I agree with almost all of what you say, but I prefer to think of ‘reality itself’ as ‘infinite’ – at least in a sense of ‘beyond our immediate grasp’ – while the results of measurements ‘of’ this reality as ‘finite’ (in a certain sense, anyway). So I like to think of an explicit measurement process from reality to numbers.

This leads to almost exactly the same positions on a number of topics as your view (I think), but perhaps some subtle differences.

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]]>You might be interested in J.L. Bell’s book ‘The Continuous and the Infinitesimal in Mathematics and Philosophy’ which discussing these issues in depth. You can even download a copy from his website http://publish.uwo.ca/~jbell/The%20Continuous.pdf

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Best,

Jun

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