Why did such highly abstract ideas as truth, knowledge, or justice become so important to us? What was the point of coming to think in these terms? This book presents a philosophical method designed to answer such questions: the method of pragmatic genealogy. Pragmatic genealogies are partly fictional, partly historical narratives exploring what might have driven us to develop certain ideas in order to discover what these do for us. The book uncovers an under-appreciated tradition of pragmatic genealogy which cuts (...) across the analytic-continental divide, running from the state-of-nature stories of David Hume and the early genealogies of Friedrich Nietzsche to recent work in analytic philosophy by Edward Craig, Bernard Williams, and Miranda Fricker. However, these genealogies combine fictionalizing and historicizing in ways that even philosophers sympathetic to the use of state-of-nature fictions or real history have found puzzling. To make sense of why both fictionalizing and historicizing are called for, the book offers a systematic account of pragmatic genealogies as dynamic models serving to reverse-engineer the points of ideas in relation not only to near-universal human needs, but also to socio-historically situated needs. This allows the method to offer us explanation without reduction and to help us understand what led our ideas to shed the traces of their practical origins. Far from being normatively inert, moreover, pragmatic genealogy can affect the space of reasons, guiding attempts to improve our conceptual repertoire by helping us determine whether and when our ideas are worth having. (shrink)

This paper presents and argues for an account of objectual understanding that aims to do justice to the full range of cases of scientific understanding, including cases in which one does not have an explanation of the understood phenomenon. According to the proposed account, one understands a phenomenon just in case one grasps a sufficiently accurate and comprehensive model of the ways in which it or its features are situated within a network of dependence relations; one’s degree of understanding is (...) proportional to the comprehensiveness and accuracy of such a model. I compare this account with accounts of scientific understanding that explicate understanding in terms of having an explanation of the understood phenomenon. I discuss three distinct types of cases in which scientific understanding does not amount to possessing an explanation of any kind, and argue that the proposed model-based account can accommodate these cases while still retaining a strong link between understanding and explanation. (shrink)

Los experimentos mentales son dispositivos epistémicos de la imaginación, o de análisis de problemas filosóficos, que recorren las fronteras de aquella, desde el sillón. Dichas fronteras tocan dilemas perennes de la filosofía: cuestiones de la metafísica, como el tiempo, el espacio y la realidad, el problema de la libertad y el determinismo, la naturaleza de la mente, la identidad personal, los argumentos acerca del significado, las posibilidades, fuentes y condiciones del conocimiento, las relaciones entre discurso y lógica, la ética, cuestiones (...) de la filosofía social y política, y la estética. Muchos problemas de la filosofía han sido abordados mediante experimentos mentales, una herramienta útil de la caja de herramientas del filósofo. No todas las herramientas son populares, no obstante. Los experimentos mentales son, pese a sus defensores, falibles, incluso si son argumentos bien planteados. Justamente, este libro recopila artículos con las principales defensas y ataques a los experimentos mentales, especialmente en términos de su confiabilidad para llegar a conclusiones, o bien de su relevancia en términos de su origen: el sillón de la filosofía. Este ha sido vapuleado por los nuevos aires de la filosofía analítica, que trata al sillón como un viejo artefacto del análisis a priori. De hecho, hay posturas que critican a los experimentos mentales por constituir bombas de intuiciones no confiables. Por supuesto, no hay razón irrefutable para aceptar los experimentos mentales y las filosofías de sillón. Pero ¿hay alguna en la filosofía? El libro no pretende convencer al lector del valor de los experimentos mentales y las filosofías de sillón. Por el contrario, su objetivo es formar una imagen propia de estos dispositivos epistémicos, tanto en relación con sus virtudes y limitaciones. Si ello se logra, habrá valido el esfuerzo llevado a cabo en esta compilación de artículos, los que muestran los límites, desafíos y críticas de la experimentación mental desde el sillón. (shrink)

