The paper distinguishes between two kinds of mathematics, naturalmathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role (...) of diagrams in mathematics, and the effectiveness of mathematics in naturalscience. (shrink)
In this book, 13 leading philosophers of science focus on the work of Professor Howard Stein, best known for his study of the intimate connection between ...
Immanuel Kant's Metaphysical Foundations of NaturalScience (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second and (...) third chapters—the Dynamics and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)
Hermeneutics, or interpretation, is concerned with the generation, transmission, and acceptance of meaning within the lifeworld, and was the original method of the human sciences stemming, from F. Schleiermacher and W. Dilthey. The `hermeneutic philosophy' refers mostly to Heidegger. This paper addresses naturalscience from the perspective of Heidegger's analysis of meaning and interpretation. Its purpose is to incorporate into the philosophy of science those aspects of historicality, culture, and tradition that are absent from the traditional analysis (...) of theory and explanation, to re-orient the current discussion about scientific realism around the hermeneutics of meaning and truth in science, and to establish some relationship between the current philosophy of naturalscience and hermeneutical philosophy. The paper has particular relevance to the history and social studies of science and technology. (shrink)
In the vast literature on human rights and natural law one finds arguments that draw on science or mathematics to support claims to universality and objectivity. Here are two such arguments: 1) Human rights are as universal (i.e., valid independently of their specific historical and cultural Western origin) as the laws and theories of science; and 2) principles of natural law have the same objective (metahistorical) validity as mathematical principles. In what follows I will examine (...) these arguments in some detail and argue that both are misplaced. A section of the paper will be devoted to a discussion of arguments relying on the historical and cultural specificity (and intrinsic superiority) of Western science. The conclusion is that both science and mathematics offer little help to anyone wanting to make use of them as paradigms of universality, objectivity, and rationality. Finally, I will draw some consequences for the idea of human rights. (shrink)
Volume 9 of the Routledge History of Philosophy surveys ten key topics in the Philosophy of Science, Logic and Mathematics in the Twentieth Century. Each article is written by one of the world's leading experts in that field. The papers provide a comprehensive introduction to the subject in question, and are written in a way that is accessible to philosophy undergraduates and to those outside of philosophy who are interested in these subjects. Each chapter contains an extensive bibliography (...) of the major writings in the field. Among the topics covered are the philosophy of logic; Ludwig Wittgenstein's Tractatus; a survey of logical positivism; the philosophy of physics and of science; probability theory and cybernetics. (shrink)
This discussion note of ( Batterman [2010] ) clarifies the modest aims of my ‘mapping account' of applications of mathematics in science. Once these aims are clarified it becomes clear that Batterman's ‘completely new approach' ( Batterman [2010] , p. 24) is not needed to make sense of his cases of idealized mathematical explanations. Instead, a positive proposal for the explanatory power of such cases can be reconciled with the mapping account.
In many of the special sciences, mathematical models are used to provide information about specified target systems. For instance, population models are used in ecology to make predictions about the abundance of real populations of particular organisms. The status of mathematical models, though, is unclear and their use is hotly contested by some practitioners. A common objection levelled against the use of these models is that they ignore all the known, causally-relevant details of the often complex target systems. Indeed, the (...) objection continues, mathematical models, by their very nature, abstract away from what matters and thus cannot be relied upon to provide any useful information about the systems they are supposed to represent. In this paper, I will examine the role of some typical mathematical models in population ecology and elsewhere. I argue that while, in a sense, these models do ignore the causal details, this move can not only be justified, it is necessary. I will argue that idealising away from complicating causal details often gives a clearer view of what really matters. And often what really matters is not the push and shove of base-level causal processes, but higher-level predictions and (non-causal) explanations. (shrink)
Foundational work in mathematics by some of the other participants in the symposium helps towards answering the question whether a heterodox mathematics could in principle be used as successfully as is orthodox mathematics in scientific applications. This question is turn, it will be argued, is relevant to the question how far current science is the way it is because the world is the way it is, and how far because we are the way we are, which (...) is a central question, if not the central question, of philosophy of science. (shrink)
Heinrich Rickert (1863-1936) was One of the leading neo-Kantian philosophers in Germany and a crucial figure in the discussions of the foundations of the social sciences in the first quarter of the twentieth century. His views were extremely influential, most significantly on Max Weber. The Limits of Concept Formation in NaturalScience is Rickert's most important work, and it is here translated into English for the first time. It presents his systematic theory of knowledge and philosophy of (...) class='Hi'>science, and deals particularly with historical knowledge and the problem of demarcating the natural from the human sciences. The theory Rickert develops is carefully argued and of great intrinsic interest. It departs from both positivism and neo-Hegelian idealism and is worked out by contrast to the views of others, particularly Dilthey and the early phenomenologists. (shrink)
This is a lively and clearly written introduction to the philosophy of naturalscience, organized around the central theme of scientific realism. It has two parts. 'Representing' deals with the different philosophical accounts of scientific objectivity and the reality of scientific entities. The views of Kuhn, Feyerabend, Lakatos, Putnam, van Fraassen, and others, are all considered. 'Intervening' presents the first sustained treatment of experimental science for many years and uses it to give a new direction to debates (...) about realism. Hacking illustrates how experimentation often has a life independent of theory. He argues that although the philosophical problems of scientific realism can not be resolved when put in terms of theory alone, a sound philosophy of experiment provides compelling grounds for a realistic attitude. A great many scientific examples are described in both parts of the book, which also includes lucid expositions of recent high energy physics and a remarkable chapter on the microscope in cell biology. (shrink)
This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.
