According to Plato ideas hold the key to understanding the world of the senses: meaning and truth can be found in the existence of individual things only to the extent that the latter partake in the ideas.14 In a similar vein Cantor envisaged his theory of sets to furnish an "organic explanation of nature" that is superior to a "mechanical" one.15 This peculiar trait in Cantor's mathematical realism finds its clearest expression in his distinction of the intrasubjective (or immanent) and transsubjective (or transient) reality of ideal entities. Zeller argued that the identification - presumably an attempt to explain how the ideas bring about the existence of physical objects - amounts to a blatant misunderstanding of Plato.84 This also seems to have been Cantor's view since he cites with approval the corresponding section in Zeller while expressing a preference for Plato's philosophy of the infinite over Aristotle's.85 Certainly one factor for this preference was Aristotle's denial of the actual existence of quantitative infinity. [...] for Cantor, who regarded (infinite) sets as "finished things," a reading of Plato that "transfers the apeiron, understood in the same sense in which it marks the peculiar trait of existence in the sensory world, to the ideas"86 would clearly be unacceptable.
展开▼
