In the Aristotelian tradition, the relationship with Aristotle’s treatment of infinity has always been ambiguous for reasons connected to theology, creation, and natural philosophy. Scholastic philosophy generally rejects the existence of real infinities in the created world, while recognising potential infinities in the doctrine of the continuum, in line with Aristotle’s views on this matter. According to this view, there is no infinite power or greatness in the world. Nevertheless, notable developments emerge in which this orthodoxy is questioned, and the possibility that God could produce an actual infinity in terms of quantity, number, or intensity becomes widespread among later scholastics – such infinist approaches sometimes drawing on highly interpretative readings of Aristotle’s own thinking. Alongside these examples of internal development, the concept of the natural infinite – the presence of infinity in nature – becomes a source of tension between the new philosophy and Aristotelianism at the beginning of the modern era, even when a general framework or vocabulary of Aristotelian descent is maintained. Such a multifaceted subject could not be exhausted in a few pages, so we will only discuss two emblematic examples: a 16th-century literary celebrity and a 17th-century mathematician and philosopher.
Despite being as different as possible, they are both signs of an interesting dependence on Aristotelian concepts and terminology, even while moving away from and fundamentally distorting the framework they were cast in.