|But isn't Science carried out in public, by definition?|
Which definition is that? On the whole the public doesn't understand science.
What about peer review?
As far as I can see, all of the requirements for good science can be satisfied in private. Publication is a vehicle for peer review, but surely not the only one. Is being paid by private enterprise is itself grounds to disqualify a reviewer?
...I think the dangers pointed out by Jordi are real, and vastly underestimated.
Nowhere did he object to scientific progress being kept secret, as such. (He complained that the free tools are not as good as Mathematica, and tried to recruit people to work on them.) But is this secrecy something that Jordi should have objected to?
There's perhaps an analogy with formal proofs of software correctness. Ultimately, the software which validates the software (which validates the software and so on) has to be eyeballed for correctness. Does it matter if the analysis by visual inspection is kept private?
If you aren't capable of writing the unit test to reveal the flaw, why would you care about the potential flaw in the proover? Does it matter what opaque source of inspiration may have motivated those scientific hypotheses considered valid, if you can't find evidence to dispute them? Not that I can see.
You may ask what motivated the disproved scientific hypothesis, if you suspect malice. By analogy, pre-emptively demanding source code would seem to indicate bad faith.
P.S. I have yet another objection to this rant. The TeXmacs manual was quoted, I am deeply convinced that only free programs are acceptable from a scientific point of view (Jordi, befittingly of an evangelist, says this "speaks for itself".)
And yet, he goes on to say, there is no reason why we can't expect as much quality and functionality from free software as we see in proprietary software, implying that free software leaves something to be desired, and of course, it does.
Hence, one might claim that open source programs are unacceptable from a scientific point of view, using similar arguments. For example, checking mathematical proofs requires dependable software.