By Edmund T. Whittaker

In 1910 I released a piece less than the identify A historical past of the Theories of Aether and electrical energy, from the age of Descartes to the shut of the 19th century. while the unique version used to be exhausted, I felt that any new factor may still describe the origins of relativity and quantum-theory, and their improvement due to the fact that 1900. My possibilities have been notwithstanding no longer adequate to let me to organize a correct and fully-documented account of this very artistic interval, and that i used to be forced to put the plan apart. Retirement from my professorial chair has made it attainable for me to take in this venture back ; it's going to occupy volumes, of which this, the 1st, offers with the classical theories. the quantity of 1910 has been to a substantial quantity rewritten, with the incorporation of a lot extra fabric ; and within the moment quantity, the tale could be persevered to the current time.

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W hile these excep­ tions can be taken care of by a more precise wording of the law, stating the conditions of its validity and the meanings of its terms more carefully, there usually re­ mains a doubt whether the new formulation is free from exception, whether we can be sure that later discoveries w ill not reveal some limitation of the improved formula­ tion. T h e development of science, with its repeated elimination of older theories and their replacement by new ones, supplies good reasons for such doubt.

Sense observa­ tion cannot tell us infallible truth, but vision can. W e see through “ the eye of the m ind” that through a given point only one parallel line can be drawn with respect to a given line. Because this theorem appears to us as an infallible truth, it cannot be derived from empirical ob­ servations; it is dictated to us by an act of vision which we can perform even while the eyes of our bodies are closed. In this form we can express Plato’s conception of geometrical knowledge. Whatever one may think of it, one must admit that it reveals a deep insight into the logical problems of geometry.

It has not dis­ couraged us, though. T h e new physics has shown that we can have knowledge outside the frame of the Kantian principles, that the human mind is not a rigid system of categories into which it packs all experiences, but that the principles of knowledge change with its content and can be adapted to a much more complicated world than that of Newtonian mechanics. W e hope that in any fu­ ture situation our minds w ill be flexible enough to sup­ ply methods of logical organization that can cope with the given observational material.

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