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Re: Vindication of Goldbach's conjecture
Posted:
Jun 19, 2012 10:37 AM
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On Jun 18, 4:53 pm, quasi <qu...@null.set> wrote:
>
> It looks to me like Luttgens is using the phrase
>
> "mutatis mutandi"
>
> as a form of reasoning.
He is using it,like everyone else who uses it, as a phrase
that introduces the next claim in his argument, akin to
"clearly" or "similarly", nothing more.
If I describe a new algorithm I invent, not in general terms,
but with, say, n fixed at 3, and then say "there is nothing
special about n = 3 here, the algorithm applies, mutatis
mutandis, to any positive integer", the only things that are
required for my description to be acceptable are that the
reader knows exactly what changes are necessary to adjust
the algorithm to the general case and that the resulting
algorithm remains correct. The phrase occurs in proofs and
examples in contexts similar to the hypothetical one I
sketched out here. British scholars of an earlier generation
were especially fond of it.
> Hence my response that (whatever it is) it's certainly not
> a valid principle of mathematical reasoning.
Since it is not even a complete sentence, it is obvious that
it cannot be a principle or an axiom or a theorem. And the
value of your response in helping the writer see what is
missing in his argument is nil.
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