There is no consensus on aging in biology, particularly regarding what the term itself designates —that is, its specific object. Consequently, the concept of "aging" remains unclear. At the same time, evolutionary theories of aging are plural, and the question of their potential unification is complex. From this starting point, we seek to examine the legitimacy of the evolution of a concept closely linked to aging : the concept of "biological age". We believe that the evolution of this concept would be highly useful, based on the hypothesis that theories of aging—notably those relating to social evolution —provide sound reasons to re-examine the "biological" nature of the concept of age. We posit that there would be a considerable epistemic gain in replacing it, insofar as the development of an alternative concept of age—which we shall call "biosocial"—would allow for a different foundation for the measurements linked to it and, potentially, for the theories of aging themselves. The primary interest would be to better understand the theoretical gap, both epistemological and ontological, existing between the two, and more precisely, the advancement offered by the substituting concept. If it is only through the explanation of the first concept (biological age) that we can grasp the specificity of the second, we will also gain a new—and hopefully better—understanding of the first concept through the lens of the second, notably by explaining its limits and singularities. 

As highlighted by studies such as Pietro Corsi’s, the reception of Darwin’s On the Origin of the Species in continental Europe was twice skewed: on the one hand, the core theses of Darwin’s theory of evolution by natural selection were readily accepted and popularized by an intellectual milieu external to mainstream scholarly institutions; on the other hand, such enthusiastic purveyors of Darwinian ideas tended to frame On the Origin’s theses through their own preconceived understandings of evolution. The case of Darwin’s reception in the German-speaking world is particularly interesting from this standpoint. Sander Gliboff’s study on the diffusion of On the Origin’s German edition notably argues that figures such as Heinrich Georg Bronn and Ernst Haeckel contributed to filtering Darwin’s thought through the legacy of German Naturphilosophie, e.g., Goethe’s morphology and theory of metamorphosis.

This contribution aims to shed further light on the history of Darwin’s reception through the following question: How did “Darwinismus,” stemming from German translations/interpretations of On the Origin of Species, differ from Darwin’s thought?

To this aim, it deploys two methodological approaches. First, it provides a distant reading of all German translations of Darwin’s works accessible on the website https://darwin-online.org.uk/. Through topic modelling and co-occurrence analysis, this approach pinpoints lexical-conceptual patterns distinctive of how Darwinian concepts and ideas were assimilated within the German context, e.g., how the rendition of “origin” as “Entstehung” affected the semantic field associated with evolutionary terminology. Second, this contribution adopts a history-of-concepts approach to elucidate the structure and function of concepts such as “Entstehung” and “Entwickelung” within the broader intellectual and social context of Darwin’s reception in Germany. This conceptual-historical analysis relies on a close reading of relevant documents identified through the first approach. 

In this talk, I will briefly review the types of arguments presented in favor of Church’s thesis: those of Church and Kleene, the convergence of attempts to define computability, Turing’s analysis, Kripke’s argument, and the axiomatic proof. I will explore whether it is possible to prove the adequacy of a concept to an intuitive notion.

There are some mathematical results that represent points of change in mathematical knowledge, they are cornerstones. These results are answers to specific problems. In this lecture, I am going to show the context of some of these problems and the process of their solutions, and I am going to explain how these results meant changes and some of their consequences for the development of mathematical knowledge.

I will inquire into the birth of algebraic geometry, and of the concepts and methods that characterize it, by studying the Isagoge ad Locos Planos et Solidos of Fermat and Descartes’ Geometry, and the lines of force that run through this theory at the crossroads of algebra, geometry, and number theory. 

My presentation will have as its objective to comment on the manner in which the notion of geometric locus nourished the development of the mathematical concept of curve in the seventeenth century. In particular, I will return to the notion of geometric locus among the Ancients before analyzing the modifications introduced by the Moderns to justify their conception of curves. 

