Enacting Infinity: Bringing Transfinite Cardinals into Being
Enacting Infinity: Bringing Transfinite Cardinals into Being
This chapter argues that cases wherein an empirically observable physical reality is lacking—when there is no pregiven world to be mentally re-presented—are provided by mathematics. In particular, it argues that mathematical infinity, as a form of cognition which by definition is not directly available to experience due to the finite nature of living systems, is an excellent candidate for fully exploring the power of enaction as a paradigm for cognitive science. The chapter focuses on a particular form of actual infinity—or infinity as a complete entity—namely, the transfinite cardinal numbers as they were conceived by one of the most controversial characters in the history of mathematics, the nineteenth-century mathematician Georg Cantor.
Keywords: empirically observable, physical reality, mathematics, mathematical infinity, enaction, cognitive science, actual infinity, transfinite cardinal numbers, Georg Cantor
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