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Reply to H. Stapp’s Comment Michael Dickson* I dispute much of Stapp’s comment, but here focus on just a few points. First, Stapp says that his characterization of Dependence was intended as only a ‘very weak sufficient condition’. Because Stapp (1990, p. 69) referred to this characterization as a ‘definition’ (and does so in his reply as well), I naturally took it to specify the necessary and sufficient conditions for Dependence, though I never claimed that Stapp intended it thus. But never mind whether I misconstrued Stapp’s intention. Stapp admits in his reply that for stochastic theories, ‘no conclusion can be drawn from my [Stapp’s] criterion for the existence of an influence’. But if Stapp’s Dependence condition does not apply to stochastic theories, then neither does his theorem. The antecedent of Stapp’s theorem is that T is a Local theory (Dickson, 1993, p. 804). And in order to determine whether T is Local, one must determine whether certain types of Dependence hold in T. If one cannot make this determination for stochastic theories, then the theorem is inapplicable to those theories. Hence Stapp needs a definition, such as mine, that does make the determination. Second, Stapp (rightly) points out that I mistakenly took his ‘condition x’ in the Rule of Inference to refer to ‘Locality’. However, he wrongly concludes that this mistake led to, in his words, ‘total nonsense’. The nonsense was independent of any substitution for X but came instead from trying to interpret Stapp’s phrase ‘having something depend nontrivially upon something that does not exist’. Stapp then says that his Rule was meant to be (in Logic 101 parlance) Denying the Consequent, and he claims that I argued against this rule. Of course, I would never commit such a sin against logic, and anyhow the interpretation on which I eventually decided (p. 804) is just a case of Denying the Consequent. But perhaps those points are mute, for Stapp agrees that my statement (pp. 806-807) of Al-B4 is correct. The question, then, is whether one can get from there (plus whatever other assumptions have been granted) to Cl-C4 (p. 808). To convince us that one can get there, Stapp observes that Al-A4 and Bl-B4 are consequences of LOG and LO&, respectively. He suggests that although the conjunction of these consequences is insufficient to get ClC4, the conjunction of LOCA and LOCa is sufficient. One interesting point here is that if we accept Stapp’s account of Dependence, then Al-A4 is equivalent to LOCA and B l-B4 is equivalent to LOCs. *Department Received
of Philosophy, 1994.
University
of Notre Dame, Notre Dame, IN 465.56, U.S.A
8 August
Stud. Hist. Phil. Sci., Vol. 25, No. 6,
965-966, 1994. Copyright 0 1995 Elsevier pp. Science Ltd Printed in Great Britain. All rights reserved 0039-3681/94 $7.00 + 0.00
Pergamon
965
966
Studies in History and Philosophy of Science
(The derivation is trivial, and I skip it for lack of space.) Hence Stapp’s move to LOG and LOG buys him nothing, if he sticks to his definition of Dependence. In any case, the key point for Stapp seems to be that one must allow the locality conditions to act ‘together’ or ‘simultaneously’ instead of merely ‘in conjunction’. But what does together involve logically beyond ‘in conjunction’? Stapp does not tell us (apart from that it gets him to Cl-C4). His worry seems to be that mere conjunction does not guarantee Locality. He argues (correctly) that the existence of a model satisfying Al-A4 conjoined with the existence of a model satisfying B l-B4 does not guarantee the existence of a model satisfying both. But to get such a guarantee, conjunction suffices: Al-A4 conjoined with Bl-B4 is enough to get the existence of a model that satisfies both, and therefore is enough to get (in Stapp’s words) ‘simultaneously no influence from RA to RB and no influence from RLI to RA’, and yet, as we know, it is not enough to get Bell’s inequality. References Dickson, M. (1993) ‘Stapp’s Theorem Without Counterfactual Commitments: Why It Fails Nonetheless’, Studies in History and Philosophy of Science 24, 791-814. Stapp, H. (1990) ‘Comments on “Nonlocal Influence and Possible Worlds” ‘, British Journal for the Philosophy of Science 41, 59-72. Stapp, H. (1994) ‘Comment on “Stapp’s Theorem Without Counterfactual Commitments” ‘, Studies in History and Philosophy of Science 25, 929-934.
