María de Paz

Henri Poincaré’s philosophy of science has been widely studied and has been related to other important scientific and philosophical figures such as Einstein, Hilbert, Helmholtz, Duhem, and even Bergson. Poincaré refers to many people in his works, but there is one name that appears repeatedly in his texts, in particular when he develops his general views on the value of science. That is Édouard Le Roy. There is a lack of secondary sources on Le Roy’s work and, when compared to Poincaré, references are usually given to Poincaré’s interpretation of his works and not to Le Roy himself. When writing on the value of science, Poincaré structures his discourse as a reply to Le Roy’s views. This paper aims at clarifying why it was so important for Poincaré to reply to Le Roy. To do that, we will discuss the figure of Le Roy in the context of the time, his philosophy (which he called nouveau positivisme), and the relation between Poincaré’s philosophical position and Le Roy’s. This will make Le Roy’s work more familiar to contemporary audiences but will also clarify some controversial aspects in Poincaré’s position.

The aim of this paper is to reconsider Mach’s position in the light of the recent approach on the interplay of mathematical practices provided by José Ferreirós’ book Mathematical Knowledge and the Interplay of Practices. In the first section the main approach of the book is presented, with a characterization of the notion of ‘scientific practice’ and the triple approach used to understand mathematical knowledge: cognitive, pragmatist and historical. In the sections 2, 3 and 4 Mach’s philosophical views are presented according to this epistemological approach. The fifth section is the conclusion.

This volume presents a selection of papers from the Poincaré Project of the Center for the Philosophy of Science, University of Lisbon, bringing together an international group of scholars with new assessments of Henri Poincaré's philosophy of science-both its historical impact on the foundations of science and mathematics, and its relevance to contemporary philosophical inquiry. The work of Poincaré (1854-1912) extends over many fields within mathematics and mathematical physics. But his scientific work was inseparable from his groundbreaking philosophical reflections, and the scientific ferment in which he participated was inseparable from the philosophical controversies in which he played a pre-eminent part. The subsequent history of the mathematical sciences was profoundly influenced by Poincaré's philosophical analyses of the relations between and among mathematics, logic, and physics, and, more generally, the relations between formal structures and the world of experience. The papers in this collection illuminate Poincaré's place within his own historical context as well as the implications of his work for ours.

Much of the focus on Poincaré’s philosophy of science has been on the notion of convention, a crucial concept that has become distinctive of his position. However, other notions have received much less attention. That is the case of verifiable hypotheses. This kind of hypotheses seems to be constituted from the generalization of several observable facts. So, in order to understand what these hypotheses are, we need to know what a fact to Poincaré is. He divides facts into brute and scientific facts. The characterization of this duality is not trivial at all, and leads us to the following questions that we will discuss in this paper: which the part of construction that exists in a scientific fact and which the part of translation, that is, what remains from the brute fact in the scientific one?; and when we conceive a generalized hypothesis, are we supposed to do it from scientific or from brute facts? The clarification of these questions could lead to distinguish the part of construction and the part of translation in the first steps of science, which is essential to get a better understanding of Poincaré’s conception of science.

Poincaré’s conventionalism has been interpreted in many writings as a philosophical position emerged by reflection on certain scientific problems, such as the applicability of geometry to physical space or the status of certain scientific principles. In this paper I would like to consider conventionalism as a philosophical position that emerged from Poincaré’s scientific practice. But not so much from dealing with scientific problems, as from the use of two specific methodologies proper to modern mathematics and the modern natural sciences: methodological structuralism and the hypothetical-deductive method—thus, as a philosophical position which emerged from a way (or rather, two ways) ofdoingscience. With this approach, I try to deepen the analysis of connections between Poincaré’s scientific practice and his philosophy.

Muita da literatura sobre a filosofia da ciência de Poincaré tem estado focada na noção de convenção, um conceito crucial que identifica a sua posição. No entanto, há outras noções que têm recebido menos atenção. Este é o caso das hipóteses verificáveis. Este tipo de hipótese parece ser constituído a partir da generalização de vários fatos observáveis. Assim, para compreender o que são estas hipóteses, temos de saber o que é um fato para Poincaré. Ele divide fatos em brutos e científicos. A caracterização desta dualidade não é de tudo trivial, e nos leva às seguintes questões que discutiremos neste artigo: (1) qual a parte de construção que existe num fato científico e qual a parte de tradução? Isto é, o que permanece do fato bruto no fato científico? E (2) quando concebemos uma hipótese generalizada, a generalização é feita a partir dos fatos científicos ou dos fatos brutos? A clarificação destas questões pode levar a distinguir a parte de construção e a parte de tradução desde os primeiros passos da ciência, o que é essencial para conseguir uma melhor compreensão da concepção de ciência de Poincaré.

