In this paper, I ask whether we should see different logical systems as appropriate for different domains (or perhaps in different contexts) and whether this would amount to a form of logical pluralism. One, though not the only, route to this type of position, is via pluralism about truth. Given that truth is central to validity, the commitment the typical truth pluralist has to different notions of truth for different domains may suggest differences regarding validity in those different domains. Indeed, (...) as we’ll see, the differences between the proposed multiple notions of truth are often of a type that is clearly significant in relation to logical features, such as whether or not a constructive notion of truth is at issue. I criticise domain-based logical pluralism. Having done so I introduce a context-based framework that operates with a context-relative notion of validity. I show that this context-based framework can be employed by the domain-specific logical pluralist, but that framework also allows for logical pluralism that does not involve several domains. Different contexts may demand rules of classical logic, where others only justify intuitionistic rules, even when the same domain (e.g. mathematics) is at issue. (shrink)

Understanding causation in social-ecological systems (SES) is indispensable for promoting sustainable outcomes. However, the study of such causal relations is challenging because they are often complex and intertwined, and their analysis involves diverse disciplines. Although there is agreement that no single research approach (RA) can comprehensively explain SES phenomena, there is a lack of ability to deal with this diversity. Underlying this diversity and the challenge of dealing with it are different causal reasonings that are rarely explicit. Awareness of hidden (...) assumptions is essential for understanding how the causal reasoning of an RA is constituted, and for promoting the integration, translation, or juxtaposition of different RAs. We identify the following elements as particularly relevant for understanding causal reasoning: methods, frameworks and theories, accounts of causation, analytical focus, and causal notions. We begin with the idea that one of these elements typically figures as an entry point to an RA. This entry point is particularly important because it generates a path dependence that orients causal reasoning. In a subsequent step, when an approach is applied, causal reasoning concretizes as a result of a particular constellation of the remaining elements. We come to these insights by studying the application of four different RAs to the same social-ecological case (the collapse of Baltic cod stocks in the 1980s). On the basis of our findings we developed a guide for the analysis of causal reasoning by raising awareness of the assumptions, key elements, and the relations between these key elements for a given RA. The guide can be used to elicit the causal reasoning of RAs, facilitate interdisciplinary collaboration, and support disclosure of ethical/political dimensions that underlie management/governance interventions that are formulated on the basis of causal findings of research studies. (shrink)

This paper argues that philosophical debates between Nyāya and Buddhists on the nature and acquisition of testimonial knowledge present contrasting images of the role played by the epistemic agent in the knowing process. According to Nyāya, an individual can acquire testimonial knowledge automatically—and with little epistemic work—from a trustworthy speaker’s say-so. On the other hand, Buddhist epistemologists, who claim that testimonial knowledge is a species of inferential knowledge, argue that, in order to acquire knowledge from a speaker’s statements, an epistemic (...) agent must possess non-testimonial evidence for the reliability of the testimony in question. This disagreement regarding the division of epistemic labour in testimonial exchanges demonstrates how differently Nyāya and Buddhist philosophers view the prevalence and practical importance of testimonial knowledge. For Nyāya, the ubiquity and easy acquisition of testimonial knowledge help explain the success of our daily actions. However, for Buddhist epistemologists, despite the regularity with which we successfully act based on what others tell us, testimonial knowledge is, in fact, less common, and more difficult to acquire, than we might think. (shrink)

I argue that biographical information is akin to other non-aesthetic, social, historical, or political information. As such, artist’s biographies are always relevant and important when interpreting art. While the meaning and value of a piece of art is not determined by any single piece of contextual information, neither is its meaning and value ever entirely separated from context. In some cases, however, a piece of art that is technically magnificent may be experienced as repugnant when the artist has committed egregious (...) acts. (shrink)

Quantic numbers variate as multiples of a fundamental quantity as the spin, that is always an entire multiple of 1/2.

