on the one hand, Smith's skeptical methodology encourages him in the enterprise to `carve off' a new self-contained discipline and how, on the other hand, his epistemological dilemma is reflected in the inner tensions of his moral and political theory as well as in a number of basic oscillations concerning the status of the new discipline. -/- 2. Chessboards and clocks: moral philosophy and method. -/- The second chapter reconstructs Smith's views on the method in the parallel field of moral philosophy, including the theory of moral sentiments and natural jurisprudence. I argue that The Theory of Moral Sentiments, when considered together with with the Lectures on Jurisprudence, where Smith's peculiar version of a `weaker' form of natural law is presented, wins special interest, not only for the history of ethics but even more for the history of political theory and the social sciences. The two most striking features of Smith's work in this area are highlighted. First, his effort at reformulating the `practical science' is a methodologically self-aware attempt at applying the Newtonian method to moral subjects. Secondly, this attempt ends in a stalemate as two distinguished kinds of normative order are introduced: one ultimate order of Reason, ultimately justifiable but inaccessible, and one weaker order of our `natural sentiments', to which we have empirical access, but which is so variable as to lack any ultimate value as a basis for grounding our normative claims. These two parallel conundrums may arguably account for the author's inability to publish during his lifetime both The History of Astronomy and the projected history and theory of law and government. -/- 3. Wheels, dams, and gravitation: the structure of scientific argument in The Wealth of Nations. -/- The third chapter provides the core of the book, dealing with the structure of the argument in WN. I argue that the main presupposition that makes the shift possible from a `natural history' to a `system' approach is the Newtonian contrast of `mathematical' with `physical' explanation; that is, Smith drops any discussion of the "original qualities" of human nature that could account for economic behaviour, while introducing, as `principles' for the system, a set of `hypothetical' statements of `observed' regularities in human behaviour and of `observed' super-individual self-regulating mechanisms. In bringing this presupposition to light, the coexistence of a teleological with a mechanistic approach is clarified; fresh light is shed on the notion of the invisible hand by a comparison of its occurrence in Smith with the occurrence of the same expression (until now overlooked) in the correspondence between Newton and Cotes. Finally, the peculiar semi-prescriptive and semi-descriptive character of political economy are highlighted, and the consistency of Smith's `impure' semi-prescriptive social science, when understood in his own terms, is defended against familiar charges with inconsistency and against even more familiar strained modernizations. -/- 4. Apples, deer, and frivolous trinkets: the construction of the economic. -/- The fourth chapter draws consequences from the third, examining how Smith's achievement in political economy, marking its transition to scientific status, carried a re-description of the phenomena, creating the comparatively independent and unified field of the economic. Smith's achievement is interpreted not as the `discovery' of an autonomous character already possessed by the economy out there, so much as a Gestalt-switch by which our perception of social phenomena is modified making us `see' the partial order of the economy as an isolated system. To sum up, the autonomy of the economic in social reality and the autonomy of the economic in social consciousness are shown to be two sides of one process. -/- 5. Concluding considerations: Political economy and the Enlightenment halved. -/- A few suggestions on the status of economic theory two centuries after The Wealth of Nations in its relationship to ‘practical philosophy’ are illustrated. (shrink)

The aim of this paper is twofold: (1) to assess whether the construct of neural representations plays an explanatory role under the variational free-energy principle and its corollary process theory, active inference; and (2) if so, to assess which philosophical stance - in relation to the ontological and epistemological status of representations - is most appropriate. We focus on non-realist (deflationary and fictionalist-instrumentalist) approaches. We consider a deflationary account of mental representation, according to which the explanatorily relevant contents of neural (...) representations are mathematical, rather than cognitive, and a fictionalist or instrumentalist account, according to which representations are scientifically useful fictions that serve explanatory (and other) aims. After reviewing the free-energy principle and active inference, we argue that the model of adaptive phenotypes under the free-energy principle can be used to furnish a formal semantics, enabling us to assign semantic content to specific phenotypic states (the internal states of a Markovian system that exists far from equilibrium). We propose a modified fictionalist account: an organism-centered fictionalism or instrumentalism. We argue that, under the free-energy principle, pursuing even a deflationary account of the content of neural representations licenses the appeal to the kind of semantic content involved in the aboutness or intentionality of cognitive systems; our position is thus coherent with, but rests on distinct assumptions from, the realist position. We argue that the free-energy principle thereby explains the aboutness or intentionality in living systems and hence their capacity to parse their sensory stream using an ontology or set of semantic factors. (shrink)

