Page 12

		that our inquiry will ultimately succeed (if the right guessing rule is applied). But we cannot be certain at any given stage of our inquiry that success has finally arrived.

		This asymmetry is a fundamental characteristic of empirical inquiry. In the usual case, scientists can never feel completely confident that their current theory will remain uncontradicted by tomorrow's data. They can only hope that the mental system by which they select hypotheses is adapted to the reality they face. Distinguishing these two issues allows us to focus on scientific success itself, rather than on the secondary question of warranted belief that success has been obtained. Thus, our question will typically be:

		What kind of scientist reliably succeeds on a given class of problems?

		rather than:

		What kind of scientist "knows" when she is successful on a given class of problems?

		Clarity about this distinction was one of the central insights that led to the mathematical study of empirical discovery (see Gold [80, pp. 465-6]).

		§1.4.5 Criteria of Success

		Compare guessing rule 1.2 to the following, revised version.

		1.5 Guessing rule: Suppose that S is the set of numbers that have been presented so far. Let m be the least positive integer that is not a member of S. If 2m is not a member of S, make no conjecture. Otherwise, emit the conjecture "all positive integers except for m" unless this was your last conjecture (in which case make no conjecture at all).

		Thus, 1.5 is just like 1.2 except that it imposes a possible delay in producing the conjecture "all positive integers except for m." Although the delay is pointless, it is easy to see that systematic use of 1.5, as with use of 1.2, guarantees success in the first paradigm introduced above.

		Rule 1.5 highlights the liberal attitude embodied in our current definition of scientific success. We require that the scientist produce a final conjecture that is correct, but there is no requirement that this final conjecture come as quickly as possible. Let us admit, however, that scientists who examine extravagant amounts of data before making a final, correct conjecture might be considered as useless as scientists who never guess correctly