Can supervaluationism successfully handle indirect speech reports? This chapter considers, and rejects, Schiffer’s claim that they cannot. One alleged problem with indirect speech reports is that the truth of “Carla said that Bob is tall” implausibly requires that Carla said all of a huge number of precise things (i.e. that Bob was over n feet tall, for values of n corresponding to precisifications of “tall”). The paper shows why the supervaluationist is not committed to this. Vague singular terms are no (...) particular problem for supervaluationism within indirect speech reports, it is argued, but there remain some issues surrounding certain vague demonstratives. The supervaluationist has good responses available, however, and any remaining questions face all theories of vagueness and are more appropriately addressed within a theory of demonstratives rather than a theory of vagueness. (shrink)

The parallel research is contemporary to analyse processes and localisation in artificial intelligence (AI) associated with connexionism and learning algorithms. In machine learning, the perceptron (or McCulloch-Pitts neuron) is an algorithm for Boolean functions of binary classifiers. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. With a pattern N we use the calculator in synthesis applying polynomial advanced systems.

Dieser Schwerpunkt dreht sich um das Konzept der Mathematik und ihrer Komponenten und die Bedeutung von Konnektoren für die Mathematik, die auf Taschenrechner angewendet werden.

Abstract-In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. From Poincaré to Turing mathematics is developed at the basis of the fundamental processes.

Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the sorites? (...) This chapter argues that it does not; indeed exploring the disanalogies contributes to a case against such a treatment of vagueness more generally. Among other views, it considers Edgington’s account of vagueness that employs a probabilistic structure of “verities”. It then contends that appeal to the framework of supervaluationism yields a better guide to reasoning in vague language than the degree-theoretic treatment can sustain. (shrink)

Cette orientation évolue autour du concept de mathématiques et de ses composants et de l'importance des connecteurs pour les mathématiques appliquées aux calculatrices.Les symboles et la synthèse sont inscrits pour remarquer leur règle dans les mathématiques et les machines intelligentes générales.

In a recently published article A. Nordmann highlighted the fact that Hertz considered it as the greatest pleasure of scientific research to be “alone with nature” and to learn “directly from nature” (see Nordmann, 1998, p. 156). Hertz contrasts this being on his own with nature with the “disputes about human opinions views and demands. (see Nordmann, 1998, p. 156) . It is this contrast between nature on the one hand and human beliefs etc. on the other that (...) is fundamental for his central epistemological pursuit: the attempt to sort out which features of our theories can be attributed to nature as opposed to those which depend on us. I will discuss the various writings in which Hertz touches this subject. (shrink)

This paper is an expanded written version of my reply to Rosanna Keefe’s paper ‘Modelling higher-order vagueness: columns, borderlines and boundaries’ (Keefe 2015), which in turn is a reply to my paper ‘Columnar higher-order vagueness, or Vagueness is higher-order vagueness’ (Bobzien 2015). Both papers were presented at the Joint Session of the the Aristotelian Society and the Mind Association in July, 2015. At the Joint Session meeting, there was insufficient time to present all of my points in response to (...) Keefe’s paper. In addition, the audio of the session, which is available online, becomes inaudible at the beginning of my reply to Keefe’s comments due to a technical defect. The following is a full version of my remarks. (shrink)

In searching for the origins of current conceptions of science in the history of physics, one encounters a remarkable phenomenon. A typical view today is that theoretical knowledge-claims have only relativized validity. Historically, however, this thesis was supported by proponents of a conception of nature that today is far from typical, a mechanistic conception within which natural phenomena were to be explained by the action of mechanically moved matter. Two of these proponents, Hermann von Helmholtz and his pupil Heinrich (...) class='Hi'>Hertz, contributed significantly to the modernization of the conception of science. Paradigmatic for their common contribution to this development is the way in which they employed the concept of image. By considering the origin and the different meanings of this concept we may trace a line of development which begins with Helmholtz's original claim that a universally and forever valid theory provides a unique representation of nature. It continues with the realization that the status of scientific knowledge is capable of revision; and it arrives at Hertz's admission that a variety of theories over a domain of objects is possible, at least at times. (shrink)

In this paper I argue against readings of Hertz that overly assimilate him into the thought of late 20th century anti-realists and pluralists. Firstly, as is well-known, various images of the same objects are possible according to Hertz. However, I will argue that this envisaged pluralism concerns the situation before all the evidence is considered i. e. before we can decide whether the images are correct and appropriate. Hertz believes in final and decisive battles of the kind (...) he participated in while doing experiments in electrodynamics. Secondly, I will argue that the concept of representation is still quite appropriately applied to important aspects of images, namely when it comes to fundamental physical equations. In this context Hertz explicitly allows that “characteristics of our image, which claim to represent observable relations of things, do really and correctly correspond to them” (Hertz [1894] 1956, 9). A final consideration is Hertz’s consistent appeal to the concept of the hypothesis. I will argue that his use of the concept does not indicate that he contributed to an increasing hypothetization of science, if this trend is understood in a strong sense, i. e. as the belief that the correctness of scientific theories cannot be established for principled reasons. As mentioned, when it comes to experimental evidence Hertz believes in decisive battles. (shrink)

