ABSTRACT
The topic of this chapter, the introduction into falsificationism of some kind of paraconsistent logic, may suggest that I have lost my grip on philosophical reality. This suggestion will be reinforced when it becomes clear that the paraconsistent logic that I have in mind, and am going to recommend as a suitable mate for falsificationism, is the Brouwerian system that was dismissed by Popper in ‘What Is Dialectic?’ as ‘an extremely weak system … of no use for drawing inferences although it may perhaps have some appeal for those who are specially interested in the construction of formal systems as such’ (Popper 1963a/1989, p. 321). The suggestion of unbalancedness may be 250redoubled if we go on to recall the following recommendation of Popper’s (1972, p. 305):
If we want to use logic in a critical context, then we should use a very strong logic, the strongest logic, so to speak, which is at our disposal; for we want our criticism to be severe. In order that the criticism should be severe we must use the full apparatus; we must use all the guns we have. Every shot is important. It doesn’t matter if we are over-critical: if we are, we shall be answered by counter-criticism.
Thus we should (in the empirical sciences) use the full or classical or two-valued logic. If we do not use it but retreat into the use of some weaker logic … then, I assert, we are not being critical enough …
