Abstract
The Received View on quantum non-individuality (RV) is, roughly speaking, the view according to which quantum objects are not individuals. It seems clear that the RV finds its standard expression nowadays through the use of the formal apparatuses of non-reflexive logics, mainly quasi-set theory. In such logics, the relation of identity is restricted, so that it does not apply for terms denoting quantum particles; this “lack of identity” formally characterizes their non-individuality. We face then a dilemma: on the one hand, identity seems too important to be given up, on the other hand the RV seems to require that identity be given up. In this paper we shall discuss how the specific characterization of the RV through non-reflexive logics came to be framed. We examine some of the main objections to this version of the RV and argue that they are misguided under this specific “non-reflexive” understanding of the RV. Finally, we shall also argue that this non-reflexive view is not the only option for a metaphysical articulation of the RV: less radical approaches to identity and logic are open. In particular, some of these alternative approaches to the RV we present may be immune to most of the criticisms presented against the non-reflexive approach.
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Notes
Of course, others may see the dilemma as a sign of deeper problems and avoid taking sides on this issue. In particular, one could follow French (2011) and locate the source of the problem in the very concept of ‘objects’; roughly speaking, given that objects lead to such troubles, one would be better getting rid of them. Without objects there is no issue regarding whether they have identity or not. Others, such as van Fraassen, see the dilemma leading to the end of realism: without scientific realism, there is no need to bother about such issues (see van Fraassen 1991, pp. 480–482). Here, we shall stick with the dilemma and discuss some of its sources and alternatives.
Of course, this interpretation of Weyl is controversial, as Muller and Saunders (2008) have already pointed out; but we take here the standard interpretation according to which Weyl is seen as claiming that fermions are indiscernible.
To make sure, French and Krause (2006, p.150) do not seem to allow such a second option. They claim that when particles are regarded as non-individuals, the status of PII simply does not come into question; that is, it doesn’t even fail, it simply does not apply. This happens because those entities have no identity to begin with. But notice that this assumes right from the start that non-individuality is cashed in terms of failure of identity according to our second option here, that is, TI individuality. Our point, as we shall argue later, is that one may cash non-individuality alternatively, in terms of entities for which the PII fails.
Recall that for most authors this is simply the only articulation of the RV available.
Muller deals only with haecceitas, while we follow French and Krause and group under TI other kinds of individuality principles, like bare particulars and primitive thisnesses; that difference needs not concern us now.
Furthermore, notice that even if in a system of logic \(L_2\) we deny a formula \(\alpha \) that is a logical law of a system \(L_1\), we do not necessarily get a contradiction: \(\alpha \) may simply not be logically valid in \(L_2\). That is, logical validity is always relative to a system.
This may not be how Rodriguez–Pereyra sees the facts, of course.
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Acknowledgments
I would like to thank two anonymous referees of the journal for their comments, which helped improve an earlier version of the paper. All the remaining mistakes and infelicities are my sole responsibility, of course.
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Arenhart, J.R.B. The received view on quantum non-individuality: formal and metaphysical analysis. Synthese 194, 1323–1347 (2017). https://doi.org/10.1007/s11229-015-0997-5
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DOI: https://doi.org/10.1007/s11229-015-0997-5