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Friedrich Waismann on Laws - Dictionary of Arguments

I 91
E.g. the sequence of the prime numbers is a sequence without a formula, but not without a law! The law is, of course, to be expressed only by language, no formula is known. Nevertheless, there is a clear rule for the formation of the sequence!

Additional difficulty: if we demand a law for the formation of consequences, this would be a strict demand, but only if we had a strict concept of the law!
E.g. we can define a sequence for x n + y n = z n: t n should be 1, if three integers can be found, it is insoluble for integers, if t n = 0. The sequence would then begin like this:


and no one can say to-day whether the two first ones are followed by zeros or not.
I 92
Is this provision a law now? Or does it make a law when Fermat's assumption is proved?

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Waismann I
F. Waismann
Einführung in das mathematische Denken Darmstadt 1996

Waismann II
F. Waismann
Logik, Sprache, Philosophie Stuttgart 1976

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