[szhorvat]

Note that I'm not saying that one can claim that a result is correct, a theorem is true, etc. based on the fact that some undocumented algorithm produced it. That's clearly unacceptable.

Nor am I saying that it's never necessary to rely on an algorithm to get such a result.

What I'm saying that when people use Mathematica or other closed source systems, they do not usually commit these mistakes.

Also note that Mathematica programs can be open source and documented (many are). Several built-in packages have accessible and documented source code (e.g. Combinatorica). There's nothing wrong with using these to obtain such a result, and cite the (public and documented) program used to create it.

[omaranto]

I think we're in complete agreement: most of the time you don't need a citation for a program you use because the result can be easily verfied. And I agree that what you call a fallacy is a fallacy, I was just pointing out that open source can be citable in a way that closed source isn't and that that is an advantage.