Focuses on Hartry Field's Instrumentalism. The ‘Conservation Theorems’, upon which Field bases so much of his form of Instrumentalism, are examined in detail, as is Field's attempt to ‘nominalize’ physics. Doubts are raised about the adequacy of Field's views of mathematics and physics, and a detailed comparison with the Constructibility Theory is presented.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Hume’s Natural Philosophy and Philosophy of Physical Science by Matias SlavovKrisztián PeteMatias Slavov. Hume’s Natural Philosophy and Philosophy of Physical Science. London: Bloomsbury Academic, 2020. Pp. 216. Hardcover. ISBN 9781350087866, £95.Although the relationship between Hume and Newton is a recurring theme in the Hume literature, Matias Slavov’s book does not seek to contribute to the debate between the traditional (Hume imitated Newton’s natural philosophy) and the critical (Hume (...) intended his “science of Man” as the foundation of all other sciences) approaches regarding the nature of this relation. The book is intended to be a summary of Hume’s natural philosophy—or rather an aggregation of his comments on natural philosophical topics—pursued by exploring and analysing themes and issues that were prominent in the natural philosophy of the early modern period. In this respect it is a pioneering undertaking.Of course, Slavov does not claim in his book that Hume is a natural philosopher. “[F]irst and foremost... [h]e is not; for his main objective is to establish a new science of human nature” (1). But Slavov does claim that Hume’s natural philosophical views can be understood and valued in themselves and in the philosophical-scientific context of his time as well. The book is not a discussion of the natural philosophical dimensions of the “science of human nature,” but rather, of the natural philosophical views which are reconcilable with his main objective. In this respect, the book is not a methodological approach to Hume’s supposed natural philosophy, but a synthesis of certain elements of Hume’s philosophy that can feature in a consistent natural philosophy. Although his arguments are generally indirect and are more about what Hume seems to be committed to and what follows from his epistemological position rather than his actual positions, Slavov’s conclusions seem mostly convincing.Thus, Slavov’s point is not that the empiricist method is compatible in every detail with Newtonian mechanics, but rather that Hume seems to be committed more to a Cartesian natural philosophy. Slavov does not write about the possibility and significance of applying natural philosophical methods to moral philosophy; rather, he wants to build a complete philosophy of nature around some of Hume’s basic ideas to “fill the gap for a book on Hume’s relation to natural philosophy and philosophy of physical science” (2).The book has two “equally important aims” (ix): to shed more light onto Hume’s relationship to natural philosophy, and to demonstrate that physics and philosophy have overlapping domains. Hume was hardly concerned with physics, so Slavov’s strategy of defining natural philosophy as an overlap between physics and philosophy (chapter 1) does, to some extent, explain the lack of textual evidence in this area. The definition of natural philosophy chosen by Slavov is also intended to ensure [End Page 170] that these two goals are intertwined, since according to Slavov’s definition, natural philosophy is “a grey area between philosophy and physics” (12).Personally, I do not feel comfortable with this definition because it is not informative enough; it says that natural philosophy is more than modern physics (mathematized natural science), but it is not quite philosophy. While the first implication is very agreeable, and a number of scholars have addressed the issue, to assess the second implication, we would need to know exactly what philosophy is in this context. Perhaps the best candidate is metaphysics, even if Slavov keeps the reader somewhat in the dark on this point, despite the fact that chapter 2 is intended to establish precisely that point. Yet, the metaphysics of this period was usually (with the possible exception of Spinoza) used to support natural scientific explanations. I believe that natural philosophy is more than a “grey area” (9, 12, 22), or a contact zone; it is a complex enterprise that evolved in different forms with different emphases: Cartesian mechanics still sought to understand nature, pursuing the Aristotelian ideal of knowledge, albeit rejecting Aristotelian methods, while empiricists increasingly envisaged a more instrumentalist role for natural explanations. Newton himself was caught between the two.In this context it is intriguing whether Hume carries forward Berkeley... (shrink)

In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theory-world relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In (...) this paper, we review two main conceptions of truth (one sentence-based and one model-based) and two of empirical adequacy (one sentence-based and one model-based), we point out their respective difficulties, and we give a first formulation of a new general view of the theory-world relationship, which we call Methodological Constructive Realism (MCR). We then show how the content of MCR can be further specified and expressed in a definite and precise form. The bulk of the paper shows in detail how it is possible to accomplish this goal for the special case of deterministic dynamical phenomena and their correlated deterministic models. This special version of MCR is formulated as an axiomatic extension of set theory, whose specific axioms constitute a formal ontology that provides an adequate framework for analyzing the two semantic relations of truth and empirical correctness, as well as their connections. (shrink)