Many philosophers, I suspect, are partial to supervaluational theories of vagueness. And with good reason. Its rivals all seem to promise metaphysical mysteries concerning hitherto unnoticed, and perhaps unnoticeable, sharp boundaries around our concepts, or radical revision in our logical practices. And not only have philosophers been so tempted. The texts are a little unclear, but it seems several economists can be read as adopting supervaluational solutions to the difficulties raised by vagueness in economic concepts. Given its popularity, and plausibility, (...) supervaluationism deserves a book-length defence. Yet this is the first such book in the philosophical canon. (shrink)

In this paper I argue against readings of Hertz that overly assimilate him into the thought of late 20th century anti-realists and pluralists. Firstly, as is well-known, various images of the same objects are possible according to Hertz. However, I will argue that this envisaged pluralism concerns the situation before all the evidence is considered i. e. before we can decide whether the images are correct and appropriate. Hertz believes in final and decisive battles of the kind (...) he participated in while doing experiments in electrodynamics. Secondly, I will argue that the concept of representation is still quite appropriately applied to important aspects of images, namely when it comes to fundamental physical equations. In this context Hertz explicitly allows that “characteristics of our image, which claim to represent observable relations of things, do really and correctly correspond to them” (Hertz [1894] 1956, 9). A final consideration is Hertz’s consistent appeal to the concept of the hypothesis. I will argue that his use of the concept does not indicate that he contributed to an increasing hypothetization of science, if this trend is understood in a strong sense, i. e. as the belief that the correctness of scientific theories cannot be established for principled reasons. As mentioned, when it comes to experimental evidence Hertz believes in decisive battles. (shrink)

A obra Eletric Waves foi o ponto de partida para a análise filosófico-metodológica das teorias científicas por parte de H. Hertz e a culminância dessa prática deu-se com a sua obra póstuma The Principles of Mechanics. Nas introduções a essas duas obras um tema metacientífico se apresenta como núcleo central. Nelas Hertz trata das diferentes representações, imagens ou modelos dos fenômenos físicos: no caso da primeira obra, dos fenômenos eletromagnéticos; no caso da segunda, dos fenômenos mecânicos. E a (...) questão que tenta resolver é a seguinte: qual é a origem da pluralidade de imagens nas teorias científicas? Seria ela inevitável? É sobre esse tipo de questões que se fixa o presente trabalho na intenção de apresentar o papel da noção de representação na concepção de ciência de Heinrich Hertz. (shrink)

En esta obra monumental de Jesper Lützen sobre la mecánica de Heinrich Hertz encontramos una magnífica exposición de la vida y obra de este insigne físico germano. Un interesante relato de las influencias intelectuales que modelaron su pensamiento científico, culmina con un exhaustivo análisis de la reformulación de la mecánica clásica que Hertz planteó poco antes de su prematuro fallecimiento.

Helmholtz initially ascribes more to theoretical knowledge than merely that it is a picture of the world: it penetrates even to the unobservable causes of the phenomena which he conceived throughout his career as matter set mechanically in motion. The introduction of the picture-concept in the 1860s to characterize scientific theories marks the beginning of the loss of a direct connection with the world. Theories now constitute only a representation of a law-like structure of the world but no longer shed (...) light on the objects themselves. Beginning in the late 1870s, this knowledge of laws takes on an increasingly hypothetical character. (shrink)

The aim of this paper is to show that a comprehensive account of the role of representations in science should reconsider some neglected theses of the classical philosophy of science proposed in the first decades of the 20th century. More precisely, it is argued that the accounts of Helmholtz and Hertz may be taken as prototypes of representational accounts in which structure preservation plays an essential role. Following Reichenbach, structure-preserving representations provide a useful device for formulating an up-to-date version (...) of a (relativized) Kantian a priori. An essential feature of modern scientific representations is their mathematical character. That is, representations can be conceived as (partially) structure-preserving maps or functions. This observation suggests an interesting but neglected perspective on the history and philosophy of this concept, namely, that structure-preserving representations are closely related to a priori elements of scientific knowledge. Reichenbach’s early theory of a relativized constitutive but non-apodictic a priori component of scientific knowledge provides a further elaboration of Kantian aspects of scientific representation. To cope with the dynamic aspects of the evolution of scientific knowledge, Cassirer proposed a re-interpretation of the concept of representation that conceived of a particular representation as only one phase in a continuous process determined by pragmatic considerations. Pragmatic aspects of representations are further elaborated in the classical account of C.I. Lewis and the more modern of Hasok Chang. (shrink)

