Abstract
In the rest of this book I modify the notion of explanatory translation in order to define a general correspondence relation, and I apply the results to some actual cases of scientific change. I shall not consider such Kuhnian questions as how scientific changes have taken place historically, how communication breakdowns have been handled and scientists persuaded by means of translation or learning, or how scientists have experienced the changes. Much of what I shall do is, however, relevant to the second question. There is nothing in principle that would prevent us from saying that translations of local utterances and literary texts are correspondence relations, but for historical reasons I reserve this term for certain relations between scientific theories — theories of the human sciences and aesthetics included.
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Notes
It is immediately seen what these notions mean in the global case on the basis of their earlier characterization for the local case.
This is tentatively sugested in my (1989), however. It extends earlier work by David Pearce and me; see, e.g., Pearce and Rantala (1983c), (1984a); and Pearce (1987).
‘Possible world’ is here used as a general term that, depending on the kind of theory, may mean such things as systems, structures, situations, courses of events, or models. Thus physical theories are often regarded as speaking of systems, mathematical ones of structures, historical ones of situations and courses of events, and formalized ones of models in the model-theoretic sense of the word.
In the contexts of reduction and explanation, the terms ‘primary theory’ and ‘secondary theory’ are sometimes used in the literature, as, e.g., in Nagel (1961) and Glymour (1970).
See Section 5.5, below. As noted earlier, there is no reason why the minimizing transformation should occur explicitly in the logical condition (4.1.1) of correspondence.
It is of some interest to notice at this juncture that if Kuhn is correct when he says, in his (1977) and elsewhere, that the laws of a theory are not independent, since theories are integrated wholes, then this and the forthcoming definitions of correspondence may not be entirely adequate, since they at least involve a tacit assumption to the effect that a translation operates on independent sentences. This suggests that a global translation of the laws and other sentences of a theory would have features of a translation of an integrated text. What this idea would ultimately mean in practice is not very clear at the moment.
It can be seen that the refinement principle is valid here, at least formally. We shall see later that the minimization principle is in force in the most important specific applications of correspondence.
In this book, I shall not present any such case studies of historical theories, or other theories in the human or social sciences.
See, e.g., Enderton (1972); Barwise (1975).
These questions will be studied in Section 5.9.
For this assumption, see Chapter 8.
If it is required that F itself is definable, it is sufficient for certain purposes that it is definable in the (weaker) sense of being a projective class. If F itself is definable (in some sense) in a logic, it is an algebraic operation rather than a func - tion in the proper sense; see Feferman (1974b); Gaifman (1974).
Balzer, Moulines and Sneed (1987) also consider it too weak to represent a translation proper, since it does not preserve meaning.
See Rantala (1988). In Section 6.9, below, the import of the notion is briefly studied.
See (3.1.3).
Recall Sections 1.1 and 1.4, above.
See the respective quotation in Section 1.4.
I shall here recapitulate the theory that can be found in earlier writings by Pearce and Rantala. The notions of nonstandard analysis that are needed are discussed and formally defined in Section 8.6.
The notion of standard approximation of a model, employed below, varies a little bit according to the form of a model.
See Pearce and Rantala (1983ab), (1984a).
If T is axiomatized in some logic, H is the class of all models in which the axioms are true (in this logic). In this sense, H can be thought of as representing the axioms of T.
Most often actual transformations are monomorphisms or other mappings between domains of models.
See Pearce and Rantala (1983b), (1984a).
See Section 8.5.
In Pearce and Rantala (1984a), the notion of symmetry is even generalized, and Curie’s Principle can be generalized accordingly. The former generalization is only defined there and in the present book, in Chapter 8, but not studied, since their relevance for actual scientific theories is not clear.
See Section 8.2 for the concepts and notation used here.
Such an expansion exists because m, is a model of T.
In cases where the minimization principle is functioning.
By (5.3.1). Therefore, K’ is a subclass of ModL.I(6).
Assume just one.
For supervenience, see, e.g, Kim (1990); for idealization, Nowak (1980); Niiniluoto (1990); and Lahti (1984) for idealization in quantum logic. Niiniluoto shows that idealization involves counterfactual conditionals. Collier and Muller (1998) argue that emergence in science is a special case of supervenience.
They may even argue that emergent properties can be eliminated in terms of physical ones.
Nagel (1961), p. 372.
It was briefly discussed above, in Section 5.9.
Cf. the criticism in the Appendix of the distinction between real and nominal definitions.
Primas (1998), p. 84.
Danto (1981), pp. 119–120.
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Rantala, V. (2002). The Correspondence Relation. In: Explanatory Translation. Synthese Library, vol 312. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1521-8_5
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