In 1792 and 1798 Kant noticed two basic problems with hisMetaphysical Foundations of NaturalScience (MAdN) which opened a crucial gap in the Critical system as a whole. Why is theMAdN so important? I show that the Analogies of Experience form an integrated proof of transeunt causality. This is central to Kant's answer to Hume. This proof requires explicating the empirical concept of matter as the moveable in space, it requires the specifically metaphysical principle that every physical event (...) has an external cause, and it requires a metaphysical principle regarding the individuation of spatio-temporal things. These three doctrines are not defended in the firstCritique, but only in theMAdN. Kant's transcendental analysis of the conditions of experience thus requires the special metaphysics of theMAdN. This marks an important shift in Kant's view of the metaphysical basis of the transcendental philosophy. (shrink)
This paper aims at a partial rehabilitation of E. A. Moody''s characterization of the 14th century as an age of rising empiricism, specifically by contrasting the conception of the naturalscience of psychology found in the writings of a prominent 13th-century philosopher (Thomas Aquinas) with those of two 14th-century philosophers (John Buridan and Nicole Oresme). What emerges is that if the meaning of empiricism can be disengaged from modern and contemporary paradigms, and understood more broadly in terms of (...) a cluster of epistemic doctrines concerned with the methodology of knowing, it characterizes very appropriately some of the differences between the ways in which late-medieval thinkers both understood and practised the science of psychology. In particular, whereas Aquinas thinks psychology is about reasoning demonstratively to the real nature of the soul from its evident operations (thereby assimilating psychology to metaphysics), Buridan and Oresme, both of whom doubt whether real animate natures can be known empirically, focus on giving detailed accounts of those operations themselves (thereby assimilating psychology to physics). (shrink)
This paper aims at a partial rehabilitation of E. A. Moody's characterization of the 14th century as an age of rising empiricism, specifically by contrasting the conception of the naturalscience of psychology found in the writings of a prominent 13th-century philosopher (Thomas Aquinas) with those of two 14th-century philosophers (John Buridan and Nicole Oresme). What emerges is that if the meaning of empiricism can be disengaged from modern and contemporary paradigms, and understood more broadly in terms (...) of a cluster of epistemic doctrines concerned with the methodology of knowing, it characterizes very appropriately some of the differences between the ways in which late-medieval thinkers both understood and practised the science of psychology. In particular, whereas Aquinas thinks psychology is about reasoning demonstratively to the real nature of the soul from its evident operations (thereby assimilating psychology to metaphysics), Buridan and Oresme, both of whom doubt whether real animate natures can be known empirically, focus on giving detailed accounts of those operations themselves (thereby assimilating psychology to physics). (shrink)
This paper is a contribution to the question of how aspects of science have been perceived through history. In particular, I will discuss how the contribution of axiomatics to the development of science and mathematics was viewed in 20th century philosophy of science and philosophy of mathematics. It will turn out that in connection with scientific methodology, in particular regarding its use in the context of discovery, axiomatics has received only very little attention. This is (...) a rather surprising result, since axiomatizations have been employed extensively in mathematics, science, and also by the philosophers themselves. (shrink)
The Enhanced Indispensability Argument (Baker [ 2009 ]) exemplifies the new wave of the indispensability argument for mathematical Platonism. The new wave capitalizes on mathematics' role in scientific explanations. I will criticize some analyses of mathematics' explanatory function. In turn, I will emphasize the representational role of mathematics, and argue that the debate would significantly benefit from acknowledging this alternative viewpoint to mathematics' contribution to scientific explanations and knowledge.
Robertson's earlier work, The New Renaissance projected the likely future impact of computers in changing our culture. Phase Change builds on and deepens his assessment of the role of the computer as a tool driving profound change by examining the role of computers in changing the face of the sciences and mathematics. He shows that paradigm shifts in understanding in science have generally been triggered by the availability of new tools, allowing the investigator a new way of seeing (...) into questions that had not earlier been amenable to scientific probing. (shrink)
In this paper, I attempt to develop the account of intellectual virtues offered by Aristotle and St. Thomas in a way which recognizes faith as a good intellectual habit. I go on to argue that, as a practical matter, this virtue is needed not only in theology, where it provides the basis of further intellectual work, but also in the natural sciences, where it is required given the complexity of the subject matter and the cooperative nature of the enterprise.
