What is heat? : a peep into nature's most hidden secrets / by Frederick Hovenden.

  • Hovenden, Frederick.
Date:
1894
Catalogue details

Licence: Public Domain Mark

Credit: What is heat? : a peep into nature's most hidden secrets / by Frederick Hovenden. Source: Wellcome Collection.

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    4. The achievements of the physicist—the mathema- tician—have been very great; no doubt the community owes to him very much. Emboldened by his successes, he, however, often assumes an infallible position—he regards his mode of reasoning as perfect, and his notions beyond all question. We, however, are not disposed to put our full faith in the metaphysician's or mathematician's concepts. If his ideas were real, the physicist should be able to solve the problems under consideration, but he cannot. It is possible that the solutions are as far beyond the knowable as are the dimensions of space, or the beginning and end of eternity. We, however, do not think these problems are beyond solution. They cannot, we believe, be solved by mathe- matics, but only by means of experiment. 5. The task we have set ourselves is a difficult one. And to clear the way, for the reasons given in § 27 and § 40, it is absolutely necessary we should begin by obtaining clear definite fundamental ideas. In order to get these we must question mathematical notions. This we proceed to do. 6. The foundation of mathematics is arithmetic. Arithmetic is the science of numbers. What is a num- ber?* Let us start with the numeral 1. What is The terms 'abstract and concrete numbers' are also fallacious and misleading. Numbers, in themselves, are essen- tially abstract. In another sense they are essentially concrete; they always stand for some particular object, relation, or opera-
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