PART V |
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ON THE NON-ARISTOTELIAN LANGUAGE CALLED MATHEMATICS |
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Once a statement is cast into mathematical form it may be manipulated in accordance with these rules and every configuration of the symbols will represent facts in harmony with and dependent on those contained in the original statement. Now this comes very close to what we conceive the action of the brain structures to be in performing intellectual acts with the symbols of ordinary language. In a sense, therefore, the mathematician has been able to perfect a device through which a part of the labor of logical thought is carried on outside the central nervous system with only that supervision which is requisite to manipulate the symbols in accordance with the rules. (583) horatio b. Williams
The toughminded suggest that the theory of the infinite elaborated by the great mathematicians of the Nineteenth and Twentieth Centuries, without which mathematical analysis as it is actually used today is impossible, has been committing suicide in an unnecessarily prolonged and complicated manner for the past half century. (22) e. t. bell
The solution goes on famously; but just as we have got rid of the other unknowns, behold!
V disappears as well, and we are left with the indisputable but irritating conclusion -0 = 0 This is a favourite device that mathematical equations resort to, when we propound stupid questions. (USD a. s. kddington
Who shall criticize the builders? Certainly not those who have stood idly by without lifting a stone. (23) E. t. bell
... let me remind any non-mathematicians . . . that when a mathematician lays down the elaborate tools by which he achieves precision in his own domain, he is unprepared and awkward in handling the ordinary tools of language. This is why mathematicians always disappoint the expectation that they will be precise and reasonable and clear-cut in their statements about everyday affairs, and why they are, in fact, more fallible than ordinary mortals. (529) Oswald veblen |
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