Este artículo comenta una conferencia de Louis de Broglie de 1952 en la que se replantea sus ideas iniciales sobre la mecánica cuántica. Defenderemos la tesis de que, en ese trabajo, pese a la referencia al indeterminismo, el objetivo del físico francés es presentar una interpretación causal de esta teoría y no poner de manifiesto su indeterminismo. Así, analizaremos la noción de causalidad que presenta con el objetivo de separarla del determinismo. Estructuraremos la noción presentada por de Broglie en tres partes y la conexión entre las mismas. Para separar causalidad de determinismo utilizaremos una definición no restrictiva de esta noción y presentaremos los problemas que tiene la noción de causalidad utilizada por de Broglie. Finalmente, defenderemos una interpretación de las ideas de de Broglie más como una concepción filosófica que científica y ofreceremos alternativas filosóficas a la misma.

Much of the focus on Poincaré’s philosophy of science has been on the notion of convention, a crucial concept that has become distinctive of his position. However, other notions have received much less attention. That is the case of verifiable hypotheses. This kind of hypotheses seems to be constituted from the generalization of several observable facts. So, in order to understand what these hypotheses are, we need to know what a fact to Poincaré is. He divides facts into brute and scientific facts. The characterization of this duality is not trivial at all, and leads us to the following questions that we will discuss in this paper: which the part of construction that exists in a scientific fact and which the part of translation, that is, what remains from the brute fact in the scientific one?; and when we conceive a generalized hypothesis, are we supposed to do it from scientific or from brute facts? The clarification of these questions could lead to distinguish the part of construction and the part of translation in the first steps of science, which is essential to get a better understanding of Poincaré’s conception of science.

The aim of this paper is to argue that there existed relevant interactions between mechanics and geometry during the first half of the nineteenth century, following a path that goes from Gauss to Riemann through Jacobi. By presenting a rich historical context we hope to throw light on the philosophical change of epistemological categories applied by these authors to the fundamental principles of both disciplines. We intend to show that presentations of the changing status of the principles of mechanics as a mere epiphenomenon of the emergence of non-Euclidean geometries are inaccurate, that the relations between the two disciplines were richer than what is usually considered in the literature. These claims will be based on historical and philosophical arguments, starting from the fact that disciplinary boundaries at the time were not rigid as we are used today. It is widely known that the main figures we target worked in different areas, which is a first piece of evidence for the plausibility of our main thesis.

In the introduction to his famous book, La Science et l’hypothèse, Poincaré remarks on the necessary role and legitimacy of hypotheses. He establishes a triple classification of hypotheses, dividing them into verifiable, useful, and apparent. However, in chapter 9, entitled ‘Les hypothèses en physique’, he gives a slightly different triadic classification: natural hypotheses, indifferent hypotheses, and real generalizations. The origin of this second classification is a lecture given at the International Congress of Physics, Paris, 1900. What are the similarities and differences between these two classifications? My main purpose is to provide a possible equivalence between the two classifications in order to clarify the role of hypotheses in Poincaré’s epistemology of natural science. The discussion will be based on the two fundamental texts mentioned above and on the contrast between Poincaré’s use of the notion of hypothesis and that of some of his contemporaries.

This paper aims at understanding the concept of convention in mechanics as a notion transferred from the field of jurisprudence. This enables us to clarify it as a new epistemic category having a pertinent role in the transformation of mechanics in the nineteenth century. Such understanding permits a separation from linguistic and arbitrary conventions, thus highlighting its epistemic features and not transforming fundamental principles into mere arbitrary agreements. After addressing the main references in the literature discussing the role of convention in mechanics, we analyze its classical use as a concept originating from law. Then we explain its use by Carl G. Jacobi, Ferdinand F. Reech, and J. Henri Poincaré. Here we also show how their uses conform to the features analyzed regarding conventions in jurisprudence. Finally, we try to explain how the use of this concept, among other factors, contributed to the transformation of mechanics.