I am reading Popper's "Conjectures and Refutations" (2002 edition) where he writes on page 54 in the footnote:
Thus the negation of any nonsense will be nonsense, and that of a meaningful statement will be meaningful. But the negation of a testable (or falsifiable) statement need not to be testable, as was pointed out, first in my "Logic of scientific dicovery" (e.g. pp. 38 f.) and later by my critics.
I understand the first part, but I have no clue about the seocnd part (the "testable"). I cannot imagine any example and unfortunately, I have no access to the book. I found something in the www, but I could not find any reference therin which explains the second statement.
Appendix thanks to many useful answers & comments:
Short version: I stop bothering about this statement as I think it is too vague and thus meaningless (I think). But I learnt a lot from the answers. :-)
- Although I already highlighted "Words are significant only as instruments for the formulation of theories, and verbal problems are tiresome: they should be avoided at all cost." (again from Popper, p. 37/38) you again showed how important this statement is. This said:
- The statement appears in the context of his "criterion of demarcation" and here with respect to Wittgenstein’s "verifiability criterion of meaning". Thus, I cannot exclude that the statement was meant in the sense of @Agent Smith proposed.
- Concerning verbal problems: it should be made clear whether "testable in theory / principle" is meant or "testable in practice". All statements which "hold for all time" are impossible to prove. Depending on the statement S or its negation NS, we cumulate evidence for S or for NS. But this was not my point for the question – I thought it was some "deep fact" which I did not see.
- As discussed here: "... the scientific method for testing the statement 'Not all swans are white' is to examine the genetic structure of swans, determine what parts render them white and see if mutation can be evoked that would render them non-white. If such a mutation would not be survivable, all swans are white. A statement is unfalsifiable if you cannot identify a procedure that would disprove it. And this could. So this statement is falsifiable just like its opposite...". Again, this was not the example I looked for. I know that testing can be tricky.