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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.
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.
Einführung in das mathematische Denken Darmstadt 1996
Logik, Sprache, Philosophie Stuttgart 1976