Metaphors and models involve correspondences between events in separate domains. They differ in the form and precision of how the correspondences are expressed. Examples include correspondences between phylogenic and ontogenic selection, and wave and particle metaphors of the mathematics of quantum physics. An implication is that the target article's metaphors of resistance to change may have heuristic advantages over those of momentum.
This essay explores Hegel’s treatment of Carl Friedrich Gauss’s mathematical discoveries as examples of “Analytic Cognition.” Unfortunately, Hegel’s main point has been virtually lost due to an editorial blunder tracing back almost a century, an error that has been perpetuated in many subsequent editions and translations.The paper accordingly has three sections. In the first, I expose the mistake and trace its pervasive influence in multiple languages and editions of the Wissenschaftder Logik. In the second section, I undertake to explain the (...) mathematical significance of Gauss’s discoveries. In the third section, I take a look at the deeperimplications of Hegel’s treatment of Gauss’s work as a window onto the nature and limitations of analytic cognition. In conclusion, I seek to explain how thelinear method embodied in deductive reason leads by its own inner principle, according to Hegel, to its dialectical Aufhebung (sublation). The result is a kindof deliberately circular reasoning that he describes as “the Absolute Idea.”. (shrink)
This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of (...) cognitive analyses of historical developments of mathematics has been primarily on the former, even if they claim to be about the latter. (shrink)
In Aristotle's teleological view of the world, natural things come to be and are present for the sake of some function or end (for example, wings are present in birds for the sake of flying). Whereas much of recent scholarship has focused on uncovering the (meta-)physical underpinnings of Aristotle's teleology and its contrasts with his notions of chance and necessity, this book examines Aristotle's use of the theory of natural teleology in producing explanations of natural phenomena. Close (...) analyses of Aristotle's natural treatises and his Posterior Analytics show what methods are used for the discovery of functions or ends that figure in teleological explanations, how these explanations are structured, and how well they work in making sense of phenomena. The book will be valuable for all who are interested in Aristotle's naturalscience, his philosophy of science, and his biology. (shrink)
ABSTRACT. May scientists rely on substantive, a priori presuppositions? Quinean naturalists say "no," but Michael Friedman and others claim that such a view cannot be squared with the actual history of science. To make his case, Friedman offers Newton's universal law of gravitation and Einstein's theory of relativity as examples of admired theories that both employ presuppositions (usually of a mathematical nature), presuppositions that do not face empirical evidence directly. In fact, Friedman claims that the use of such presuppositions (...) is a hallmark of "science as we know it." But what should we say about the special sciences, which typically do not rely on the abstruse formalisms one finds in the exact sciences? I identify a type of a priori presupposition that plays an especially striking role in the development of empirical psychology. These are ontological presuppositions about the type of object a given science purports to study. I show how such presuppositions can be both a priori and rational by investigating their role in an early flap over psychology's contested status as a naturalscience. The flap focused on one of the field's earliest textbooks, William James's Principles of Psychology. The work was attacked precisely for its reliance on a priori presuppositions about what James had called the "mental state," psychology's (alleged) proper object. I argue that the specific presuppositions James packed into his definition of the "mental state" were not directly responsible to empirical evidence, and so in that sense were a priori; but the presuppositions were rational in that they were crafted to help overcome philosophical objections (championed by neo-Hegelians) to the very idea that there can be a genuine science of mind. Thus, my case study gives an example of substantive, a priori presuppositions being put to use—to rational use—in the special sciences. In addition to evaluating James's use of presuppositions, my paper also offers historical reflections on two different strands of pragmatist philosophy of science. One strand, tracing back through Quine to C. S. Peirce, is more naturalistic, eschewing the use of a priori elements in science. The other strand, tracing back through Kuhn and C. I. Lewis to James, is more friendly to such presuppositions, and to that extent bears affinity with the positivist tradition Friedman occupies. (shrink)
Wigner famously referred to the `unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics, I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.
