The Critical Rationalist Vol. 03 No. 01 ISSN: 1393-3809 [DRAFT: 11-Feb-1998]
(26) It may be concluded that when Popper's original assumption holds, so that there exists an infinite set of statements that pairwise are contradictory and individually do not entail t, then t includes amongst its consequences an infinite independent set. A simple and revealing example is provided by Kepler's three laws, augmented by a finite set of initial conditions sufficiently copious for the prediction of the positions of the planets at all future times. It is plain that within the content of this theory we can find an infinite set of statements that, taken in isolation, are logically independent of each other; statements of the positions of Venus at different times suffice for this, since it is only in the presence of universal laws that there is any logical connection between the position of Venus at one time and its position at any other time. But we should not be eager to conclude that there is any important sense in which Kepler's laws say infinitely many distinct things. On the contrary, one of the virtues of logical systematization and axiomatization is that it enables us to replace scattered sets of results by unifying principles. There is something suspiciously retrograde about the claim that Kepler's laws have an infinity of things to say (just as there is something retrograde about the claim that a theory may be replaced by its Ramsey sentence). We must note in any case that to obtain the full force of Kepler's laws (plus initial conditions) we should need to add to the infinite set of predictions concerning Venus (or any other infinite independent subset of the content of Kepler's laws) some statement (or finite set of statements) that renders all but finitely many of those predictions redundant.
The Critical Rationalist Vol. 03 No. 01 ISSN: 1393-3809 [DRAFT: 11-Feb-1998]
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TCR Issue Timestamp: Fri Mar 27 14:21:33 GMT 1998