ABSTRACT
The apparatus of PIM may be used to describe AIM’s other strategies as well. The passage from Musgrave that was quoted above (ibid.: 378) suggests that we have to distinguish between two types of negligibility strategies. One, which for the moment I will call a type-one negligibility strategy, refers to a case in which the factor that is neglected does affect the prediction, but the effect is not detectable. This negligibility strategy may be shown as the transition from (1) to (1′):
(x)(p1(x) > 0&p2(x) > 0& · · ·&pn(x) = 0⇒ F(x) = 0), (1) (x)(p1(x) > 0&p2(x) = 0& · · ·&pn(x) = 0⇒ F ′(x) = 0), (1′)
where F ′ is an approximation of F .5 The other type of negligibility strategy which is suggested by the quotation is
the case where neglecting the influence of a particular factor does not lead to a different prediction. This might be called a type-two negligibility assumption, and it might be thought that this can be described in terms of PIM as the transition from (1) to
(x)(p1(x) > 0&p2(x) = 0& · · ·&pn(x) = 0⇒ F(x) = 0). (2)
Despite the assumption that p2(x) = 0 (the factor whose influence is indicated by the characteristic parameter p2 is ruled out), the consequent F(x) = 0 is claimed to remain unaffected. However, this would be a mistake. A so-called type-two negligibility assumption is no idealization at all. If a factor does not
make a difference to the prediction of a model, its characteristic parameter (p2) does not figure in the model at all. If we wanted to describe this situation in terms of PIM at all, it would look like
(x)(p1(x) > 0&p3(x) = 0& · · ·&pn(x) = 0⇒ F(x) = 0). (2′)
Krajewski’s examples from physics illustrate that a negligibility assumption often is not introduced by scientists with some express purpose, but that it is discovered that a particular theory or model implicitly makes one. That is why in PIM this move is described as the revealing of idealizing conditions. The syntactical analysis of PIM is incapable of capturing the distinction between
a negligibility strategy and a domain strategy; both are described by the transition from (3) to (4).