This paper aims to assess the credibility of the legitimation thesis; the claim that the development of experimental science involved a legitimation of certain aspects of artisanal practice or craft knowledge. My goal will be to provide a critique of this idea by examining Francis Bacon’s notion of ‘mechanical history’ and the influence it exerted on attempts by later generations of scholars to appropriate the knowledge of craft traditions. Specifically, I aim to show how such projects were often premised upon (...) socio-epistemological ideals that served to reinforce, rather than relinquish boundaries between artisans and natural philosophers. It will be my claim that a closer examination of the presuppositions underlying attempts by early modern natural philosophers to appropriate craft knowledge reveals, not a desire to legitimize aspects of artisanal practice, but rather strategies aimed at demonstrating the inferiority of the local ways of knowing upon which it was based. (shrink)

I examine the reasons Aristotle presents in Physics VIII 8 for denying a crucial assumption of Zeno’s dichotomy paradox: that every motion is composed of sub-motions. Aristotle claims that a unified motion is divisible into motions only in potentiality (δυνάμει). If it were actually divided at some point, the mobile would need to have arrived at and then have departed from this point, and that would require some interval of rest. Commentators have generally found Aristotle’s reasoning unconvincing. Against David Bostock (...) and Richard Sorabji, inter alia, I argue that Aristotle offers a plausible and internally consistent response to Zeno. I defend Aristotle’s reasoning by using his discussion of what to say about the mobile at boundary instants, transitions between change and rest. There Aristotle articulates what I call the Changes are Open, Rests are Closed Rule: what is true of something at a boundary instant is what is true of it over the time of its rest. By contrast, predications true of something over its period of change are not true of the thing at either of the boundary instants of that change. I argue that this rule issues from Aristotle’s general understanding of change, as laid out in Phys. III. It also fits well with Phys. VI, where Aristotle maintains that there is a first boundary instant included in the time of rest, but not a “first in which the mobile began to change.” I then show how this rule underlies Aristotle’s argument that a continuous motion cannot be composed of actual sub-motions. Aristotle distinguishes potential middles, points passed through en route to a terminus, from actual middles. The Changes are Open, Rests are Closed Rule only applies to actual middles, because only they are boundaries of change that the mobile must arrive at and then depart from. On my reading, Aristotle argues that the instant of arrival, the first instant at which the mobile has come to be at the actual middle, cannot belong to the time of the subsequent motion. If it did, the mobile would already be moving towards the next terminus and thus, per Phys. VI 6, would have already left. But it cannot have moved away from the midpoint at the very same moment it has arrived there. This means that the instant of arrival must be separated from the time of departure by an interval of rest. I show how Aristotle’s reasoning applies generally to rule out any continuous reflexive motion or continuous complex rectilinear motion. On my interpretation, however, the argument does not apply to every change of direction. When, as in the case of projectile motion, multiple movers and their relative powers explain why the mobile changes directions, distinct sub-motions are not involved. Aristotle holds that such motions cannot be continuous, not because they involve intervals of rest, but because they involve multiple causes of motion. My interpretation of the Changes are Open, Rests are Closed Rule allows us to make better sense of Aristotle’s argument than any previous interpretation. (shrink)

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O (...) comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type. (shrink)

It is now fashionable to say that science and technology are social constructions. This is true, or rather, a truism. Man is a social animal. Man is a linguistic animal, and language is social. Hence all products of human activities and everything that involves language are social constructions. But an assertion that covers everything becomes empty. The constructionist mantra that science or technology is “not a simple input from nature” attacks a straw man, for no one denies the necessity of (...) enormous human efforts in research, development, and design. To say that these are social activities should not imply that they are indistinguishable from other social activities such as politicking or profiteering. An investigation into their peculiarities will bring to relief their intellectual and technical characteristics. The argument that science and technology are social constructions because they involve many assumptions is again a truism. Whenever we think, whenever we find things intelligible, we invariably have used some concepts and made some assumptions. Philosophers such as Kant have painstakingly analyzed concepts without which intelligibility is impossible. The important questions are not whether scientists and engineers make assumptions but what kind of assumptions they make; not whether they make judgments, but what kind of reasons they offer to support their judgments. Are the assumptions and justifications all social? Or are they mainly technical? Admittedly, the boundaries between the two are not always sharp, but is it impossible to make any differentiation at all? (shrink)

This paper shows that Kant's investigation into mathematical purposiveness was central to the development of his understanding of synthetic a priori knowledge. Specifically, it provides a clear historical explanation as to why Kant points to mathematics as an exemplary case of the synthetic a priori, argues that his early analysis of mathematical purposiveness provides a clue to the metaphysical context and motives from which his understanding of synthetic a-priori knowledge emerged, and provides an analysis of the underlying structure of mathematical (...) purposiveness itself, which can be described as unintentional, but also as objective and unlimited. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...

Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this (...) time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this ‘equal time’ property, instantaneous motion. (shrink)

Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is inadequate. Here we see from simple examples, not that Euclidean theories of set (...) size are wrong, but that they must be either very weak and narrow or largely arbitrary and misleading. (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)

ig Brother, the tyrant of George Orwell's 1984, directed his daily Two Minutes Hate against Emmanuel Goldstein, enemy of the people. When I studied evolutionary biology in graduate school during the mid 1960s, official rebuke and derision focused upon Richard Goldschmidt , a famous geneticist who, we were told, had gone astray. Although 1984 creeps up on us, I trust that the world will not be in Big Brother's grip by then. I do, however, predict that during this decade Goldschmidt (...) will be largely vindicated in the world of evolutionary biology. (shrink)

What should be the ontology of the world such that life and cognition are possible? In this essay, I undertake to outline an alternative ontological foundation which makes biological and cognitive phenomena possible. The foundation is built by defining a model, which is presented in the form of a description of a hypothetical but a logically possible world with a defined ontological base. Biology rests today on quite a few not so well connected foundations: molecular biology based on the genetic (...) dogma; evolutionary biology based on neo-Darwinian model; ecology based on systems view; developmental biology by morphogenetic models; connectionist models for neurophysiology and cognitive biology; pervasive teleonomic explanations for the goal-directed behavior across the discipline; etc. Can there be an underlying connecting theme or a model which could make these seemingly disparate domains interconnected? I shall atempt to answer this question. By following the semantic view of scientific theories, I tend to believe that the models employed by the present physical sciences are not rich enough to capture biological (and some of the non-biological) systems. A richer theory that could capture biological reality could also capture physical and chemical phenomena as limiting cases, but not vice versa. (shrink)

The aggregate EIRP of an N-element antenna array is proportional to N 2. This observation illustrates an effective approach for providing deep space networks with very powerful uplinks. The increased aggregate EIRP can be employed in a number of ways, including improved emergency communications, reaching farther into deep space, increased uplink data rates, and the flexibility of simultaneously providing more than one uplink beam with the array. Furthermore, potential for cost savings also exists since the array can be formed using (...) small apertures. (shrink)

Cartwright attempts to argue from an analysis of the composition of forces, and more generally the composition of laws, to the conclusion that laws must be regarded as false. A response to Cartwright is developed which contends that properly understood composition poses no threat to the truth of laws, even though agreeing with Cartwright that laws do not satisfy the "facticity" requirement. My analysis draws especially on the work of Creary, Bhaskar, Mill, and points towards a general rejection of Cartwright's (...) view that laws, especially fundamental laws, should be seen as false. (shrink)

By carefully examining one of the most famous thought experiments in the history of science—that by which Galileo is said to have refuted the Aristotelian theory that heavier bodies fall faster than lighter ones—I attempt to show that thought experiments play a distinctive role in scientific inquiry. Reasoning about particular entities within the context of an imaginary scenario can lead to rationally justified concluusions that—given the same initial information—would not be rationally justifiable on the basis of a straightforward argument.

