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Mathematics and creativity



   

If existence consciousness  then questions about the existence of infinite set  s are questions about the possible structure of consciousness  . Consciousness is both individual and collective. I see that dot at the end the sentence the paragraph and the monitor that display them all. I am conscious of all this as individual elements and as elements in relation to the whole. A finite structure could be conscious in this sense but not an infinite one. Things can be added to infinite structures without changing them. There is not the same particularness of their elements that exists with finite structures. This suggests that there are no infinite structures 

although the totality of all finite structures may be infinite. I have equated the existence of a structure with the direct experience 

of that structure. Direct experience is always particular and individual but infinite structures cannot be particular and individual. That is what I mean when I say there are no infinite structures but only infinite collections. The universe may be potentially infinite but all structures and all experience is finite.

In mathematics a class  is used to define the universe of all sets  . That universe cannot be a set or we fall into a Russell paradox  such as the barber   who shaves everyone who does not shave himself. If one equates existence with consciousness as we have then the distinction between class and set  must occur at the boundary between the finite and infinite  . No infinite structures or sets exist there is only the unstructured infinite collections of all finite structures.






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