By Sylvester J.J.

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Additional resources for Collected mathematical papers, volume 4

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2. : Harvard University Press, 1990). A version of the same problem is discussed in my "Modality, Invariance, and Logical Truth," Journal of Philosophical Logic 16 (1987): 423-43. 20 RADICAL INTERPRETATION AND INDETERMINACY any domain, so that [i] is again counted as valid. But it is not necessarily truth-preserving, as we see by considering possible situations in which (p is false. In this case, however, both A(x) and P(x) satisfy the extensional invariance condition. The difficulty illustrated by such examples is that there can be accidental invariance; and the natural remedy that suggests itself is to strengthen Mostowski's condition to require the invariance of a logical expression over all possible situations.

35 Somewhat easier to digest is Putnam's example of alternative spacetime geometries, one of which takes spacetime points as primitive and identifies regions with sets of points; the other takes regions as primitive and identifies any point p with the sequence (Nk(p)), where for each natural number k, Nk(p) is the piece of spacetime corresponding to the open ball around p of radius 1/2k. There are then translations mapping each of these geometries into the other. Thus, for example, the term 'point' in the first description will be rendered in the second by something like 'contracting sequence of spheres'; in the other direction, the term 'region' in the second version is interpreted in the first by something like 'connected open set of points'.

Not at all. On the 'irrealist' view, the suggested rationale of the notion of reference in terms of conformal explanation is fully available, save that the question of the correctness of the underlying object language explanations must be referred to a 'description' (Reichenbach), 'theory' (Putnam), or 'theory formulation' (Quine). 6 Credo In the concluding paragraphs of his seminal paper, Lewis canvasses the possibilities of indeterminacy: It seems hopeless to deny, in the face of such examples as have been offered by Quine, that the truth conditions of full sentences in M [the 41 See Arthur Fine, The Shaky Game: Einstein, Realism, and the Quantum Theory (Chicago: University of Chicago Press, 1986), p.