My questioning, based on three words—and I could have added "things" in the manner of Aristotle—may not concern a mathematician engaged in the act of creation, which nonetheless involves a collective element and therefore questions of vocabulary, as we have known since Euclid's Elements. My introspection touches on the narrative or account, even the judgment, of historians and philosophers, but also that of authors of mathematical treatises (and not only Bourbaki). I want to frame questions on a case that did not appear before the scientific revolution, that of the notion of function, invented by Leibniz in 1673 although underlying that of "law of nature", and a source of ambiguity in the 18th century despite a major practice with the various functional equations. It received a delimitation for the variable, therefore perhaps becoming an object (interval of definition) only with Fourier at the beginning of the 19th century; it was enriched with the qualifications of regularity (continuity, differentiability, Lipschitz character, then computability today) which transform such functions into so many “percepts” in the manner of Deleuze. The notion was fixed as a concept by Cantor, and seemed to lose its connection with the notion of a variable, due to Lebesgue's "almost everywhere" conception, and above all the Schwartz and Sobolev distributions, seen as “generalizations” of functions. It has become common vocabulary (a “thing)” both in secondary education and in the economic world, although losing the quantitative notion of a law in favor of that of a shape (for example an S-curve or Σ), and perhaps supplanted by the notion of an algorithm whose complexity is measurable. Essentially, starting from a history of functions that has already been largely written and was proven to have been very changeable, the aim is to probe the formal and syntactic processes of a mathematization of causality.

In this talk, I explore the reception and reworking of Pappus of Alexandria’s Mathematical Collection in seventeenth-century New Spain through a specific case: Proposition 164 of Book VII. Drawing on manuscript evidence, I suggest that, despite the absence of this text from known inventories, its circulation in the New Spanish context can be traced and was likely mediated by Federico Commandino’s Latin edition (1588), whose translation and commentary served as a key vehicle for the transmission of Pappus’s work in the early modern period.

Against this background, I focus on how this problem reached the hands of fray Diego Rodríguez and how he engaged with it mathematically. I argue that, rather than being a passive recipient, Diego subjected the problem to a rigorous and original treatment, positioning himself within the broader geometrical discussions of his time as the first professor of mathematics at the Royal and Pontifical University of Mexico.

This communication proposes to reexamine the contribution of Hélène Metzger to historical epistemology by situating it between two poles: the analysis of the sciences as rational structures and their understanding as cultural phenomena. Contrary to a focus on the sole context of justification, Metzger invites us to think about the conditions of elaboration of scientific concepts.

Taking up the Kantian framework, she assigns a central role to transcendental imagination. The synthesis between experience and intellect would not be primarily conceptual, but rather analogical and metaphorical. Scientific concepts, like other general concepts, are formed through a work of analogy that is rooted in a common mythopoietic background, upon which logico-mathematical formalisms come to be structured. This transcendental is, however, historicized: it refers to collective, cultural, and anthropological forms of imagination.

Science thus appears as a historicized rhetoric, and the philosophy of science as an anthropology of symbolic practices. This perspective will be illustrated through the comparative analysis of contemporary scientific concepts from heterogeneous fields. It will be shown that the Metzgerian approach offers an innovative and relevant methodology for thinking the history of science as a cultural history of forms of thought, capable of articulating analytical rigor and attention to the historical conditions of rationality.

During the 20th century, biological nitrogen fixation (BNF) was understood as a phenomenon strictly associated with free-living bacteria or symbionts of leguminous plants. This approach integrated concepts from microbiology and plant physiology, and focused on the symbiotic process as the object of study. Therefore, scientific explanations were organized around the identification of microorganisms, the analysis of their interactions with plants, and the characterization of the BPN process. Towards the end of the 1970s and early 1980s, the development of bacterial molecular genetics and genetic engineering allowed these problems to be rethought from new experimental practices. BNF began to be explained at the level of specific genes and metabolic pathways, shifting the object of study from ecological interaction to genetic engineering and sequencing. This change did not imply the abandonment of symbiosis, but rather its insertion into a different set of practices, instruments, and research questions. In Mexico, this process enabled the development of genetic engineering in a context marked by the search for self-sufficiency and food production, as well as the reduction of chemical fertilizer use. Thus, BNF acquired strategic relevance in a local context with studies on nitrogen-fixing bacteria and their genes. The possibility of genetically transferring nitrogen fixation processes to other organisms using genetic engineering techniques redefined the objects of study. What was traditionally researched in large controlled crops began to be studied—and manipulated—in in vitro systems using molecular cloning techniques. This paper allows us to reflect on how scientific practices and concepts can be transformed and acquire new meanings when integrated into reconfigured experimental systems. Conceptual evolution thus appears to be linked to the co-production of concrete research practices, rather than to abstract definitions or abrupt theoretical breaks. 