For many decades, Duhem has been considered a paradigmatic instrumentalist, and while some commentators have argued against classifying him in this way, it still seems prevalent as an interpretation of his philosophy of science. Yet such a construal bears scant resemblance to the views presented in his own works—so little, indeed, that it might be said to constitute no more than a mere phantom with respect to his actual thought. In this article, we aim to deconstruct this phantom, tracing the (...) sources of the misconceptions surrounding his ideas and pinpointing the sources and/or causes of its proliferation. We subsequently point out and discuss those elements of his philosophy that, taken together, support the view of him as a scientific realist of a sophisticated kind. Finally, we defend our own interpretation of his thought against suggestions to the effect that it is oriented towards neither instrumentalism nor scientific realism. (shrink)

Edmund Husserl, founder of the phenomenological movement, is usually read as an idealist in his metaphysics and an instrumentalist in his philosophy of science. In _Nature’s Suit_, Lee Hardy argues that both views represent a serious misreading of Husserl’s texts. Drawing upon the full range of Husserl’s major published works together with material from Husserl’s unpublished manuscripts, Hardy develops a consistent interpretation of Husserl’s conception of logic as a theory of science, his phenomenological account of truth and rationality, his ontology (...) of the physical thing and mathematical objectivity, his account of the process of idealization in the physical sciences, and his approach to the phenomenological clarification and critique of scientific knowledge. Offering a jargon-free explanation of the basic principles of Husserl’s phenomenology, _Nature’s Suit_ provides an excellent introduction to the philosophy of Edmund Husserl as well as a focused examination of his potential contributions to the philosophy of science. While the majority of research on Husserl’s philosophy of the sciences focuses on the critique of science in his late work, _The Crisis of European Sciences_, Lee Hardy covers the entire breadth of Husserl’s reflections on science in a systematic fashion, contextualizing Husserl’s phenomenological critique to demonstrate that it is entirely compatible with the theoretical dimensions of contemporary science. (shrink)

Edmund Husserl, founder of the phenomenological movement, is usually read as an idealist in his metaphysics and an instrumentalist in his philosophy of science. In _Nature’s Suit_, Lee Hardy argues that both views represent a serious misreading of Husserl’s texts. Drawing upon the full range of Husserl’s major published works together with material from Husserl’s unpublished manuscripts, Hardy develops a consistent interpretation of Husserl’s conception of logic as a theory of science, his phenomenological account of truth and rationality, his ontology (...) of the physical thing and mathematical objectivity, his account of the process of idealization in the physical sciences, and his approach to the phenomenological clarification and critique of scientific knowledge. Offering a jargon-free explanation of the basic principles of Husserl’s phenomenology, _Nature’s Suit_ provides an excellent introduction to the philosophy of Edmund Husserl as well as a focused examination of his potential contributions to the philosophy of science. While the majority of research on Husserl’s philosophy of the sciences focuses on the critique of science in his late work, _The Crisis of European Sciences_, Lee Hardy covers the entire breadth of Husserl’s reflections on science in a systematic fashion, contextualizing Husserl’s phenomenological critique to demonstrate that it is entirely compatible with the theoretical dimensions of contemporary science. (shrink)

In this paper I review three different positions on the wave function, namely: nomological realism, dispositionalism, and configuration space realism by regarding as essential their capacity to account for the world of our experience. I conclude that the first two positions are committed to regard the wave function as an abstract entity. The third position will be shown to be a merely speculative attempt to derive a primitive ontology from a reified mathematical space. Without entering any discussion about nominalism, (...) I conclude that an elimination of abstract entities from one’s ontology commits one to instrumentalism about the wave function, a position that therefore is not as unmotivated as it has seemed to be to many philosophers. (shrink)

Pierre Duhem's well-known argument for the underdetermination of theory choice by evidence is often cited in current discussion of scientific realism and antirealism. I argue that the familiar account of it that participants draw on is incomplete. After studying Duhem's philosophy of scientific language, which he regards as both abstract and symbolic, I conclude that, for Duhem, underdetermination rests on the observation that instruments are ubiquitous in mathematical sciences. This ties auxiliary assumptions to the use of instruments and completes (...) the familiar account of underdetermination. Even when complete, however, this account has no obvious implications for the debates about realism, nor does it settle how Duhem's own philosophy should be interpreted. An interpretive problem arises because there is textual support for both antirealist and realist readings of his work. Accordingly, in the recent literature he has been interpreted both as a fictionalist and as a structural realist. I argue that neither of these readings will do. First, the reasoning that might motivate a fictionalist interpretation assumes a certain semantical view that Duhem would not accept. To develop his pragmatic alternative, I address his conception of theory-ladenness and his account of how scientists come to understand phenomena. Second, the realist conviction that mitigates his apparent instrumentalism---specifically, the belief that physical theory is approaching a logically unified and natural classification---does not implicate him as a structural realist. For Duhem, natural classifications are ontologically significant and preserved over conceptual revolutions because they pick out essential features of real things and order phenomena accordingly. To properly classify Duhem's philosophy, I study his realist and antirealist claims and point out that they are different. In his view, scientific reasoning leads straight to antirealism but feelings, hunches, and intuitions motivate, without justifying, a kind of realism. I argue that Duhem's approach is characteristic of motivational realism. (shrink)