In this paper some classical representational ideas of Hertz and Duhem are used to show how the dichotomy between representation and intervention can be overcome. More precisely, scientific theories are reconstructed as complex networks of intervening representations (or representational interventions). The formal apparatus developed is applied to elucidate various theoretical and practical aspects of the in vivo/in vitro problem of biochemistry. Moreover, adjoint situations (Galois connections) are used to explain the relation berween empirical facts and theoretical laws in a (...) new way. (shrink)

The Polish philosophy of mathematics in the 19th century had its origins in the Romantic period under the influence of the then-predominant idealist philosophies. The decline of Romantic philosophy precipitated changes in general philosophy, but what is less well known is how it triggered changes in the philosophy of mathematics. In this paper, we discuss how the Polish philosophy of mathematics evolved from the metaphysical approach that had been formed during the Romantic era to the more modern positivistic paradigm. These (...) evolutionary changes are attributed to the philosophers Henryk Struve, Antoni Molicki and Julian Ochorowicz, and mathematicians Karol Hertz and Samuel Dickstein. We also show how implicit ideas (i.e., those not declared openly) from the area between the philosophy of science and general philosophy played a crucial role in the paradigm shift in the Polish philosophy of mathematics. (shrink)

In this paper I will compare Hertz and Wittgenstein in order to bring forth a new interpretation of the Tractatus. I shall look at Wittgenstein’s ideas about simple objects and compare them with Hertz’s material particles. I shall then claim that if one understands Hertz’s material particles as logical entities that are more co-ordinate like than physical, one can reach an interpretation of the Tractatus that is deliberately silent about the nature of reality, therefore escaping both objectivist (...) and subjectivist interpretations of the book. This, I think, is just one of the great results of re-thinking Wittgenstein’s ideas through Hertz’s. (shrink)

Maxwellian electrodynamics genesis is considered in the light of the author’s theory change model previously tried on the Copernican and the Einstein revolutions. It is shown that in the case considered a genuine new theory is constructed as a result of the old pre-maxwellian programmes reconciliation: the electrodynamics of Ampere-Weber, the wave theory of Fresnel and Young and Faraday’s programme. The “neutral language” constructed for the comparison of the consequences of the theories from these programmes consisted in the language of (...) hydrodynamics with its rich content of analogous models ranging from the uncompressible fluid up to molecular vortices. The programmes’ meeting led to construction of the whole hierarchy of crossbred objects beginning from the displacement current and up to common hybrids. After that the interpenetration of the pre-maxwellian programmes began that marked the beginning of theoretical schemes of optics and electromagnetism unification. Maxwell’s programme did assimilate some ideas of the Ampere-Weber programme, as well as the presuppositions of the programmes of Fresnel and Faraday; and the significance of this fact for further methodology of scientific research programmes development is discussed. It is argued that the core of Maxwell’s unification strategy was formed by Kantian epistemology looked through the prism of William Whewell and such representatives of Scottish Enlightenment as Thomas Reid and William Hamilton. All these enabled Maxwell to start to unify not only optics and electromagnetism, but British and continental research traditions as well. Maxwell’s programme did supersede the Ampere-Weber one because Maxwell did put forward as a synthetic principle the idea, that differed from that of Ampere-Weber by its flexible and contra-ontological, strictly epistemological, Kantian character. For Maxwell, ether was not the last building block of physical reality, from which fields and charges should be constructed . “Action at a distance”, “incompressible fluid”, “molecular vortices” were only analogies for Maxwell, capable to direct the researcher on the “right” mathematical relations. From the “representational” point of view all this hydrodynamical models were doomed to failure efforts to describe what can not be described in principle – things in themselves, the “nature” of electrical and magnetic phenomena. On the contrary, Maxwell aimed his programme to find empirically meaningful mathematical relations between the electrodynamics basic objects, i.e. the creation of inter - coordinated electromagnetic field equations system. Namely the application of this epistemology enabled Hermann von Helmholtz and his pupil Heinrich Hertz to arrive at such a version of Maxwell’s theory that served a heuristical basis for the radiowaves discovery. (shrink)