Contemporary philosophy's three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion's share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed (...) more briefly in section 6. (shrink)
This is a transcript of Milne's manuscript notes for a talk which he gave to fellow members of the Cambridge University NaturalScience Club in his rooms at Trinity College, Cambridge, on February 6, 1922. The notes are deposited in the Bodleian Library, University of Oxford, Special Collections and Western Manuscripts. The background and essential points of Milne's talk are analysed in the article preceding this one. As far as is known, the text has not hitherto been published. (...) Milne's handwriting is difficult to read, and square brackets [...] denote the addition of a word for clarity of meaning. Meg Weston Smith and Simon Rebsdorf have ventured to fill in some chapter titles just in order to help with the separation of the varying content, hence we have made up all the headlines. All italics correspond to underlined words in the original. The Bergson citations and the Eddington passage at the end of the original text have not been transcribed. (shrink)
This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in the (...) sciences, Spinoza sided with those that criticized the aspirations of those (the physico-mathematicians, Galileo, Huygens, Wallis, Wren, etc) who thought the application of mathematics to nature was the way to make progress. In particular, he offers grounds for doubting their confidence in the significance of measurement as well as their piece-meal methodology (see section 2). Along the way, this chapter offers a new interpretation of common notions in the context of treating Spinoza’s account of motion (see section 3). (shrink)
Our lives, states of health, relationships, behavior, experiences of the natural world, and the technologies that shape our contemporary existence are subject to a superfluity of competing, multi-faceted and sometimes incompatible explanations. Widespread confusion about the nature of "explanation" and its scope and limits pervades popular exposition of the natural sciences, popular history and philosophy of science. This fascinating book explores the way explanations work, why they vary between disciplines, periods, and cultures, and whether they have any (...) necessary boundaries. In other words, Explanations aims to achieve a better understanding of explanation, both within the sciences and the humanities. It features contributions from expert writers from a wide range of disciplines, including science, philosophy, mathematics, and social anthropology. (shrink)
The widespread impression that recent philosophy of science has pioneered exploration of the “social dimensions of scientific knowledge‘ is shown to be in error, partly due to a lack of appreciation of historical precedent, and partly due to a misunderstanding of how the social sciences and philosophy have been intertwined over the last century. This paper argues that the referents of “democracy‘ are an important key in the American context, and that orthodoxies in the philosophy of science tend (...) to be molded by the actual regimes of science organization within which they are embedded. These theses are illustrated by consideration of three representative philosophers of science: John Dewey, Hans Reichenbach, and Philip Kitcher. [Copyright &y& Elsevier]. (shrink)
The aim of the paper is an extension of the idealizational theory of science in order to explicate intuitions of historians and philosophers of history about unpredictability and contingency of history. The author identifies two types of essential structures: the first kind dominated by the main factor and the second kind which is dominated by a class of secondary factors. In an essential structure dominated by the main factor, the power of influence it exerts is greater than the sum (...) of the power of influence of secondary factors. In an essential structure dominated by secondary factors, their total influence is greater than the influence exerted by the main factor, although the power of the latter influence is greater than the power of influence of each secondary factor taken separately. In the latter kind of essential structure the so-called cascade effect can occur which means that at certain moment the power of influence of secondary factors can be greater than influence of main factor. In the further part of this paper, the author examines consequences of cascade effect for construction of scientific theory and historical narrative. (shrink)
In 1801 Hegel charged that, on Kant’s analysis, forces are ‘either purely ideal, in which case they are not forces, or else they are transcendent’. I argue that this objection, which Hegel did not spell out, reveals an important and fundamental line of internal criticism of Kant’s Critical philosophy. I show that Kant’s basic forces of attraction and repulsion, which constitute matter, are merely ideal because Kant’s arguments for them are circular and beg the question, and they have no determinate (...) connection to any of the basic forces of Newtonian physics. Hence they are mere Gedankendinge. I argue further, that real physical forces transcend Kant’s analysis by showing that his proof of Newton’s law of inertia is unsound. I then show that this apparently specific disagreement underlies the enormous philosophical shift from Kant’s anti-naturalist transcendental idealism to Hegel’s naturalistic use of regressive, quasi-transcendental arguments. (shrink)
This paper deals with Hobbes's theory of optical images, developed in his optical magnum opus, 'A Minute or First Draught of the Optiques' (1646), and published in abridged version in De homine (1658). The paper suggests that Hobbes's theory of vision and images serves him to ground his philosophy of man on his philosophy of body. Furthermore, since this part of Hobbes's work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics (...) in Hobbes's philosophy. The paper points to some difficulties in the thesis of Shapin and Schaffer, who presented geometry as a 'paradigm' for Hobbes's natural philosophy. It will be argued here that Hobbes's application of geometry to optics was dictated by his metaphysical and epistemological principles, not by a blind belief in the power of geometry. Geometry supported causal explanation, and assisted reason in making sense of appearances by helping the philosopher understand the relationships between the world outside us and the images it produces in us. Finally the paper broadly suggests how Hobbes's theory of images may have triggered, by negative example, the flourishing of geometrical optics in Restoration England. (shrink)
