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)

Reductionism relies on expectations that it is possible to make sense of the whole by studying its parts, whereas emergentism considers that program to be unattainable, partly due to the existence of emergent properties. The emergentist holistic stance is particularly relevant in biology and cognitive neuroscience, where interactions amongst system components and environment are key. Here we consider Alfred North Whitehead's philosophy as providing important insights to metaphysics of science in general, and to the reductionism vs. emergentism debate in particular. (...) An appraisal of Whitehead's perspective reveals a difficulty shared by both approaches, referred to him as “simple location”: the commitment to the idea that the nature of things is exhausted by their intrinsic or internal properties, and does not take into account relations or dynamic interactions denoting “togetherness.” In a word, that things are simply where they are. Whitehead criticizes this externalist ontological perspective in which each interacting element exists, and can be thought, without essential reference to other elements. The aim of this work is to uncover such a stance, particularly in the context of dynamical systems, and to show its shortcomings. We propose an alternative relational approach based on Whitehead's notion of “internal relations,” which we explicate and illustrate with several examples. Our work aims to criticize the notion of simple location, even in the framework of emergentist accounts, so as to contribute to a “relational turn” that will conceive “inter-identities” as “intra-identities” in which interactants are not enduring substances, but internally related processes. In sum, we argue that the notion of internal relations has a strong theoretical power to overcome some fundamental difficulties in the study of life and mind. (shrink)