I argue that current projects in ‘naturalized metaphysics’ fail to be properly naturalistic, and thereby fail in their stated aim to take one’s metaphysics from science. I argue that naturalism must involve the idea of taking science seriously, and that this can only be spelled out in terms of taking not only the theories of science seriously, but also its practice and its socio-linguistic situatedness seriously as well. This accords with naturalism because not doing so draws an artificial (non-natural) distinction (...) between the epistemic products of science as essence, and its socio-linguistic and practical features as accidents. The picture of naturalism which falls out of this is a form of pragmatism. Once this is spelled out, the question becomes, what is the appropriate attitude for the pragmatist/naturalist to have toward ontology? It is not the same as that of traditional metaphysics, since such an attitude (that metaphysical theorizing can make positive epistemic contributions) requires a priori commitments which themselves are (1) not subject to empirical review, and (2) are anthropocentric and so potentially distorted. But the pragmatist/naturalist will not go the opposite way, and say that metaphysics is meaningless either, since (true to their pragmatic commitments) ontology does things for the scientist and the layperson. It is a mistake to reject it wholesale, since the task of asserting what there is, exposing such an ontology to criticism, both empirical and logical, and revising it, has both small-scale and large-scale consequences. On the small-scale, ontologies are a guide for thinking—scientists, engineers, and lay people can and do use models of existence to navigate occurent problems in their day-to-day lives. Whether this is posing research hypotheses, developing protocols for generating new materials, or cooling off a cup of coffee, ontology plays a role. Large-scale consequences are more weighty, and more difficult to see. These large-scale consequences have to do with the aims and values which individuals and societies possess, and their interrelation with ontology. This certainly was at the forefront of the earliest ontologies—the Epicureans and Stoics built their moral philosophy on the basis of what ontology they thought was correct. This sort of practice goes on, unabated, today, though with virtually no overt acknowledgement of this important interdependency. How, for the pragmatist, do we make sense of ontological talk, if we are to eschew traditional metaphysics? Ontology—the naturalist/pragmatist declares—is a tool. Ontology helps us do things, whether it be predict behavior, understand phenomena, blame or forgive someone, and hope or despair about a life after this one (for example). Building an ontology is about building our own concepts, and this, in turn is a negotiation between our beliefs, experiences, and commitments, and the beliefs, experiences, and commitments of with whom we’re discursively engaged. (shrink)

Düşünce deneylerinden beklenen şeylerden biri de mevcut bilgimizi test etmesi ya da bilgimizi artırmasıdır. Ancak adından da kolayca anlaşılacağı gibi, yalnızca düşüncede yürütülen böyle bir deney, örneğin bize ne şekilde yeni bir bilgi sağlayabilir? Bu zamana kadar söz konusu soruya, bilim felsefesi literatüründe, başlıca beş temel yanıt verilmiştir. Bu makalede, tüm bu yaklaşımların -Platoncu yaklaşım hariç- ortak bir varsayımını ele alacağım. Bu varsayıma göre düşünce deneylerinin tüm yönlerini açıklayabilecek kapsayıcı bir teori bulunmaktadır. Düşünce deneylerinin doğasına ilişkin bu tekçi varsayım, en (...) azından iki yönden oldukça sorunlu görünmektedir. İlk olarak, belirli bir düşünce deneyinin tek bir yaklaşımla açıklanamayan yönleri bulunmaktadır. İkincisi, şimdiye kadar önerilen yaklaşımlar tüm düşünce deneylerini açıklayamamaktadır. Bu iddiaları temellendirmek ve bahsedilen yaklaşımların eksikliklerini belirtmek için Galileo’nun ve Darwin’in öne sürdüğü düşünce deneyi örneklerini ele alacağım. Son olarak çoğulcu bir yaklaşımın düşünce deneylerinin doğasını açıklamada çok daha uygun bir çerçeve sağladığını öne süreceğim. (shrink)

EXPANDED EDITION (eBook): -/- Infinity Is Not What It Seems...Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes (...) in a divine Creator infinite in knowledge, power, and benevolence. -/- According to this treatise, such assumptions are mistaken. In reality, to be is to be finite. The implications of this assessment are profound: the Universe and even God must necessarily be finite. -/- The author makes a compelling case against infinity, refuting its most prominent advocates. Any defense of the infinite will find it challenging to answer the arguments laid out in this book. But regardless of the reader’s position, FOREVER FINITE offers plenty of thought-provoking material for anyone interested in the subject of infinity from the perspectives of philosophy, mathematics, science, and theology. -/- This electronic edition of FOREVER FINITE is offered free online for all and is expanded with content that does not appear in the published edition due to print production page limitations. From the Introduction to the Conclusion, Chapters 1–27 are identical to the published print edition, including the page numbering for the chapters. This electronic edition adds an appendix and associated content—specifically, updates to the book’s back matter (68 new endnotes, 17 new bibliographic references, 3 new figure credits, 14 new glossary terms) and front matter (an updated table of contents and this preface note). (shrink)

