Refutation of the \"Language-Only\" Interpretation of Math (The limitations of science)

by George Jelliss , Crewe, Wednesday, February 17, 2010, 17:39 (5391 days ago) @ xeno6696

Perhaps I should open my own discussion forum on finitism, since I don't want to monopolise too much of dhw's space on this only loosely related topic.-It seems from your links to various wikipedia pages that there are getting on for an infinity of varieties of philosophy on this subject! My own views are not represented there. I don't deny basic logic.-Your statement that algorithms for calculating pi always produce the same result is incorrect, it depends where you stop the calculation. You have to stop it at some stage. Any summation of an infinite series up to a certain value, for example Taylor's or Maclaurin's series, ends with an error term.-In the same way calculating successive ratios of numbers in the Fibonacci sequence doesn't give you the exact golden ratio no matter how far you go.-It may be useful to recognise different categories of "existence" for numbers. Thus numbers you actually write down, say 12345, exist within the current context. Numbers such as pi, e, root-2, i, can be said to exist symbolically since we have a symbol for them, though they cannot be written down in the same complete way as 12345 can.-This idea of different forms or degrees of existence may have wider applications to the agnosticism debate. For instance, in what sense do fictional beings like Sherlock Holmes or Pagasus exist? Do legendary figures like Robin Hood, King Arthur or Jesus have a greater claim to existence? Can gods be said to have subjective existence, though not founded on objective evidence? Just a passing thought.

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GPJ