Although George Berkeley himself made no major scientific discoveries, nor formulated any novel theories, he was nonetheless actively concerned with the rapidly evolving science of the early eighteenth century. Berkeley's works display his keen interest in natural philosophy and mathematics from his earliest writings (Arithmetica, 1707) to his latest (Siris, 1744). Moreover, much of his philosophy is fundamentally shaped by his engagement with the science of his time. In Berkeley's best-known philosophical works, the Principles and Dialogues, (...) he sets up his idealistic system in opposition to the materialist mechanism he finds in Descartes and Locke. In De Motu, Berkeley refines and extends his philosophy of science in the context of a critique of the dynamic accounts of motion offered by Newton and Leibniz. And in Siris, Berkeley's flirtation with neo-Platonism draws inspiration from the fire theory of Boerhaave as well as Newton's aetherial speculations in the Queries of the Optics. In examining Berkeley's critical engagement with the natural philosophy of his time, we will thus improve our understanding of not just his philosophy of science, but of his philosophical corpus as a whole. (shrink)
In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed (...) in polynomial time. Additionally, we suggest that plausible semantic theories of the everyday fragment of natural language can be formulated in the existential fragment of second-order logic. -/- In Chapter 2 we give an overview of the basic notions of generalized quantifier theory, computability theory, and descriptive complexity theory. -/- In Chapter 3 we prove that PTIME quantifiers are closed under iteration, cumulation and resumption. Next, we discuss the NP-completeness of branching quantifiers. Finally, we show that some Ramsey quantifiers define NP-complete classes of finite models while others stay in PTIME. We also give a sufficient condition for a Ramsey quantifier to be computable in polynomial time. -/- In Chapter 4 we investigate the computational complexity of polyadic lifts expressing various readings of reciprocal sentences with quantified antecedents. We show a dichotomy between these readings: the strong reciprocal reading can create NP-complete constructions, while the weak and the intermediate reciprocal readings do not. Additionally, we argue that this difference should be acknowledged in the Strong Meaning hypothesis. -/- In Chapter 5 we study the definability and complexity of the type-shifting approach to collective quantification in natural language. We show that under reasonable complexity assumptions it is not general enough to cover the semantics of all collective quantifiers in natural language. The type-shifting approach cannot lead outside second-order logic and arguably some collective quantifiers are not expressible in second-order logic. As a result, we argue that algebraic (many-sorted) formalisms dealing with collectivity are more plausible than the type-shifting approach. Moreover, we suggest that some collective quantifiers might not be realized in everyday language due to their high computational complexity. Additionally, we introduce the so-called second-order generalized quantifiers to the study of collective semantics. -/- In Chapter 6 we study the statement known as Hintikka's thesis: that the semantics of sentences like ``Most boys and most girls hate each other'' is not expressible by linear formulae and one needs to use branching quantification. We discuss possible readings of such sentences and come to the conclusion that they are expressible by linear formulae, as opposed to what Hintikka states. Next, we propose empirical evidence confirming our theoretical predictions that these sentences are sometimes interpreted by people as having the conjunctional reading. -/- In Chapter 7 we discuss a computational semantics for monadic quantifiers in natural language. We recall that it can be expressed in terms of finite-state and push-down automata. Then we present and criticize the neurological research building on this model. The discussion leads to a new experimental set-up which provides empirical evidence confirming the complexity predictions of the computational model. We show that the differences in reaction time needed for comprehension of sentences with monadic quantifiers are consistent with the complexity differences predicted by the model. -/- In Chapter 8 we discuss some general open questions and possible directions for future research, e.g., using different measures of complexity, involving game-theory and so on. -/- In general, our research explores, from different perspectives, the advantages of identifying meaning with algorithms and applying computational complexity analysis to semantic issues. It shows the fruitfulness of such an abstract computational approach for linguistics and cognitive science. (shrink)
The naturalism versus interpretivism debate the in philosophy of social science is traditionally framed as the question of whether social science should attempt to emulate the methods of naturalscience. I show that this manner of formulating the issue is problematic insofar as it presupposes an implausibly strong unity of method among the natural sciences. I propose instead that what is at stake in this debate is the feasibility and desirability of what I call the (...) Enlightenment ideal of social science. I argue that this characterization of the issue is preferable, since it highlights the central disagreement between advocates of naturalism and interpretivism, makes connections with recent work on the topics of causal inference and social epistemology, while avoiding unfruitful comparisons between the social and natural sciences. (shrink)
Gerd Buchdahl's international reputation rests on his masterly writings on Kant. In them he showed how Kant transformed the philosophical problems of his predecessors and he minutely investigated the ways in which Kant related his critical philosophy to the contents and methods of naturalscience. Less well known, if only because in large part unpublished, are the writings in which Buchdahl elaborated his own views on the methods and status of the sciences. In this paper I examine the (...) roles of hermeneutics in Buchdahl's reconstruction of Kant's philosophical system and in his own 'transcendental methodological' approach to the philosophy of science. The first section looks at Buchdahl's views on the theory and practice of historical interpretation and at the Husserlian hermeneutic scheme of reduction and realisation that he used in his later accounts of the philosophies of science of Kant and himself. The second section concentrates on Buchdahl's treatment of the grounds of science in Kant; and the third on the hermeneutic strategies Buchdahl employed in articulating and justifying his own views. The paper closes with reflections on the impact and importance of Buchdahl's interpretation of Kant's critical philosophy in relation to the sciences and of his own hermeneutically based philosophy of science. (shrink)