In this paper I discuss Mark Steiner’s view of the contribution of mathematics to physics and take up some of the questions it raises. In particular, I take up the question of discovery and explore two aspects of this question – a metaphysical aspect and a related epistemic aspect. The metaphysical aspect concerns the formal structure of the physical world. Does the physical world have mathematical or formal features or constituents, and what is the nature of these constituents? The related (...) epistemic question concerns humans’ cognitive ability to reach the formal structure of the physical world. Among other things, I explore the interaction of mathematical and non-mathematical cognition in physical discovery. (shrink)

While the predominant focus of the philosophical literature on scientific modeling has been on single-scale models, most systems in nature exhibit complex multiscale behavior, requiring new modeling methods. This challenge of modeling phenomena across a vast range of spatial and temporal scales has been called the tyranny of scales problem. Drawing on research in the geosciences, I synthesize and analyze a number of strategies for taming this tyranny in the context of conceptual, physical, and mathematical modeling. This includes several strategies (...) that can be deployed in physical modeling, even when strict dynamical scaling fails. In all cases, I argue that having an adequate conceptual model—given both the nature of the system and the particular purpose of the model—is essential. I draw a distinction between depiction and representation, and use this research in the geosciences to advance a number of debates in the philosophy of modeling. (shrink)

The question of where the knowledge comes from when we conduct thought experiments has been one of the most fundamental issues discussed in the epistemological position of thought experiments. In this regard, Pierre Duhem shows a skeptical attitude on the subject by stating that thought experiments cannot be evaluated as real experiments or cannot be accepted as an alternative to real experiments. James R. Brown, on the other hand, states that thought experiments, which are not based on new experimental evidence (...) or logically derived from old data, called the Platonic thought experiment, provide intuitive access to a priori knowledge. Unlike Brown, John D. Norton strictly criticizes the idea that thought experiments provide mysterious access to the knowledge of the physical world, and states that thought experiments cannot provide knowledge that transcends empiricism. In the context of the NortonBrown debate, in this article, Brown's stance on thought experiments is supported by critically analyzing the thoughts put forward on the subject. -/- Düşünce deneylerini gerçekleştirdiğimizde sonucunda elde edilen bilginin nereden geldiği sorusu düşünce deneylerinin epistemolojik konumuna ilişkin tartışılan en temel konulardan bir tanesidir. Bu doğrultuda, Pierre Duhem düşünce deneylerinin gerçek deneyler ile aynı statüde değerlendirilemeyeceğini ve hatta düşünce deneylerinin gerçek deneylerin bir alternatifi olarak bile kabul edilemeyeceğini belirterek konuya ilişkin şüpheci bir tavır sergilemektedir. James R. Brown ise yeni deneysel kanıtlara dayanmayan ya da eski verilerden mantıksal olarak türetilmeyen, Platoncu düşünce deneyi olarak adlandırılan düşünce deneylerinin a priori bilgiye sezgisel erişim sağladığını ifade etmektedir. Brown’ın aksine, John D. Norton düşünce deneylerinin fiziksel dünyanın bilgisine gizemli bir erişim sağladığı yönündeki düşünceyi kesin bir dille eleştirmekte ve düşünce deneylerinin ampirizmi aşan bir bilgi sağlamasının mümkün olamayacağını ifade etmektedir. Norton-Brown tartışması çerçevesinde bu makalede, Brown'un düşünce deneylerine ilişkin tutumu, konuyla ilgili düşüncelerin eleştirel olarak analiz edilmesiyle desteklenmektedir. (shrink)

This study considers the short list of Nature of Science features frequently published and widely known in the science education discourse. It is argued that these features were oversimplified and a refinement of the claims may enrich or sometimes reverse them. The analysis shows the need to address the range of variation in each particular aspect of NOS and to illustrate these variations with actual events from the history of science in order to adequately present the subject. Another implication of (...) the proposal is the highlighting of the central role of science educators who, facing various strong claims of researchers in education and philosophy of science, often have difficulty in making a choice of what to teach about NOS. It is suggested that a representative variation with regard to the traditional NOS claims may be appropriate for a genuine understanding of the subject. In that, using the discipline-culture structure of the fundamental theories of physics and addressing the plurality of scientific methods may be helpful in the actual teaching and learning of NOS. (shrink)

The inductive problem of extending the sequence 1, 3, 5, 7, is solved when these numbers are the ratios of the incremental distances fallen in successive unit times. The controlling fact is Galileo’s assumption that these ratios are invariant under a change of the unit of time. It admits few laws and only one is compatible with the two-numbered initial sequence 1, 3.

