Norton’s sense, and so cannot be used directly to create an idealization. Norton argues that qualitatively similar behavior is common in the physical sciences--that perfectly respectable approximations of a given system frequently fail to neatly correspond to perfectly respectable idealizations of the same system.
Of course, we might wonder what it even means in those cases to say that a given system is an idealization of another system. If idealization involves the genesis of a novel system that can differ not just in parameterization values but in dynamical form the original target system, then how do idealizations represent at all? The transition from an approximation to its target system is clear, as such a transition merely involves reparameterization; the connection between target system and idealization is far more tenuous (if it is even coherent). Given this, it seems that we should prefer (when possible) to work with approximations rather than idealizations. Norton shares this sentiment, arguing that since true idealizations can incorporate “infinite systems” of the type we explored above and “[s]ince an infinite system can carry unexpected and even contradictory properties, [idealization] carries considerably more risk [than approximation]. [...] If idealizations are present, a dominance argument favors their replacement by approximations.”[1]
6.3.3 Idealization and Pragmatism
It’s interesting to note that the examples in Norton (2012) are almost uniformly drawn from physics and statistical mechanics. These cases provide relatively easy backdrops against which to frame the discussion, but it’s not immediately apparent how to apply these lessons to the
- ↑ Norton (2012), p. 227
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