Professor Franklin is correct to say that there are significant areas of agreement between his account of formal science (Franklin, 1994) and my critique of his account. We both agree that the domain-independence exhibited by the formal sciences is ontologically and epistemically interesting, and that the concept of ‘structure’ must be central in any analysis of domain-independence. We also agree that knowledge of the structural, relational properties of physical systems should count as empirical knowledge, and that it makes sense to (...) talk about an empirical ‘science’ of structure. Where we disagree is over the frequency of occasions where ‘practical certainty’ is actually attained: Franklin argues that practical certainty is not uncommon in the formal sciences, while I argue that there are barriers to practical certainty that Franklin fails to appreciate. In Franklin’s response, he briefly presents and offers criticisms of my two main arguments against his central thesis. Franklin asserts that the flaw in my first argument is that it does not appreciate that modern mathematical models exhibit structural stability, and thus that many of their predictions are robust under small variations in input or parameter values (and hence, insensitive to the inevitable gaps between estimates and actual values). Nevertheless, what I had in mind in using the term ‘realistic modelling situations’ were models of fairly complex natural systems, such as the dripping faucet, spruce budworm and ecosystem ecology examples. My objection is not that mathematical models of such systems cannot legitimately and accurately describe structural properties that are genuinely predicable of real-world systems, but simply that for.. (shrink)

Replies to Kevin de Laplante’s ‘Certainty and Domain-Independence in the Sciences of Complexity’ (de Laplante, 1999), defending the thesis of J. Franklin, ‘The formal sciences discover the philosophers’ stone’, Studies in History and Philosophy of Science, 25 (1994), 513-33, that the sciences of complexity can combine certain knowledge with direct applicability to reality.