This article presents the main features of the work of Domenico Vandelli (1735-1816), an Italian-born man of science who lived a large part of his life in Portugal. Vandelli's scientific interests as a naturalist paved the way to his activities as a reformer and adviser on economic and financial issues. The topics covered in his writings are similar to those discussed by Linnaeus, with whom Vandelli corresponded. They clearly reveal that the scientific preparation indispensable for a better knowledge of (...)natural resources was also a fundamental condition for correctly addressing problems of efficiency in their economic allocation. The key argument put forward in this article is that the relationship between natural history and the agenda for economic reform and development deserves to be further analysed. It is indeed a central element in the emergence of political economy as an autonomous scientific discourse during the last decades of the eighteenth century. (shrink)
As many cultural historians of the sciences have recently indicated, eighteenth-century illustrations of natural historical works represent an important source that can be used to explore the ways in which nature and the study of nature were regarded in the period. Naturalistic illustrations, however, are not the only genre of images that may help the historian in this investigation. Another interesting source is represented by images of nature and natural objects connected with fictional literature. Yet, little attention has (...) been devoted so far to this genre of images. In this paper I analyse some of the engravings which illustrate Retif de la Bretonne's imaginary voyage La Decouverte australe par un homme volant (1781). My aim is to show that these illustrations convey a well-defined image of the natural universe, and that their analysis may contribute to our understanding of the various significances and roles attached to Nature in the period-particularly bringing to the fore its moral and political uses. Further, by analysing the ways in which they connect and integrate a variety of artistic and discursive traditions related to fiction, travel, and natural history, I hope to suggest some of the ways in which this genre of images may be used to shed light on the eighteenth-century interplay between spheres of knowledge later assigned to such distinct disciplines as 'science', 'literature', or 'art'. (shrink)
This paper considers the role of mathematics in the process of acquiring new knowledge in physics and astronomy. The defining of the notions of continuum and discreteness in mathematics and the natural sciences is examined. The basic forms of representing the heuristic function of mathematics at theoretical and empirical levels of knowledge are studied: deducing consequences from the axiomatic system of theory, the method of generating mathematical hypotheses, “pure” proofs for the existence of objects and processes, (...) mathematical modelling, the formation of mathematics on the basis of internal mathematical principles and the mathematical theory of experiment. (shrink)
Recent discussion of mechanism has suggested new approaches to several issues in the philosophy of science, including theory structure, causal explanation, and reductionism. Here, I apply what I take to be the fruits of the Ônew mechanical philosophyÕ to an analysis of a contemporary debate in evolutionary biology about the role of natural selection in speciation. Traditional accounts of that debate focus on the geographic context of genetic divergence— namely, whether divergence in the absence of geographic isolation is (...) possible (or significant). Those accounts are at best incomplete, I argue, because they ignore the mechanisms producing divergence and miss what is at stake in the biological debate. I argue that the biological debate instead concerns the scope of particular speciation mechanisms which assign different roles to natural selection at various stages of divergence. The upshot is a new interpretation of the crux of that debate—namely, whether divergence with gene flow is possible (or significant) and whether the isolating mechanisms producing it are adaptive. Ó 2005 Elsevier Ltd. All rights reserved. (shrink)
Turning Images in Philosophy, Science, and Religion: A New Book of Nature brings together new essays addressing the role of images and imagination recruited in the perennial debates surrounding nature, mind, and God. -/- The debate between "new atheists" and religious apologists today is often hostile. This book sets a new tone by locating the debate between theism and naturalism (most "new atheists" are self-described "naturalists") in the broader context of reflection on imagination and aesthetics. The eleven essays will (...) be of interest to anyone who is fascinated by the power of imagination and the role of aesthetics in deciding between worldviews or philosophies of nature. Representing a variety of points of view, authors include outstanding philosophers of religion and of science, a distinguished art historian, and a visual artist. -/- The book begins with Martin Kemp's essay on the work of the biologist, mathematician and classical scholar D'Arcy Wentworth Thompson in which Kemp develops the idea of "structural intuitions and a critique of reductive thinking about the natural world. This is followed by Geoffrey Gorham's overview and analysis of images of nature and God found in early modern science and philosophy. Anthony O'Hear questions a reductive, naturalist account of the origin of mind and values. Dale Jacquette offers a thoroughgoing naturalistic philosophy of the emergence of intentionality and a unique argument about the emergence of art and the aesthetic appreciation of nature. E.J. Lowe brings to light some challenges facing naturalistic approaches to human imaginative sensibility. Douglas Hedley articulates and defends a cognitive account of imagination, highlighting some of the difficulties confronting naturalism. Daniel N. Robinson offers a sweeping treatment of nature and naturalism, historically engaging Aristotle, Kant, Hegel and others. Conor Cunningham provides an aggressive critique of contemporary naturalism. Gordon Graham investigates the resources of naturalism in accounting for our sense of the sacred. Mark Wynn provides a subtle understanding of imagination and perception, suggesting how these may play into the theism - naturalism debate. The book concludes with Jil Evans' reflections on how images of the Galapagos Islands have been employed philosophically to picture either a naturalist or theistic image of nature. (shrink)