Sound is one of the types of waves that can be felt by the sense of hearing (ears). In physics, the definition of sound is something that is produced from objects that vibrate. Objects that produce sound are called sound sources. The sound source that vibrates will vibrate the molecules into the air around it. Sound is mechanical compression or longitudinal waves that propagate through the medium. This medium or intermediate agent can be liquid, solid, gas. So, sound waves can (...) propagate for example in water, coal, or air. Most sounds are a combination of various vibratory signals composed of harmonic waves, but pure sound can theoretically be explained by oscillating vibrational speed or frequency measured in Hertz (Hz) vibration units and amplitude or loudness of sound with measurements in decibels (dB). The effect sounds can have on us humans is simply astounding. While everyday life becomes stressful, overcrowded and increasingly hectic, we seek ways for inner peace and balance. The power of music, felt through overtone-rich sound therapy and sound massage, can be a solution. No matter how much scientific explanation is behind it, healing through music remains fascinating, even magical. This paper introduces a new field called cymatics and sound healing with their plausible impact to spirituality and consciousness research. (shrink)

What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to (...) the ordering over sentences this relation generates. I say it is not a linear ordering, so it cannot be represented by the real numbers. I also argue that since there is higher-order vagueness, any mapping between sentences and mathematical objects is bound to be inappropriate. This is no cause for regret; we can say all we want to say by using the comparative truer than without mapping it onto some mathematical objects. From supervaluationism I take the idea that we can keep classical logic without keeping the familiar bivalent semantics for classical logic. But my preservation of classical logic is more comprehensive than is normally permitted by supervaluationism, for I preserve classical inference rules as well as classical sequents. And I do this without relying on the concept of acceptable precisifications as an unexplained explainer. The world does not need another guide to varieties of theories of vagueness, especially since Timothy Williamson (1994) and Rosanna Keefe (2000) have already provided quite good guides. I assume throughout familiarity with popular theories of vagueness. (shrink)

It is ironic that the prototype of the oscilloscope--for that is what Hertz's apparatus amounted to--should be instrumental in demonstrating that cathode rays have no closer relation to electricity than has light produced by an electric lamp. Indeed, Hertz argued that since "cathode rays are electrically indifferent,... the phenomenon most nearly allied to them is light.".

It gives me great pleasure and honor to introduce myself as the incoming Editor-in-Chief of Polis: The Journal for Ancient Greek and Roman Political Thought. For the last decade I have served as an Associate Editor and the Book Review Editor of the journal. I am very excited about charting new paths for the journal, while continuing to publish first-rate scholarship in our area strengths. Although ‘polis’ is a Greek word that identifies a specific Greek historical political institution, in many (...) important ways the culture of Greek political thought interacted with the political culture of Regal, Republican, and Imperial Rome through Greek settlements in the Western Mediterranean, Roman military conquest, and cultural Hellenization. In the last year the editorial staff of Polis decided to expand the domain of our journal to include scholarship on Roman political thought and Greek-language political thought from the Hellenistic and Roman Imperial periods. Although Polis has been publishing reviews of books devoted to these new domains for several issues, it is quite gratifying to publish an entire special issue, edited by Grant Nelsestuen and Associate Editor Daniel Kapust, devoted to Roman political thought. Additional articles on Roman political thought are in the journal’s publication queue and we look forward to becoming an important venue for the publication of original scholarship and book reviews on Roman political thought and its subsequent reception, along with our original remit for Greek political thought and its reception. The editorial staff of Polis has undergone a number of changes in conjunction with my new role. First and foremost, my mentor and predecessor Kyriakos Demetriou has retired from the position of Editor-in-Chief and become a member of our Editorial Board. I have had the privilege of working with Kyriakos for over 15 years, during which time he transformed the newsletter of the Society for Ancient Greek Political Thought into a pre-eminent peer-reviewed academic journal. I may only hope 15 years from now, that Polis has continued to grow as a source for landmark scholarship on Greek and Roman political thought. During the editorial transition, Associate Editors Rosanna Lauriola and Essam Safty have left our editorial staff. We are grateful for their service to the journal and wish them well in their scholarly endeavors. Finally, I am pleased to announce several additions to our editorial staff. Dimitri El Murr, Professor of Ancient Philosophy at the Ecole Normale Supérieure (Université Paris Sciences et Lettres), has joined the journal as an Associate Editor responsible for the refereeing and editing of Francophone submissions to Polis. Demetra Kasimis, Assistant Professor of Political Science at the University of Chicago, has joined as an Associate Editor responsible for the refereeing of submissions on the political aspects of Greek literature (such as epic, tragedy, and comedy). Matthew Simonton, Associate Professor of History at Arizona State University, has joined the journal as an Associate Editor and Book Review Editor. Finally, Dr. Alexandra Wilding has joined our editorial staff as the journal’s copy-editor. Learn from and enjoy the scholarship of our current issue. Submit to Polis your scholarship on ancient Greek and Roman political thought. Be a part of the future of Polis. Thornton Lockwood Editor-in-Chief. (shrink)

