Posted by: Alexandre Borovik | December 22, 2008

Bishop Berkeley’s unanswered Query

The Analyst by Bishop George Berkeley, the famous pamphlet against vagueness of early Analysis, ends with a list of 67 Queries. Quite a number of them, in my humble opinion, remain unanswered, this one in particular:

Qu. 38. Whether tedious Calculations in Algebra and Fluxions be the likeliest Method to improve the Mind? And whether Mens being accustomed to reason altogether about Mathematical Signs and Figures, doth not make them at a loss how to reason without them?

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Responses

  1. To answer the first part of this question with, I would remark that there is usually some meaning behind these calculations that drives and motivates them. It’s like a pianist doesn’t just press the keys, but does so to make music. As for the second part, I’m not sure, there might be some truth to that observation.

  2. we were *already* at a loss how to reason
    without ‘em; introducing the symbols
    hasn’t done any actual *harm* …

    but i exaggerate. the trouble arises,
    in my opinion, because practice in maths
    leads to the idea that every statement
    should have a well-defined *meaning*.
    this is very seldom the case outside
    of mathematics and makes us
    hard to “reason” with because we keep
    expecting people to care about things
    like logical consequences.

    like i tell my students:
    a lot of people think math is hard–
    and it *is* hard — it’s just easier
    than anything else.


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