Multiplicity and indiscernibility

Heathcote, Adrian

doi:10.1007/s11229-020-02600-8

Cited by 3 publications

(4 citation statements)

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“…That this is especially fruitful has been argued often, as far back asWeyl (1931) orWigner (1939). For additional comments on this seeHeathcote (2021).…”

mentioning

confidence: 87%

Realism, irrationality, and spinor spaces

Heathcote

2023

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Mathematics, as Eugene Wigner noted, is unreasonably effective in physics. The argument of this paper is that the disproportionate attention that philosophers have paid to discrete structures such as the natural numbers, for which a nominalist construction may be possible, has deprived us of the best argument for Platonism, which lies in continuous structures—in fields and their derived algebras, such as Clifford algebras. The argument that Wigner was making is best made with respect to such structures—in a loose sense, with respect to geometry rather than arithmetic. The purpose of the present paper is to make this connection between mathematical realism and geometrical entities. It thus constitutes an argument against formalism, for which mathematics is merely a game with humanly set rules; and nominalism, in which whatever mathematics is used is eliminable in the final analysis, by often insufficiently specified means. The hope is that light may be cast on the stubborn mysteries of the nature of quantum mechanics and its mathematical formulation, with particular reference to spinor representations—as they have been developed by Andrej Trautman. Thus, according to our argument, quantum mechanics (QM) may appear more natural, as we have better reasons to take spinor structures as irreducibly real, a view consonant with the work of Trautman and Penrose in particular.

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“…That this is especially fruitful has been argued often, as far back asWeyl (1931) orWigner (1939). For additional comments on this seeHeathcote (2021).…”

mentioning

confidence: 87%

Realism, irrationality, and spinor spaces

Heathcote

2023

ZFN

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“…In Weyl (1931) we find the following paragraph: (I've given a more technical discussion of this paragraph and how it fits into Weyl's larger discussion in Heathcote (2020). But the main point can be made quite simply and it is worth doing so.…”

Section: The Argument For Indistinguishabilitymentioning

confidence: 99%

“…All we know is that it is two or more; we cannot infer that it is limited to just two. Elsewhere it is argued (Heathcote 2020) that there can be up to four Black spheres -arranged in space in a tetrahedral formation (a Platonic solid) -with the same distance between them all. Five would be impossible.…”

Section: Universality and Cardinalitymentioning

confidence: 99%

“…(French and Krause (2006) p. 105) 20 This misses out the crucial point that the eigenvalue sum E 1 + E 2 only appears once -and it gives the impression that the central argument is something to do with permuting Ike and Mike -rather than the impossibility of doing this when they are electrons! 21 It also creates a mystery as to why Weyl says that the Leibniz principle is maintained -a point that appears to have created a second level of confusion (see Heathcote (2020)). French and Krause focus their attention on what Weyl says later in Weyl (1949), which, though important, does not give an argument for indistinguishability.…”

Section: The Argument For Indistinguishabilitymentioning

confidence: 99%

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