According to Ernst Cassirer, the transition from the concept of substance to that of mathematical function as a guide of knowledge coincided with the end of ancient and the beginning of modern theoretical thought. In the first part of this article we argue that a similar transition has also taken place in the practical sphere, where mathematical function occurs in one of its specific forms, which is that of the algorithm concept. In the second part we argue that with the (...) rise of modernity the idea of substance and the related concepts of category and classification, which are deeply embedded in western culture, have not been totally supplanted by that of function. The intertwining of the concepts of substance and function has generated contradictory hybrids. These hybrids are used as a key for the understanding of the different repercussions of algorithmic logic on society in terms of social integration. (shrink)

This article is both a comment on Neyland’s ‘On organizing algorithms’ and a supplementary note to our ‘The concept of algorithm as an interpretative key of modern rationality’. In the first part we discuss the concepts of algorithm and recursive function from a different perspective from that of our previous article. Our cultural reference for these concepts is once again computability theory. We give additional arguments in support of the idea that a culture informed by an algorithmic logic has promoted (...) modern rationality both in science and in society. We stress again the importance of distinguishing between algorithms applied to quantifiable entities such as space, time and value and those applied to ontological entities such as human actions. In the second case, the algorithm is applied outside its domain of definition and leads to social disaggregation. (shrink)

The theory of numbers, the theory of computation and well-known biological and neurological studies on cognition and consciousness all indicate the concept of recursion as their common denominator. Mathematical recursion owes its meaning and properties to a dual relationship between its results, which always constitute a sequence, and the operator that generated them, which is instead invariant. This article proposes that this duality in recursion originates from the duality between the biological homeostatic equilibrium in living systems and the adaptive physico-chemical (...) changes required to sustain such equilibria. Such duality gives order and meaning to the experiences of a living system. One of the many implications of this innovative perspective is that this duality can decouple computational results from our intuitive order relations, and that this can cause a rarefaction of the capacity of digital systems to convey communication and favour adaptation to the environment. (shrink)