The Marburg neo-Kantians argue that Hermann von Helmholtz's empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz's account raises the 'problem of validity' (Gueltigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz's and Ludwig Wittgenstein's Bild theoretic answer to the problem of validity: that scientists and philosophers can depict (...) the necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz's original account. (shrink)

We present an epistemological schema of natural sciences inspired by Peirce's pragmaticist view, stressing the role of the \emph{phenomenological map}, that connects reality and our ideas about it. The schema has a recognisable mathematical/logical structure which allows to explore some of its consequences. We show that seemingly independent principles as the requirement of reproducibility of experiments and the Principle of Sufficient Reason are both implied by the schema, as well as Popper's concept of falsifiability. We show that the schema has (...) some power in demarcating science by first comparing with an alternative schema advanced during the first part of the 20th century which has its roots in Hertz and has been developed by Einstein and Popper. Further, the identified differences allow us to focus in the construction of Special Relativity, showing that it uses an intuited concept of velocity that does not satisfy the requirements of reality in Peirce. While the main mathematical observation connected with this issue has been known for more than a century, it has not been investigated from an epistemological point of view. A probable reason could be that the socially dominating epistemology in physics does not encourage such line of work. We briefly discuss the relation of the abduction process presented in this work with discussions regarding ``abduction'' in the literature and its relation with ``analogy''. (shrink)

"From the Proceedings of the British Academy, London, volume LXV (1979)" - title page. Series: Henrietta Hertz Trust annual philosophical lecture -- 1978 Other Titles: Proceedings of the British Academy. Vol.65: 1979.

In my dissertation, I present Hermann Cohen's foundation for the history and philosophy of science. My investigation begins with Cohen's formulation of a neo-Kantian epistemology. I analyze Cohen's early work, especially his contributions to 19th century debates about the theory of knowledge. I conclude by examining Cohen's mature theory of science in two works, The Principle of the Infinitesimal Method and its History of 1883, and Cohen's extensive 1914 Introduction to Friedrich Lange's History of Materialism. In the former, Cohen gives (...) an historical and philosophical analysis of the foundations of the infinitesimal method in mathematics. In the latter, Cohen presents a detailed account of Heinrich Hertz's Principles of Mechanics of 1894. Hertz considers a series of possible foundations for mechanics, in the interest of finding a secure conceptual basis for mechanical theories. Cohen argues that Hertz's analysis can be completed, and his goal achieved, by means of a philosophical examination of the role of mathematical principles and fundamental concepts in scientific theories. (shrink)

This paper aims to show that Frege’s and Hilbert’s mutual disagreement results from different notions of Anschauung and their relation to axioms. In the first section of the paper, evidence is provided to support that Frege and Hilbert were influenced by the same developments of 19th-century geometry, in particular the work of Gauss, Plücker, and von Staudt. The second section of the paper shows that Frege and Hilbert take different approaches to deal with the problems that the developments in 19th-century (...) geometry posed for the traditional Kantian philosophy of mathematics. Frege maintains that Anschauung is a source of knowledge by which we acknowledge geometrical axioms as true. For Hilbert, in contrast, axioms provide one of several correct “pictures” of reality. Hilbert’s position is thereby deeply influenced by epistemological ideas from Hertz and Helmholtz, and, in turn, influenced the neo-Kantian Cassirer. (shrink)