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end of their (...) master’s degree in two European universities. The course had two main goals: To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and To expand students’ repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students’ views on the role of mathematics in physics, an increase in the participants’ awareness of the difficulties faced by learners to understand physics equations and a broadening in the students’ repertoire to answer “Why?” questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived. (shrink)

For nearly a decade we have taught the history and philosophy of science as part of courses aimed at the professional development of physics teachers. The focus of the history of science instruction is on the stages in the development of the concepts and theories of physics. For this instruction, we designed activities to help the teachers organize their understanding of this historical development. The activities include scientific modeling using archaic theories. We conducted surveys to gauge the impact on the (...) teachers of including the conceptual history of physics in the professional development courses. The teachers report greater confidence in their knowledge of the history of physics, that they reflect on this history for their teaching, and that they use of the history of physics for their classroom instruction. In this paper, we provide examples of our activities, the rationale for their design, and discuss the outcomes for the teachers of the instruction. (shrink)

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...) is, I think, widespread agreement that recent insights here have lead to a genuine deepening of our understanding. (shrink)

: An examination of two thought experiments in contemporary physics reveals that the same thought experiment can be reanalyzed from the perspective of different and incompatible theories. This fact undermines those accounts of thought experiments that claim their justificatory power comes from their ability to reveal the laws of nature. While thought experiments do play a genuine evaluative role in science, they do so by testing the nonempirical virtues of a theory, such as consistency and explanatory power. I conclude that, (...) while their interpretation presupposes a whole set of background theories and putative laws, thought experiments nonetheless can evolve and be retooled for different theories and ends. (shrink)

It has been argued that the fundamental laws of physics do not face a ‘problem of provisos’ equivalent to that found in other scientific disciplines (Earman, Roberts and Smith 2002) and there is only the appearance of exceptions to physical laws if they are confused with differential equations of evolution type (Smith 2002). In this paper I argue that even if this is true, fundamental laws in physics still pose a major challenge to standard Humean approaches to lawhood, as they (...) are not in any obvious sense about regularities in behaviour. A Humean approach to physical laws with exceptions is possible, however, if we adopt a view of laws that takes them to be the algorithms in the algorithmic compressions of empirical data. When this is supplemented with a distinction between lossy and lossless compression, we can explain exceptions in terms of compression artefacts present in the application of the lossy laws. (shrink)

Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collectionAis properly included in a collectionBthen the ‘size’ ofAshould be less than the (...) ‘size’ ofB(part–whole principle). This second intuition was not developed mathematically in a satisfactory way until quite recently. In this article I begin by reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers (Thabit ibn Qurra, Grosseteste, Maignan, Bolzano). Then, I review some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion (Katz, Benci, Di Nasso, Forti). Finally, I show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics which argue either for the inevitability of the Cantorian notion of infinite number (Gödel) or for the rational nature of the Cantorian generalization as opposed to that, based on the part–whole principle, envisaged by Bolzano (Kitcher). (shrink)

The ArgumentThis paper is a study of the role of language in scientific activity. It recommends that language be viewed as a community's means of patterning its affairs. Language represents where the boundaries of the community are and who is entitled to speak within it, and it displays the structures of authority in the community. Moreover, language precipitates the community's view of what the world is like, such that linguistic usages can be taken as referring to that world. Thus, language (...) connects on the one side to a community's practical life, and, on the other, to the reality on which it “reports.”The example treated is Robert Boyle's view of the language proper for experimental practice, and his arguments against the value and legitimacy of mathematical representations within the experimental community. Boyle argued that the use of mathematics was inappropriate because (i) it would restrict the number of potential participants; (ii) it would give rise to unwarranted expectations of the certainty and accuracy to be expected of real physical inquiries; (iii) it would suggest views of natural law and God's relations with the natural world which were incorrect and possibly dangerous; and because (iv) the world upon which the experimentalist operated was not such as was represented by mathematical idealizations. I try to establish that decision about the appropriate language for the experimental community was a moral choice. (shrink)

