A primer of logic by Henry Bradford Smith PDF

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Tarski, A. Mostowski and R. Robinson, Undecidable Theories (Amsterdam: North-Holland, 1953), section 1. 26 RADICAL INTERPRETATION AND INDETERMINACY sublanguage; and finally, the translations preserve explanations of phenomena described in that observational sublanguage. 37 I shall adopt this picture as providing at least a necessary condition for the equivalence relation in question. Consider now the situation in which we have two interpretations of an agent related by a pair of Quinean transformations, in the specified way, that ascribe equivalent belief-systems to the agent.

Putnam has suggested the following formulation of this requirement: first, T1 and T2 share a common observational language, in terms of which they can frame a description of the phenomena to be explained; second, the translations in question coincide on this invariant article, "Equivalence," in Realism and Reason: Philosophical Papers, vol. : Cambridge University Press, 1983), and by Quine, "On Empirically Equivalent Systems of the World," Erkentnis 9 (1978): 313-28. Putnam's discussion is in part a critical reaction to Hans Reichenbach's doctrine of coordinating definitions in Experience and Prediction (Chicago: University of Chicago Press, 1938).

27 In fact, in the absence of any restrictions on which expressions are to count as 'logical', the condition may easily be seen to fail in some cases. Consider, for example, two predicates, A(x) and P(x), whose extensions contingently coincide. Let us suppose that both of these predicates are treated as constants in a semantical characterization of the concept of logical consequence for L. Then the schema will count as valid; but it is not necessarily truth-preserving. The TarskiMostowski condition helps here, but only so far.

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