It is exhibited that maxwellian electrodynamics grew out of the old pre-maxwellian programmes reconciliation: the electrodynamics of Ampere-Weber, the wave theory of Young-Fresnel and Faraday’s scientific research programme. The programmes’ meeting led to construction of the whole hierarchy of theoretical objects starting from the genuine crossbreeds (the displacement current) and up to usual mongrels. After the displacement current invention the interpenetration of the pre-maxwellian programmes began that marked the beginning of theoretical schemes of optics and electromagnetism real unification. Maxwell’s programme (...) did supersede its rivals because it had assimilated some ideas of the Ampere-Weber programme, as well as the presuppositions of the programmes of Young-Fresnel and Faraday. Maxwellian programme’s victory over its rivals became possible because the core of Maxwell’s unification strategy was formed by Kantian epistemology looked through the prism of William Whewell and such representatives of Scottish Enlightenment as Thomas Reid and William Hamilton. It was Kantian epistemology that enabled Hermann von Helmholtz and Heinrich Hertz to arrive at such a version of Maxwell’s theory that could serve a heuristical basis for the radio waves discovery. (shrink)

A well known conception of axiomatization has it that an axiomatized theory must be interpreted, or otherwise coordinated with reality, in order to acquire empirical content. An early version of this account is often ascribed to key figures in the logical empiricist movement, and to central figures in the early “formalist” tradition in mathematics as well. In this context, Reichenbach’s “coordinative definitions” are regarded as investing abstract propositions with empirical significance. We argue that over-emphasis on the abstract elements of this (...) approach fails to appreciate a rich tradition of empirical axiomatization in the late nineteenth and early twentieth centuries, evident in particular in the work of Moritz Pasch, Heinrich Hertz, David Hilbert, and Reichenbach himself. We claim that such over-emphasis leads to a misunderstanding of the role of empirical facts in Reichenbach’s approach to the axiomatization of a physical theory, and of the role of Reichenbach’s coordinative definitions in particular. (shrink)

Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany (...) and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture. (shrink)

This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explaining the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving the (...) sorites paradox without positing indefensible borders to the correct application of vague terms. (shrink)

According to the conventionalist doctrine of space elaborated by the French philosopher-scientist Henri Poincaré in the 1890s, the geometry of physical space is a matter of definition, not of fact. Poincaré's Hertz-inspired view of the role of hypothesis in science guided his interpretation of the theory of relativity (1905), which he found to be in violation of the axiom of free mobility of invariable solids. In a quixotic effort to save the Euclidean geometry that relied on this axiom, Poincaré (...) extended the purview of his doctrine of space to cover both space and time. The centerpiece of this new doctrine is what he called the "principle of physical relativity," which holds the laws of mechanics to be covariant with respect to a certain group of transformations. For Poincaré, the invariance group of classical mechanics defined physical space and time (Galilei spacetime), but he admitted that one could also define physical space and time in virtue of the invariance group of relativistic mechanics (Minkowski spacetime). Either way, physical space and time are the result of a convention. (shrink)

The main concern of this paper is the proper analysis of the NP celui-ci in French. The contribution of L. Tasmowski to this discussion is well known. In my view, this contribution makes two important points: 1) in its anaphoric uses, celui-ci cannot be analysed as a "nominal anaphoric" along the lines suggested by Corblin for its exophoric uses. This point is also made in Kleiber, Zribi-Hertz, Imoto ; 2) eventhough celui-ci like pronouns and definite NPS must be linked (...) in its anaphoric uses to a familiar discourse referent, it involves "une rupture de familiarité" [a familiarity break]. Basically, I will argue in this paper that these two points are correct, although they seem to draw the analysis of celui-ci in two opposite directions and look somewhat paradoxical. In this paper, I propose a solution to those difficulties which is based on the analysis of celui-ci as a "mentional NP". Other mentional NPs in French are, for instance, le premier, le second, ce dernier. Mentional NPS, it will be claimed, are just NPs which are associated to a previously established discourse referent by using only the properties of the previous mention having evoked this discourse referent in the discourse context. I will claim that there is a strong association between mentionals and NPs without a noun in French, namely that mentional references are achieved by NPs without a noun. I will show moreover that this specific kind of reference based on contingent properties of a discourse referent is the key for understanding how a coindexed NP produces the break in topic continuity noted by Tasmowski. (shrink)