In Mexico, it is unclear how evolutionary content was chosen and introduced into the first textbooks used at the National Preparatory School. The school was founded in 1867 based on a positivist scientific model. Its first director, Gabino Barreda (1818-1881), considered incorporating the teaching of natural history into the curriculum and, with it, notions of evolutionism. However, classical literature suggests that evolutionism first appeared in schools in 1877, in the book Compendio de la Historia de la Antigüedad (Compendium of Ancient History), written by Justo Sierra (1848-1912) (Moreno, 1984). After reviewing the aforementioned book, it was found that there are only two paragraphs that discuss Darwinism and its basic concepts. On the other hand, recent literature suggests that evolution officially appeared in Mexico in the early 20th century, through the books and courses of Alfonso Luis Herrera (1860-1942) (Cueva, 2024). 

In accordance with the previous, this paper analyzes how and when the first evolutionary content appeared in Mexican schools, demonstrating that Sierra's Darwinism was not necessarily the only or the first to appear on this subject, and taking into account that the documents from 1867 to 1877 have not yet been reviewed in detail. On the other hand, it analyzes the possible evolutionary content that appeared between 1877 and 1887, with the intention of showing the richness of evolutionary notions prior to the turn of the century and the official presence of evolution in the country. 

This paper is part of the author's PhD research.

An expression of a biological diversity in crisis, “biodiversity” must respond to the political challenge of its conservation (Casetta & Delord, 2014). Since the mid-1980s, part of the efforts in ecology and conservation biology has been concentrated on the quantification of biodiversity at its different levels of integration and spatio-temporal scales (Devictor, 2015). We will endeavor to show that the reduction of biodiversity to its quantified representations can be described as ‘quantophrenic’ (Desrosières, 1993; Porter, 1995) and also affects the production of predictions.

Relying on a distinction between uncertainties (among which quantified imprecision) and ignorances (which emerge when scientific uncertainties are confronted with a norm of action), we will show how this quantophrenia has as a consequence the emergence of a form of scientific ignorance in which biodiversity appears as an exclusively technical problem, thus orienting public decisions.

In The Structure of Scientific Revolutions and in his subsequent texts, Thomas Kuhn grants a central place to the notion of incommensurability. This notion is applied to a great many cases which at first glance seem different. The objective of this presentation is to put this notion of incommensurability to the test by comparing (a) the context in which it was first conceived by Kuhn, (b) the more specific case of mathematized theories, and (c) the use made of it in contemporary developmental psychology. The aim of this comparison is to underscore the necessity of distinguishing the types of relations that different conceptual systems can maintain with one another, in order ultimately to nuance the scope of Kuhn’s voluntarism.

In 2008, the historian of physics Olivier Darrigol proposed a new vision of the formation and evolution of physical theories based on the concept of ‘module.’ A module is a kind of fundamental building block of a physical theory, and is itself defined as a physical theory. It contains at once a symbolic universe, that is, a set of symbols that characterize the states of a physical system; fundamental laws, which condition the behavior of physical systems in the symbolic universe; and interpretative schemes, which give physical meaning to the formalism by associating it with possible experiments to be conceived.

From this perspective, physics appears as a vast network of modules connected to one another, and capable of evolving over time. This approach makes it possible in particular to account for transfers of knowledge that may occur between different fields of physics, and which can be interpreted in this context as a sharing of modules. This is what I will illustrate using an example drawn from my own research, namely that of quantum optics. I will show, indeed, that the birth of this field of research results from a transfer of knowledge from quantum electrodynamics (QED) to the domain of optics, and that QED can, for this reason, be considered as a module of quantum optics.