Two main theories aim at understanding carcinogenesis: the reductionist smt locates cancer in cancer cells, while the organicist toft locates cancer at the tissue level. For toft, the ‘cancer cell’ is a phlogiston, smt is an old paradigm which ought to be replaced. Recently two critics have argued that toft and smt, despite their apparent strong incompatibilities, are actually compatible. Here we review their arguments. We show that these arguments are based on interpretation mistakes that become understandable once one grants that criticizing a paradigm from the point of view of another, in which words do not have the same signification, bears the risk of strong misunderstandings. These misunderstandings, in our experience, are common. We hope that this discussion will help clarifying the differences between toft and smt.

Keywords: TOFT, reductionism, organicism, levels of organization, SMT

This short text summarizes the work in biology proposed in our book, Perspectives on Organisms, where we analyse the unity proper to organisms by looking at it from different viewpoints. We discuss the theoretical roles of biological time, complexity, theoretical symmetries, singularities and critical transitions. We explicitly borrow from the conclusions in some key chapters and introduce them by a reflection on "incompleteness", also proposed in the book. We consider that incompleteness is a fundamental notion to understand the way in which we construct knowledge. Then we will introduce an approach to biological dynamics where randomness is central to the theoretical determination: randomness does not oppose biological stability but contributes to it by variability, adaptation, and diversity. Then, evolutionary and ontogenetic trajectories are continual changes of coherence structures involving symmetry changes within an ever-changing global stability.

Keywords: Incompleteness, symmetries, randomness, critical transitions, biological evolution and ontogenesis

Repetitiveness and reversibility have long been considered as characteristic features of scientific knowledge. In theoretical population genetics, repetitiveness is illustrated by a number of genetic equilibria realized under specific conditions. Since these equilibria are maintained despite a continual flux of changes in the course of generations (reshuffling of genes, reproduction…), it can legitimately be said that population genetics reveals important properties of invariance through transformation. Time-reversibility is a more controversial subject. Here, the parallel with classical mechanics is much weaker. Time-reversibility is unquestionable in some stochastic models, but at the cost of a special, probabilistic concept of reversibility. But it does not seem to be a property of the most basic deterministic models describing the dynamics of evolutionary change at the level of populations and genes. Furthermore, various meanings of “reversibility” are distinguished. In particular, time-reversibility should not be confused with retrodictability.

Keywords: population genetics, repetition, retrodiction, reversibility