Count Dracula wrote: >quasi 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.
In the context used, I interpreted the Luttgens' use of the phrase "mutatis mutandis" as intending to mean "By similar reasoning, the result is true for all even n > 4"
To clarify my objection, what I was trying to get across was that the "mutatis mutandis" part was indefensible, given what he has done up to that point. It's not that the phrase "mutatis mutandis" can never be used, but rather, that his successful resolving of the particular case n = 26 does automatically allow an extension to all even n > 4.
Thus, as I see it, Luttgens' first error was his claim that the rest follows by the same reasoning (by mutatis mutandis).
But I get your point.
If a proof has the phrase "and similarly for the rest", and if that phrase is not justified by the prior part of the proof, then the correct objection is not that "and similarly" is not a valid principle of mathematical reasoning, but rather that it's not valid reasoning in the context of the given proof.
>And the value of your response in helping the writer see >what is missing in his argument is nil.
Well, obviously Luttgens thinks "mutatis mutandis" is justified. I was trying to get him to look more closely at his use of that phrase. Perhaps I could have worded it better.
In any case, if you feel that the value of my response was nil, why don't you take a cut at providing a more helpful response?