Strict Finitism and Transhumanism

Peter Rothman, Humanity+, Dec 19, 2014
Commentary by Stephen Downes

I have a very unhappy relationship with the concept of infinity. I maintain that I can't comprehend infinity, and infinity insists on inserting itself into my cognition. This impacts what I think about pretty much everything (including, even, what I mean when I say 'everything'). For me, the pragmatic question is that, if infinity is in any sense 'real', then it may be impossible to 'grow' or 'develop' cognitive processes that rely on it. This has a direct impact on what I can (or want to) say about learning and cognition - for example, a network process that does not have 'infinity' somehow built in will be incapable of performing 'real' mathematics or other cognitive functions. My own thought is that the concept of infinity is a convenient fiction - there are no 'real' infinities, and a system of reasoning (such as mathematics) that produces one is to that extent also a convenient fiction. To get a sense of the sort of debate I have in mind here, read this article.

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