Category theory and foundations of life science: A structuralist perspective on cognition

Abstract

Category theory has recently been applied successfully beyond mathematics and its foundations, for example, in quantum physics, quantum computing, linguistics, and natural language processing in artificial intelligence. Category theory today is arguably foundations of science as well as foundations of mathematics. Yet applications of category theory to the life sciences are still limited, and there are seemingly no clearly successful paradigmatic cases of them. Here we address foundational aspects of category theory in and across the sciences, and potential structural interconnections between category theory and the life sciences, in particular cognitive science. More specifically, we first address the two aspects of category theory as foundations of science and as foundations of mathematics in particular, and then discuss what category theory could do for foundations of life science, in particular cognitive science. We propose, amongst other things, a categorical structuralist approach to the mind-body problem as an alternative to reductionist approaches, which is arguably of both scientific and metaphysical significance at the same time. Category theory allows us to elucidate structural interconnections between the laws of cognition and the laws of reality, thus paving the way for overcoming the Cartesian dualism separating the cognitive and physical worlds. Put another way, category theory suggests that there may be higher laws governing both worlds at once; the higher structuralist theory of cognition may embody the double aspect theory of information by David Chalmers.