Two things about Hilary Putnam have not changed throughout his career: some (including Putnam himself) have regarded him as a “realist” and some have seen him as a philosopher who changed his positions (certainly with respect to realism) almost continually. Apparently, what realism meant to him in the 1960s, in the late seventies and eighties, and in the nineties, respectively, are quite different things. Putnam indicates this by changing prefixes: scientific, metaphysical, internal, pragmatic, commonsense, but always realism. Encouraged by Putnam's own attempts to distinguish his views from one time to another, his work is often regarded as split between an early period of “metaphysical realism” (his characterization) and a later and still continuing period of “internal realism”. Late Putnam is understood to be a view that insists on the primacy of our practices, while the early period is taken to be a view from outside these, a “God's Eye view”. As Putnam himself stresses (1992b), this way of dividing his work obscures continuities, the most important of which is a continuing attempt to understand what is involved in judging practices of inquiry, like science, as being objectively correct. Thus Putnam's early and his current work appear to have more in common than the division between “early” and “late” suggests. In fact, Putnam's earlier writings owe much of their critical force to his adopting the pragmatic perspective of an open-minded participant in practices of empirical inquiry, a stance not explicitly articulated in these writings but rather taken simply as a matter of course.
But this conclusion [nonlocality] needs careful discussion in order to clarify what is going on.
Within the foundations of physics in recent years, Bell's theorem has played the role of what Thomas Kuhn calls a ‘paradigm’: that is, an exemplary piece of work that others learn from, imitate and develop. Following a period of articulation and consolidation, the first generation of developments of the Bell theorem was initiated by Heywood and Redhead (1983). They produced a nonlocality result in the algebraic style of the Bell–Kochen–Specker theorem (Bell 1966; Kochen and Specker 1967), moving away from the probabilistic relations characteristic of the Bell theorems proper. More recently a second generation develops results by Peres (1990), Greenberger–Horne–Zeilinger (1990), and Hardy (1993). In addition to moving away from probabilities, this generation tries to dispense with the limiting inequalities of the Bell theorem to yield socalled ‘Bell theorems without inequalities’. With respect to probabilities, however, Hardy is a half-way house. It requires no inequalities but the result contradicts quantum mechanics under certain locality assumptions only if the statistical predictions of quantum mechanics hold in at least one case.
I want to examine the Hardy theorem and its interpretation. Initially, I intend to ignore respects in which it dispenses with probabilities because I want to point out the interesting significance of the theorem in a probabilistic context. We will see that when probabilities are restored, so are inequalities. Then we will see what the theorem has to contribute on the topic of locality.
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