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Problems in the Philosophy of Mathematics: A View from Cognitive Science (PDF Download Link)
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Author: u/xamueljones My arch-enemy is entropy*
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URL: http://colala.bcs.rochester.edu/papers/piantadosi2015problems.pdf
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Score: 12
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Created: 2015-07-21T17:10:30
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Comments:
u/xamueljones [+3] My arch-enemy is entropy (a minute later)
I wanted to post this because I feel like it really hits on the biggest problem(s) I sometimes have when examining my own thinking processes.
u/None [+2] (10 hours later)
One of the really weird things here, which I don't see covered in the paper up to where I am, is that on the one hand, cognition is inherently probabilistic, but on the other hand, admitting a probabilistic foundation for mathematics does funny things, like refuting the Continuum Hypothesis by ordering between naturals < measurable reals < reals.
u/None [+4] (a day later)
Great resource! Reminds me a lot of these two sequences:
http://wiki.lesswrong.com/wiki/A_Human%27s_Guide_to_Words http://wiki.lesswrong.com/wiki/Mysterious_Answers_to_Mysterious_Questions
This type of thing has always bothered me about philosophy, and maybe I just haven't been exposed to the right philosophers, but many of the questions that are asked don't seem to fundamentally mean anything. Whether one answers 'do numbers really exist?' in the affirmative or in the negative, I don't expect the answer to tell me anything new about the nature of reality.
u/None [+2] (2 days later)
Well, philosophers tend to think in terms of words, sentences, and some mathematical logic rather than maps, territories, and statistics. If they tried the latter, they could get a lot better. I'll pass you an example link later.
u/None [+2] (2 days later)
Here. Sometimes you get a philosopher who can think with the right notions and metaphors.
u/None [+1] (10 hours later)
Instead, categorization and conceptualization may work based on the similarity to stored examples, as in prototype theory (using a single stored example) or exemplar theory (using many) (for an overview see [24]).
lrn2probability, people.