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XVII.—Axiomatic Treatment of Kinematical Relativity
Published online by Cambridge University Press: 14 February 2012
Extract
The suggestion has recently been put forward that the laws of nature can be established by purely deductive reasoning instead of by induction from observation. We may, with Eddington, start the chain of reasoning from epistemological premises or, with E. A. Milne, from axiomatic statements regarding the nature of the system to be studied. Different opinions may be held regarding the value of a deductive method, but a final judgment can hardly be passed on a deductive theory until the initial premises are clearly revealed. We may, indeed, justly require of the author of such a theory that he fulfil the following conditions. He should, firstly, be himself aware of all the axioms which he employs. If he is not, there is the obvious danger that he may use inductions from observation without being aware of doing so. But he may also arrive at quite erroneous conclusions about the range of validity of his results. For instance, a deductive theory may produce a formula which is interpreted as the inverse square law of gravitation. It is then very necessary to know whether the initial premises are axioms concerning the nature of the universe as a whole or whether they merely define local conditions. In the first case the law of gravitation is deduced from the nature of the universe as a whole, in the second it is shown to be merely a “local” law.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 61 , Issue 3 , 1943 , pp. 210 - 222
- Copyright
- Copyright © Royal Society of Edinburgh 1943
References
page 212 note * Milne, E. A. and Whitrow, G. J., Zeits. Astrophys., vol. xv, 1938, p. 263, § 22.Google Scholar
page 215 note * E.g. Whitrow, G. J., Proc. L.M.S., ser. 2, vol. xli, 1936, p. 418.CrossRefGoogle Scholar
page 216 note * Milne, E. A., Quart. Journ. Math., vol. viii, March 1937, p. 22, § 8.CrossRefGoogle Scholar
page 217 note * E.g. Milne, E. A. and Whitrow, G. J., Zeits. Astrophys., vol. xv, 1938, p. 263.Google Scholar
† Namely, A11 himself, one observer of type Aμ1 and a third of type Aμλ (λ ≠ 1). We may again remind the reader that axioms I to VIII all occur in Milne's development of the theory.
page 217 note * Milne, E. A. and Whitrow, G. J., Zeits. Astrophys., vol. xv, 1938, p. 263.Google Scholar
† Milne, E. A and Whitrow, G. J., loc. cit., §§ 14, 15.Google Scholar These authors use a double-suffix notation for signal-functions in which θpq stands for our θμ and θqp stands for its inverse function θμ-1.
page 221 note * See, e.g., McCrea, W. H., Zeits. Astrofihys., vol. ix, 1935, p. 290, § 13, equ. (45).Google Scholar