Abstract
This paper offers a critical assessment of the current state of the debate about the identity and individuality of material objects. Its main aim, in particular, is to show that, in a sense to be carefully specified, the opposition between the Leibnizian ‘reductionist’ tradition, based on discernibility, and the sort of ‘primitivism’ that denies that facts of identity and individuality must be analysable has become outdated. In particular, it is argued that—contrary to a widespread consensus—‘naturalised’ metaphysics supports both the acceptability of non-qualitatively grounded (both ‘contextual’ and intrinsic) identity and a pluralistic approach to individuality and individuation. A case study is offered that focuses on non-relativistic quantum mechanics, in the context of which primitivism about identity and individuality, rather than being regarded as unscientific, is on the contrary suggested to be preferable to the complicated forms of reductionism that have recently been proposed. More generally, by assuming a plausible form of anti-reductionism about scientific theories and domains, it is claimed that science can be regarded as compatible with, or even as suggesting, the existence of a series of equally plausible grades of individuality. The kind of individuality that prevails in a certain context and at a given level can be ascertained only on the basis of the specific scientific theory at hand.
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Notes
There is, of course, also an important connection with the work of Quine (1960, 1976). On the basis of ideas of Hilbert and Bernays, Quine showed that (provided that the vocabulary of non-analysed general terms is finite) the identity sign can be paraphrased away in any first-order language, and replaced with a conjunction of non-identity-involving formulas (in particular, conditionals of the form ‘if Fx then Fy’ for any x and y and any number of places in F). This must be mentioned, as authors that we will discuss later on worked in an explicitly Quinean setting.
And by no means limited to historical figures in philosophy: for the influence of Schopenhauer’s view of space on Einstein’s thoughts on separability, for instance, see Howard (1997).
It could be objected that Black doesn’t explicitly rule out the existence of an absolute spatial background. This exegetical point, however, doesn’t affect the strength of the counterexample: the location occupied by each sphere must in any case be described in absolutely general terms, turning out to be the same for the two spheres.
Black’s argument might be rejected as question-begging (as in, for example, Odegard (1964)) or as re-describable in reductionist terms (as in Hacking (1975)). But the former objection has no force here, as we are looking for a justification of PII in the first place. With respect to the latter, it must be noticed instead that a re-description may not always be available, and Hacking’s strategy might in any case not be regarded as a legitimate reductionist response. An ‘extreme’ option is to follow O’Leary-Hawthorne (1995) in claiming that in Black’s universe there is only one sphere at some distance from itself, but this really looks like a last resort for the defender of PII, especially from a naturalistic viewpoint.
We are grateful to an anonymous referee for pressing us on this point concerning mathematical as opposed to physical ontology.
In other words, haecceitism and the view that individuals (may) possess haecceitates are distinct and largely independent theses.
Remember our distinction above between two ways of understanding naturalism.
In particular, Muller and Saunders use only spin degrees of freedom (specifically, total spin relations) in finite Hilbert spaces; and more general commutator relations holding between distinct single-particle operators (e.g., position and momentum) in the case of infinite-dimensional Hilbert spaces.
We do not attribute this presupposition to MSS themselves because they seem quite neutral on this. In fact, what they say seems best interpreted as motivated by the idea that the question whether physical objects can adequately be described using PII is an interesting one in itself.
Notice, in this connection, that a reductionist viewpoint seems to be shared also by authors who disagree with MSS. For instance, Dieks and Versteegh (2008) conclude their critique of MSS by arguing that one should opt for a holistic interpretation of quantum systems of identical particles (i.e., one where the total system simply has no component particles) (compare Hawley’s (2009) ‘summing defence’ of PII). This clearly suggests that Dieks and Versteegh too reject primitivism as unscientific.
Interestingly, Ladyman and Bigaj (2010, p. 135) express ideas similar to ours when they suggest that perhaps “anything that is the value of a first-order variable is an individual” , but do not emphasise the role played by countability assumptions in the arguments in favour of the weak discernibility of quantum particles.
For instance, to the effect that quantum field theory is in general more empirically adequate than quantum mechanics.
We are grateful to an anonymous referee for pressing us on this point.
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Dorato, M., Morganti, M. Grades of individuality. A pluralistic view of identity in quantum mechanics and in the sciences. Philos Stud 163, 591–610 (2013). https://doi.org/10.1007/s11098-011-9833-z
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DOI: https://doi.org/10.1007/s11098-011-9833-z