Modern science began as natural philosophy. In the time of Newton, what we call science and philosophy today – the disparate endeavours – formed one mutually interacting, integrated endeavour of natural philosophy: to improve our knowledge and understanding of the universe, and to improve our understanding of ourselves as a part of it. Profound, indeed unprecedented discoveries were made. But then natural philosophy died. It split into science on the one hand, and philosophy on (...) the other. This happened during the 18th and 19th centuries, and the split is now built into our intellectual landscape. But the two fragments, science and philosophy, are defective shadows of the glorious unified endeavour of natural philosophy. Rigour, sheer intellectual good sense and decisive argument demand that we put the two together again, and rediscover the immense merits of the integrated enterprise of natural philosophy. This requires an intellectual revolution, with dramatic implications for how we understand our world, how we understand and do science, and how we understand and do philosophy. There are dramatic implications, too, for education, and for the entire academic endeavour, and its capacity to help us discover how to tackle more successfully our immense global problems. (shrink)
The question of how and why mathematics can be applied to physical reality should be approached through the history of science, as a series of case studies which may reveal both generalizable patterns and salient differences in the grounds and nature of that application from era to era. The present examination of Descartes' Principles of Philosophy Part II, reveals a deep ambiguity in the relation of Euclidean geometry to res extensa, and a tension between geometrical form and 'common (...) motion of parts' as principles of individuation for matter in Cartesian physics. (shrink)
Since antiquity well into the beginnings of the 20th century geometry was a central topic for philosophy. Since then, however, most philosophers of science, if they took notice of topology at all, considered it as an abstruse subdiscipline of mathematics lacking philosophical interest. Here it is argued that this neglect of topology by philosophy may be conceived of as the sign of a conceptual sea-change in philosophy of science that expelled geometry, and, more generally, mathematics, from (...) the central position it used to have in philosophy of science and placed logic at center stage in the 20th century philosophy of science. Only in recent decades logic has begun to loose its monopoly and geometry and topology received a new chance to find a place in philosophy of science. (shrink)
J. W. Goethe is well known as one of the world's greatest poets. Some are also aware that throughout his long and active life Goethe devoted much of his time to naturalscience. His theory of colour and studies in the morphology of plants are acknowledged contributions in their fields. What is much less known is that in his scientific work Goethe was attempting to elaborate and justify a new basic methodology for the natural sciences. He opposed (...) and wished to refute the one-sided quantitative-mechanistic method which had been dominant since Galileo and Newton (and in principle still prevails today) and to set up against it a qualitative method. An essential characteristic of this qualitative method, according to Goethe, is that it is immune to a Humean reduction of the status of 'natural laws' to mere hypotheses. This claim makes Goethe's view directly relevant for current discussion of such questions as the status of scientific 'laws' and the correct method of theory construction. The present essay tries to show the fruitfulness of Goethe's view for such discussions, partly by means of an exposition of the view — drawn from various works — and partly by drawing consequences from it which bring it into direct contact with contemporary discussions in philosophy of science. (shrink)
In this paper, I discuss the key role played by Carl G. Hempel's work on theoretical realism and scientific explanation in effecting a crucial philosophical transition between the beginning and the end of the twentieth century. At the beginning of the century, the dominant view was that science is incapable of furnishing explanations of natural phenomena; at the end, explanation is widely viewed as an important, if not the primary, goal of science. In addition to its intellectual (...) benefits, this transition has important practical consequences with respect to dealing with the global problems humans everywhere will face in the twenty-first century. (shrink)
An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.
Mainstream philosophy of science has embraced an “empiricist” approach to scientific method. To be slightly more precise, I venture that most philosophers of science today would endorse the view that experience is the source of most scientific knowledge. The aim of this essay will be to challenge the consensus, by showing how we cannot and should not abandon all elements of the “rationalist” tradition, a tradition often identified with philosophers such as Descartes. There are several elements frequently identified (...) with “rationalist” science (Stump, 2005): questioning of sense experience, the attempt to rethink the “metaphysical” foundations of one’s science, using either thought experiment, or appealing to demonstrative arguments purporting to establish ‘necessary’ truths, often using either mathematics or geometry, and appeal to “virtues” not usually considered “strictly empirical,” such as simplicity. This essay explores the effective deployment of such considerations in the history and current practice of science. (shrink)
It is common wisdom in intellectual history that eighteenth-century science of man evolved under the aegis of Newton. It is also frequently suggested that David Hume, one of the most influential practitioners of this kind of inquiry, aspired to be the Newton of the moral sciences. Usually this goes hand in hand with a more or less explicit reading of Hume’s theory of human nature as written in an idiom of particulate inert matter and active forces acting on it, (...) i.e. essentially that of Newton’s Principia. Hume’s outlook on the mental world is thus frequently described in terms of conceptual atoms whose association is compared to interparticulate attractions analogous with Newtonian forces in general, and gravity in particular. In the present paper I argue that Hume’s theory can indeed be understood in Newton’s wake, but not in the context of the Principa’s reception but that of the Opticks, which exerted a more significant influence on natural inquiry in eighteenth-century Scotland. I intend to show that Hume speaks a language and represents an outlook on human matters convergent with “philosophical chemistry” in Scotland at that time, and particularly to his later friend and physician William Cullen. (shrink)
