The Critical Rationalist                       Vol. 03  No. 01
ISSN: 1393-3809                                    [DRAFT: 11-Feb-1998]


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2.12 Sceptical Summary

(30) I have been trying without success to find something defensible in the view that the infinitude of a theory's content has more than psychological significance; that there is an objective sense in which it is true that an axiomatizable theory must say more than we can ever appreciate. In his discussion of the syllogism Mill (1843, Book II, Chapter III, section II) rightly dismisses any attempt `to attach any serious scientific value to such a mere salvo as the distinction drawn between being involved by implication in the premises, and being directly asserted in them'. In other words, an axiomatizable theory t does directly (if not transparently) assert in finitely many words everything that its infinitely many consequences take infinitely many words to assert. Mill expresses puzzlement that `a science, like geometry, can be all ``wrapt up'' in a few definitions and axioms' (loc. cit.). But we should not allow ourselves to be taken in here. Although virtually all theories `wrap up' infinitely many thoughts in the sense that we can find infinitely many thoughts within them, it is a capital mistake to suppose that a theory's content is synthesized from logically more primitive (weaker) components. As we have seen, in many cases there are no weakest components. (Aristotle's treatment of Zeno's paradox of Achilles and the tortoise invites comparison.) I am not of course defending the view that the understanding of a rich scientific theory is a straightforward business, and that some acquaintance with the theory's consequences is not essential to its understanding. As I have already noted, I incline to the view that understanding a theory fundamentally means understanding the problem situation it addresses, and how well it addresses it. It is possible to go further and to recognise that understanding may be enhanced when it is realized that the theory solves, or is unable to solve, some unexpected, some newly emerged problem. I am quite happy to admit that newly identified consequences may lead to a sharp improvement in the understanding of a theory. My purpose here is only to question the doctrine that much can be explained by the infinitude of a theory's content alone. It is such a flimsy matter that we could hardly expect it to yield substantial returns.



next 3 The Application of Scientific Theories
previous 2.11 A More Model-theoretic Approach
contents

The Critical Rationalist                       Vol. 03  No. 01
ISSN: 1393-3809                                    [DRAFT: 11-Feb-1998]


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TCR Issue Timestamp: Fri Mar 27 14:21:33 GMT 1998

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