In order to carry out “a great and important piece of work, and that in a complete and lasting way”, Kant claims that one must join one’s “effort with that of the author”. The reading of a work, therefore, must try to embrace “the articulation or structure of the system, which yet matters most when it comes to judging its unity and soundness”. This structure and articulation, however, may not be so easily accessible; it may, rather, be latent under “bright (...) colours [that] paint over and make unrecognizable” the argument’s essence, often confusing the reader, who “cannot quickly enough attain a survey of the whole”. Now, it would be expected, then, that Kant, condemning such “ornaments”, would not employ those resources I n his writings. However, it is curious that not infrequently he makes use of such “bright colours”. The present paper aims at pointing out some passages of Kant's theoretical and practical philosophy in which it is possible to identify such “colouring”. (shrink)

ABSTRACT I suggest how a broadly Kantian critique of classical logic might spring from reflections on constructibility conditions. According to Kant, mathematics is concerned with objects that are given through ‘arbitrary synthesis,’ in the form of ‘constructions of concepts’ in the medium of ‘pure intuition.’ Logic, by contrast, is narrowly constrained – it has no objects of its own and is fixed by the very forms of thought. That is why there is not much room for developments within logic, as (...) compared to the progress in mathematics. Kant’s view of logic remains critical, though – through considerations that are effectively on the scope and limits of classical logic and which play a part in his transcendental idealism. The most important ones are to be found in his critique of the use of reductio ad absurdum proofs in metaphysics and his solutions to the ‘antinomies of pure reason.’ Arguably, these considerations carry over to mathematics as well – by way of ‘analogues’ to the antinomies – in particular in resolving infinity paradoxes. (shrink)

The question of how the university can relate to the world is centuries old. The poles of the debate can be characterized by the plea for an increasing instrumentalization of the university as a producer and provider of useful knowledge on the one hand (cf. the knowledge factory), and the defense of the university as an autonomous space for free inquiry and the pursuit of knowledge for knowledge’s sake on the other hand (cf. the ivory tower). Our current global predicament, (...) however, forces us to rethink the relation between university and world. Indeed, an easy nstrumentalization of the university for the purposes of society is no longer possible in troubled times when the future of society itself seems to be at stake. Nevertheless, urgent societal concerns do need to be addressed by the university. Hence, the disinterested position seems a highly irresponsible option. The aim of this dissertation is to reconsider the relation between the university and the world from an educational perspective by addressing the question “How to situate study in the relation between university and society?” The dissertation consists of three parts. In Part One, the existing literature on the relation between university and society will be discussed. The first chapter discerns two main approaches to this issue, namely the transcendental-philosophical approach (cf. the idea of the university) and the critical-sociological approach (cf. academic capitalism) that conceive of the university, respectively, as an idea and as an organization. By means of an excursus on the emergence of the university in the Middle Ages, the case is made for an ecological approach to the university. In the second chapter, the work of two authors who have recently adopted such an ecological approach is briefly presented. Whereas Ronald Barnett’s theory of the ecological university is situated more in the transcendental-philosophical tradition, Susan Wright’s investigations of the university in the knowledge ecology can be placed in the critical-sociological tradition. Both conceptions, however, are hinged on an institutional understanding of the university. In line with recent developments in social theory, namely the focus on practices, it is proposed to work towards an ecology of study practices. Part Two presents Isabelle Stengers’ idea of the ecology of practices. The third chapter elucidates Stengers’ work on scientific practices by first situating it within the so-called Science Wars, which provided the impetus to elaborate a theoretical framework for a civilized dialogue between scientists and the broader public. The basic tenets and concepts of her approach, such as the understanding of practice as a set of requirements and obligations, are presented, explained, and discussed. In the fourth chapter, the focus shifts from scientific practices to study practices. Assisted by Stengers’ writings on Whitehead’s speculative philosophy, this chapter aims to flesh out Whitehead’s description of the university as a ‘home of adventures’ in order to come to an educational understanding of the study practices of the university. A conceptual inquiry into how study practices activate certain worldly problems and turn them into matters of study is presented. Part Three develops the conceptual work on study practices further in relation to the activities of the Palestinian experimental university Campus in Camps. Chapter Five presents the work of Campus in Camps and explains how it relates to the theoretical discussion offered in the second part. On the basis of Stengers’ conception of practice, which discerns requirements and obligations as vital ingredients, this chapter argues that life in exile is what drives the study practices of Campus in Camps, and hence, that it is the issue of life in exile that participants are obligated to when they study. Whereas Chapter Five is focused on what is being studied in Campus in Camps, Chapter Six inquires in to the specific requirements its activities need to fulfill in order to be study practices; in other words, how the participants study. Four requirements are discerned that, taken together, seem indispensable to understand the study practices of Campus in Camps; namely, storytelling, comparing, mapmaking, and using. The concluding chapter returns to the research question and again takes up the main ideas developed in the dissertation, such as the adventure of study and the cohabitation of scientific and study practices in the university. The last two sections of the conclusion deal with two remaining issues of a more practical nature; namely, how to relate to institutionalization when working from a practice-theoretical point of view, and lastly the question of what can be done. In all, and returning to the initial problem, the dissertation asks what it means to conceive of the university as situated by and engaged with worldly questions. (shrink)