An overview is provided of how the concept of the thought experiment has developed and changed for the natural sciences in the course of the 20th century. First, we discuss the existing definitions of the term 'thought experiment' and the origin of the thought experimentation method, identifying it in Greek Presocratics epoch. Second, only in the end of the 19th century showed up the first systematic enquiry on thought experiments by Ernst Mach's work. After the Mach's work, a negative (...) attitude towards thought experiments came in the beginning of the 20th century, which went on until the Thomas Kuhn's and Karl Popper's work on thought experiments. Only from the mid-1980s did thought experiments begin to be considered relevant to scientific enterprise. Finally, we show the existing empirical and 'functional' theories which have developed about the nature and purpose of thought experiments. (shrink)
The mathematical nature of modern science is an outcome of a contingent historical process, whose most critical stages occurred in the seventeenth century. ‘The mathematization of nature’ (Koyré 1957 , From the closed world to the infinite universe , 5) is commonly hailed as the great achievement of the ‘scientific revolution’, but for the agents affecting this development it was not a clear insight into the structure of the universe or into the proper way of studying it. Rather, it (...) was a deliberate project of great intellectual promise, but fraught with excruciating technical challenges and unsettling epistemological conundrums. These required a radical change in the relations between mathematics, order and physical phenomena and the development of new practices of tracing and analyzing motion. This essay presents a series of discrete moments in this process. For mediaeval and Renaissance philosophers, mathematicians and painters, physical motion was the paradigm of change, hence of disorder, and ipso facto available to mathematical analysis only as idealized abstraction. Kepler and Galileo boldly reverted the traditional presumptions: for them, mathematical harmonies were embedded in creation; motion was the carrier of order; and the objects of mathematics were mathematical curves drawn by nature itself. Mathematics could thus be assigned an explanatory role in natural philosophy, capturing a new metaphysical entity: pure motion. Successive generations of natural philosophers from Descartes to Huygens and Hooke gradually relegated the need to legitimize the application of mathematics to natural phenomena and the blurring of natural and artificial this application relied on. Newton finally erased the distinction between nature’s and artificial mathematics altogether, equating all of geometry with mechanical practice. (shrink)
This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics (...) of mathematics--the view that mathematics is about things that really exist. (shrink)
The role of mathematics in the development of Gilles Deleuze's (1925-95) philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic is demonstrated in this paper by differentiating Deleuze's interpretation of the problem of the infinitesimal in Difference and Repetition from that which G. W. F Hegel (1770-1831) presents in the Science of Logic . Each deploys the operation of integration as conceived at different stages in the development of the infinitesimal calculus (...) in his treatment of the problem of the infinitesimal. Against the role that Hegel assigns to integration as the inverse transformation of differentiation in the development of his dialectical logic, Deleuze strategically redeploys Leibniz's account of integration as a method of summation in the form of a series in the development of his philosophy of difference. By demonstrating the relation between the differential point of view of the Leibnizian infinitesimal calculus and the differential calculus of contemporary mathematics, I argue that Deleuze effectively bypasses the methods of the differential calculus which Hegel uses to support the development of the dialectical logic, and by doing so, sets up the critical perspective from which to construct an alternative logic of relations characteristic of a philosophy of difference. The mode of operation of this logic is then demonstrated by drawing upon the mathematical philosophy of Albert Lautman (1908-44), which plays a significant role in Deleuze's project of constructing a philosophy of difference. Indeed, the logic of relations that Deleuze constructs is dialectical in the Lautmanian sense. (shrink)
My title, of course, is an exaggeration. The world no more became mathematical in the seventeenth century than it became ironic in the nineteenth. Either it was mathematical all along, and seventeenth-century philosophers discovered it was, or, if it wasn’t, it could not have been made so by a few books. What became mathematical was physics, and whether that has any bearing on the furniture of the universe is one topic of this paper. Garber says, and I agree, that for (...) Descartes bodies are the things of geometry made real ( Ref). That is a claim about the world: what God created, and what we know in physics, is nothing other than res extensa and its modes. Others, including Marion, hold that in modern science, here represented at its origins by Descartes, representation displaces beings: the knower no longer confronts Being or beings but rather a system of signs, a “code” as Marion calls it, to which the knower stands in the relation of subject to object. The Meditations, or perhaps even the Regulæ, are the first step toward the transcendental idealism of Kant. Most of this paper will be devoted to a more concrete question. Physics in the seventeenth century increasingly became a matter of applying mathematical knowledge to the solution of physical problems. The “mixed sciences” of astronomy, optics, and music, sciences then distinct from physics, became models of understanding for all of natural philosophy. My interest here is in one aspect of that development: how particular physical situations are transformed into mathematical. I will look at the work of Descartes and Isaac Beeckman, contrasting their visions of “physico-mathematics”. (shrink)
