What is Scientific Progress?

For some such sequence of approximation operators, will be a sequence of true propositions whose later
members do add to the truths entailed by the earlier members. Since researchers can see that the
later values are within the bounds of earlier ones, they can have reason to believe that the later
approximations are better than the earlier ones (in addition to whatever reason they may have for
thinking that their techniques are more accurate). Hence they are likely to have beliefs where the
later ones involve attributions of better approximation (even if the belief is merely of the form
‘(c=Val(c+ε2)) is a better approximation than (c=Val(c+ε0))’). Given the assumption of appropriate
confirmation, the relevant sequence of beliefs will also represent the accumulation of knowledge.
Although though there is still a margin for error, we know the value of the velocity of light with
greater accuracy than previously.
To be clear, I have not argued that where there is increasing verisimilitude there is also the
accumulation of knowledge. Obviously there might not be, as would be the case if the increasing
verisimilitude were accidental. What I have argued in this section is defensive—it argued against
the claim in (O) that we need the verisimilitude account rather than the cumulative truth or
cumulative knowledge accounts, because only the verisimilitude account can cope with progress in
a sequence of theories none of which is fully true (such as Ptolemy-Copernicus-Kepler). That claim
is mistaken; we saw that where there is increasing verisimilitude there is also the accumulation of
truth and so at least the possibility of the accumulation of knowledge.
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