This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...) to mathematics and a top-down naturalisation. Articulating my particular understanding of what realism and naturalism should commit us to, I propose a creative fusion of Badiou’s attention to metamathematical results with a structural-informational metaphysics, proposing a ‘matherialism’ uniting the more daring speculative insights of the former with the naturalist and empiricist commitments motivating the latter. (shrink)

This book is a sustained defense of the compatibility of the presence of idealizations in the sciences and scientific realism. So, the book is essentially a detailed response to the infamous arguments raised by Nancy Cartwright to the effect that idealization and scientific realism are incompatible.

We investigate the way physical laws objectively refer to the entities they are about. Laws of mathematical physics do not refer directly to the “real world” but to an ideal specific domain of objects, which we term “scope”. In order to find out which real objects physical laws deal with, reference to the scope is not sufficient. We need in addition the search for domains to which laws apply — i. e. “empirical domains”— in order to establish their reference to (...) the “real world”. It is just in such empirical domains that we are able to discover the real entities physical laws objectively refer to. “Physical reality” turns out to be not something “given” but rather something “to come out” of the very process of scientific inquiry. (shrink)

In this article I am going to reconstruct Stephen Toulmin’s procedural theory of concepts and explanations in order to develop two overlooked ideas from his philosophy of science: methods of representations and inferential techniques. I argue that these notions, when properly articulated, could be useful for shedding some light on how scientific reasoning is related to representational structures, concepts, and explanation within scientific practices. I will explore and illustrate these ideas by studying the development of the notion of instantaneous speed (...) during the passage from Galileo’s geometrical physics to analytical mechanics. At the end, I will argue that methods of representations could be considered as constitutive of scientific inference; and I will show how these notions could connect with other similar ideas from contemporary philosophy of science like those of models and model-based reasoning. (shrink)

An informal theory is set forth of relations between abstract entities, includingcolors, physical quantities, times, andplaces in space, and the concrete things thathave them, or areat orin them, based on the assumption that there are close analogies between these relations and relations between abstractsets and the concrete things that aremembers of them. It is suggested that even standard scientific usage of these abstractions presupposes principles that are analogous to postulates of abstraction, identity, and other fundamental principles of set theory. Also (...) discussed is the significance of important disanalogies between sets and physical abstractions, including especiallymodal andtemporal aspects of physical abstractions, which is related to the problem of the characterizingconstancy, of colors, physical attributes, and locations in space. (shrink)

Brown (The laboratory of the mind. Thought experiments in the natural science, 1991a , 1991b ; Contemporary debates in philosophy of science, 2004 ; Thought experiments, 2008 ) argues that thought experiments (TE) in science cannot be arguments and cannot even be represented by arguments. He rest his case on examples of TEs which proceed through a contradiction to reach a positive resolution (Brown calls such TEs “platonic”). This, supposedly, makes it impossible to represent them as arguments for logical reasons: (...) there is no logic that can adequately model such phenomena. (Brown further argues that this being the case, “platonic” TEs provide us with irreducible insight into the abstract realm of laws of nature). I argue against this approach by describing how “platonic” TEs can be modeled within the logical framework of adaptive proofs for prioritized consequence operations. To show how this mundane apparatus works, I use it to reconstruct one of the key examples used by Brown, Galileo’s TE involving falling bodies. (shrink)