Duhem has generally been understood to have maintained that the major Greek astronomers were instrumentalists. This view has emerged mainly from a reading of his 1908 publication To Save the Phenomena. In it he sharply contrasted a sophisticated Greek interpretation of astronomical models (for Duhem this was that they were mathematical contrivances) with a naive insistence of the Arabs on their concrete reality. But in Le Système du monde, which began to appear in 1913, Duhem modified his views on (...) Greek astronomy considerably; his more subtle understanding included the recognition that many Greeks subordinated mathematical astronomy to physical theory. But he could not completely repudiate his earlier views about Greek astronomy in part because his extreme nineteenth century prejudices led him to continue to insist on a clear-cut demarcation between Greek and Arabic astronomy. The inevitable result is a certain unevenness in the Système and some glaring inconsistencies. (shrink)

The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable models; models that allow a realist interpretation. In this thesis some of these proofs are discussed, like von Neumann’s Theorem, the Kochen-Specker Theorem and the Bell-inequalities. Some more recent developments are also investigated, like Meyer’s nullification of the Kochen-Specker Theorem, the MKC-models and Conway and Kochen’s (...) Free Will Theorem. This last one is taken to suggest that the problems that arise for certain interpretations of quantum mechanics are not limited to realist interpretations only, but also affect certain instrumentalist interpretations. It is argued that one may arrive at a more satisfying interpretation of quantum mechanics if one adopts a logic that seems more compatible with the instrumentalist viewpoint namely, intuitionistic logic. The motivations for adopting this form of logic rather than classical logic or quantum logic are linked to some of the philosophical ideas of Bohr. In particular a new interpretation of Bohr’s notion of complementarity is proposed. Finally some possibilities are explored for linking the intuitionistic interpretation of quantum mechanics to the mathematical formalism of the theory. (shrink)

As in the case of great books in all branches of philosophy, Pierre Duhem's Le Théorie Physique , first published in 1906, can be looked to as the progenitor of many different and even conflicting currents in subsequent philosophy of science. On a superficial reading, it seems to be an expression of what later came to be called deductivist and instrumentalist analyses of scientific theory. Duhem's very definition of physical theory, put forward early in the book, is the quintessence of (...) instrumentalism: A physical theory is not an explanation. It is a system of mathematical propositions, deduced from a small number of principles, which aim to represent as simply, as completely, and as exactly as possible a set of experimental laws [p. 19]. (shrink)

The new explanatory or enhanced indispensability argument alleges that our mathematical beliefs are justified by their indispensable appearances in scientific explanations. This argument differs from the standard indispensability argument which focuses on the uses of mathematics in scientific theories. I argue that the new argument depends for its plausibility on an equivocation between two senses of explanation. On one sense the new argument is an oblique restatement of the standard argument. On the other sense, it is vulnerable to an (...) instrumentalist response. Either way, the explanatory indispensability argument is no improvement on the standard one. (shrink)

In this study I argue that Husserl’s phenomenology is compatible with a realistic interpretation of scientific theories. That said, I distinguish between the realistic interpretation of scientific theories and scientific realism. The former holds that the theoretical terms of a scientific theory are intended to refer, and that if we have good reason to believe that a scientific theory is true then we also have good reason to believe the entities it refers to exist. Scientific realism holds that the world (...) as described by the physical sciences not only exists, it is the only world that exists—the world of everyday perceptual experience must be demoted to the status of a mere appearance. My case for the compatibility of Husserl’s phenomenology with a realistic interpretation of scientific theories is based on a distinction between scientific laws and scientific theories. I hold that Husserl’s instrumentalism, if one can call it that, is restricted to an interpretation of scientific laws; accordingly, his anti-realism is directed against the reification of ideal objects constructed in the course of the exact mathematical representation of scientific laws, not against the theoretical entities postulated in the explanation of those laws. At the end of the study I seek to allay the fear that if one adopts a realistic interpretation of scientific theories one is thereby committed to some version of scientific realism. (shrink)