We provide a new perspective on the relation between the space of description of an object and the appearance of novelties. One of the aims of this perspective is to facilitate the interaction between mathematics and historical sciences. The definition of novelties is paradoxical: if one can define in advance the possibles, then they are not genuinely new. By analyzing the situation in set theory, we show that defining generic (i.e., shared) and specific (i.e., individual) properties of elements of a (...) set are radically different notions. As a result, generic and specific definitions of possibilities cannot be conflated. We argue that genuinely stating possibilities requires that their meaning has to be made explicit. For example, in physics, properties playing theoretical roles are generic; then, generic reasoning is sufficient to define possibilities. By contrast, in music, we argue that specific properties matter, and generic definitions become insufficient. Then, the notion of new possibilities becomes relevant and irreducible. In biology, among other examples, the generic definition of the space of DNA sequences is insufficient to state phenotypic possibilities even if we assume complete genetic determinism. The generic properties of this space are relevant for sequencing or DNA duplication, but they are inadequate to understand phenotypes. We develop a strong concept of biological novelties which justifies the notion of new possibilities and is more robust than the notion of changing description spaces. These biological novelties are not generic outcomes from an initial situation. They are specific and this specificity is associated with biological functions, that is to say, with a specific causal structure. Thus, we think that in contrast with physics, the concept of new possibilities is necessary for biology. (shrink)

We characterize access to empirical objects in biology from a theoretical perspective. Unlike objects in current physical theories, biological objects are the result of a history and their variations continue to generate a history. This property is the starting point of our concept of measurement. We argue that biological measurement is relative to a natural history which is shared by the different objects subjected to the measurement and is more or less constrained by biologists. We call symmetrization the theoretical and (...) often concrete operation which leads to considering biological objects as equivalent in a measurement. Last, we use our notion of measurement to analyze research strategies. Some strategies aim to bring biology closer to the epistemology of physical theories, by studying objects as similar as possible, while others build on biological diversity. (shrink)

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that (...) symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not just processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions. (shrink)

This article proposes an abstract mathematical frame for describing some features of cognitive and biological time. We focus here on the so called “extended present” as a result of protentional and retentional activities (memory and anticipation). Memory, as retention, is treated in some physical theories (relaxation phenomena, which will inspire our approach), while protention (or anticipation) seems outside the scope of physics. We then suggest a simple functional representation of biological protention. This allows us to introduce the abstract notion of (...) “biological inertia”. (shrink)

The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a (...) book and several articles, quoted throughout. (shrink)

In this paper, we apply the perspective of intra-organismal ecology by investigating a family of ecological models suitable to describe a gene therapy to a particular metabolic disorder, the adenosine deaminase deficiency (ADA-SCID). The gene therapy is modeled as the prospective ecological invasion of an organ (here, bone marrow) by genetically modified stem cells, which then operate niche construction in the cellular environment by releasing an enzyme they synthesize. We show that depending on the chosen order (a choice that cannot (...) be made on \textit{a priori} assumptions), different kinds of dynamics are expected, possibly leading to different therapeutic strategies. This drives us to discuss several features of the extension of ecology to intra-organismal ecology. (shrink)

This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal …) and properly biological (heart beating, respiration, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (...) (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The “visual” representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3- dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for “representation time”, with a cognitive significance. (shrink)

In this paper, we discuss the perspective of intra-organismal ecology by investigating a family of ecological models. We consider two types of models. First order models describe the population dynamics as being directly affected by ecological factors (here understood as nutrients, space, etc). They might be thought of as analogous to Aristotelian physics. Second order models describe the population dynamics as being indirectly affected, the ecological factors now affecting the derivative of the growth rate (that is, the population acceleration), possibly (...) through an impact on non-genetically inherited factors. Second order models might be thought of as analogous to Galilean physics. In the joint paper, we apply these ideas to a situation of gene therapy. (shrink)

n this text, we revisit part of the analysis of anti-entropy in Bailly and Longo (2009} and develop further theoretical reflections. In particular, we analyze how randomness, an essential component of biological variability, is associated to the growth of biological organization, both in ontogenesis and in evolution. This approach, in particular, focuses on the role of global entropy production and provides a tool for a mathematical understanding of some fundamental observations by Gould on the increasing phenotypic complexity along evolution. Lastly, (...) we analyze the situation in terms of theoretical symmetries, in order to further specify the biological meaning of anti-entropy as well as its strong link with randomness. (shrink)

The book A critical overview of biological functions is a short monograph by J. Garson, which provides a survey of the views on biological functions in the analytic tradition of philosophy. The notion of function is ubiquitous in biology and all of its subfields. Behind the notion of biological functions lurks the shadow of final causes. Overcoming this shadow is a challenge that has stimulated many philosophers and the literature on this topic is very rich. In the analytic tradition, researchers (...) focus on providing naturalized accounts of functions. To do so, the main difficulty is to provide accounts of functions that exclude the use of final causes. The outcome of this collective work is a diversity of accounts of functions. Some of these accounts are fairly recent while others have been proposed several decades ago and are the object of many discussions. (shrink)