Reply to H. Stapp’s Comment Michael Dickson* I dispute much of Stapp’s comment, but here focus on just a few points. First, Stapp says that his characterization of Dependence was intended as only a ‘very weak sufficient condition’. Because Stapp (1990, p. 69) referred to this characterization as a ‘definition’ (and does so in his reply as well), I naturally took it to specify the necessary and sufficient conditions for Dependence, though I never claimed that Stapp intended it thus. But never mind whether I misconstrued Stapp’s intention. Stapp admits in his reply that for stochastic theories, ‘no conclusion can be drawn from my [Stapp’s] criterion for the existence of an influence’. But if Stapp’s Dependence condition does not apply to stochastic theories, then neither does his theorem. The antecedent of Stapp’s theorem is that T is a Local theory (Dickson, 1993, p. 804). And in order to determine whether T is Local, one must determine whether certain types of Dependence hold in T. If one cannot make this determination for stochastic theories, then the theorem is inapplicable to those theories. Hence Stapp needs a definition, such as mine, that does make the determination. Second, Stapp (rightly) points out that I mistakenly took his ‘condition x’ in the Rule of Inference to refer to ‘Locality’. However, he wrongly concludes that this mistake led to, in his words, ‘total nonsense’. The nonsense was independent of any substitution for X but came instead from trying to interpret Stapp’s phrase ‘having something depend nontrivially upon something that does not exist’. Stapp then says that his Rule was meant to be (in Logic 101 parlance) Denying the Consequent, and he claims that I argued against this rule. Of course, I would never commit such a sin against logic, and anyhow the interpretation on which I eventually decided (p. 804) is just a case of Denying the Consequent. But perhaps those points are mute, for Stapp agrees that my statement (pp. 806-807) of Al-B4 is correct. The question, then, is whether one can get from there (plus whatever other assumptions have been granted) to Cl-C4 (p. 808). To convince us that one can get there, Stapp observes that Al-A4 and Bl-B4 are consequences of LOG and LO&, respectively. He suggests that although the conjunction of these consequences is insufficient to get ClC4, the conjunction of LOCA and LOCa is sufficient. One interesting point here is that if we accept Stapp’s account of Dependence, then Al-A4 is equivalent to LOCA and B l-B4 is equivalent to LOCs. *Department Received
of Philosophy, 1994.
University
of Notre Dame, Notre Dame, IN 465.56, U.S.A
8 August
Stud. Hist. Phil. Sci., Vol. 25, No. 6,
965-966, 1994. Copyright 0 1995 Elsevier pp. Science Ltd Printed in Great Britain. All rights reserved 0039-3681/94 $7.00 + 0.00
Pergamon
965
966
Studies in History and Philosophy of Science
(The derivation is trivial, and I skip it for lack of space.) Hence Stapp’s move to LOG and LOG buys him nothing, if he sticks to his definition of Dependence. In any case, the key point for Stapp seems to be that one must allow the locality conditions to act ‘together’ or ‘simultaneously’ instead of merely ‘in conjunction’. But what does together involve logically beyond ‘in conjunction’? Stapp does not tell us (apart from that it gets him to Cl-C4). His worry seems to be that mere conjunction does not guarantee Locality. He argues (correctly) that the existence of a model satisfying Al-A4 conjoined with the existence of a model satisfying B l-B4 does not guarantee the existence of a model satisfying both. But to get such a guarantee, conjunction suffices: Al-A4 conjoined with Bl-B4 is enough to get the existence of a model that satisfies both, and therefore is enough to get (in Stapp’s words) ‘simultaneously no influence from RA to RB and no influence from RLI to RA’, and yet, as we know, it is not enough to get Bell’s inequality. References Dickson, M. (1993) ‘Stapp’s Theorem Without Counterfactual Commitments: Why It Fails Nonetheless’, Studies in History and Philosophy of Science 24, 791-814. Stapp, H. (1990) ‘Comments on “Nonlocal Influence and Possible Worlds” ‘, British Journal for the Philosophy of Science 41, 59-72. Stapp, H. (1994) ‘Comment on “Stapp’s Theorem Without Counterfactual Commitments” ‘, Studies in History and Philosophy of Science 25, 929-934.