Exclusion principle and the identity of indiscernibles: A response to Margenau's argument (Q2756990)

The paper discusses the question whether Pauli's Exclusion Principle (EP) (and its reformulations, see \textit{W. Pauli} [Z. Phys. 31, 765-783 (1925; JFM 51.0742.03)], \textit{P. A. M. Dirac} [Proc. R. Soc. Lond., Ser. 112, 661-667 (1926; JFM 52.0975.01)] and \textit{W. Heisenberg} [Z. Phys. 38, 411-426 (1926; JFM 52.0962.02)]) vindicates the contingent truth of Leibniz's Principle of the Identity of Indiscernibles (PII) [\textit{Monadology}, N. Rescher, (ed.), London, Routledge (1991)]. Strong PII requires that two particulars must differ at least in some monadic properties, while weak PII (which is outside the main scope of this paper) states that two particulars must differ at least in some either monadic properties or relational properties. According to an argument first stated by \textit{H. Margenau} [`The exclusion principle and its philosophical importance', Philos. Sci. 11, 187-208 (1944); `The nature of physical reality', New York, McGraw-Hill (1950; Zbl 0039.24309)], EP would refute PII since fermions in a composite system have to be in an antisymmetric state and by means of a mathematical reduction procedure one can attribute a state function to each of the individual subsystems which turn out to be the same mixture, implying that both fermions have the same monadic state-dependent properties and are therefore indiscernibles.NEWLINENEWLINENEWLINEOne way to circumvent this argument is to shift from the orthodox interpretation of quantum mechanics to a hidden variables interpretation, e.g., van Fraassen's modal interpretation [\textit{B. C. van Fraassen}, Quantum mechanics: An empiricist view, Oxford, Clarendon Press (1991)], such that the preexisting hidden properties differentiate between the two particles and PII would still be valid. This means that PII can be saved by sacrificing quantum completeness.NEWLINENEWLINENEWLINEHowever, there is yet another possible answer to Margenau's argument, brought forward by the author of the paper. She points out that there is a crucial, misleading assumption, underlying Margenau's argument, which does not even hold in the orthodox interpretation of quantum mechanics. Although the mathematical procedure of reduction results into two reduced states for the subsystems which are equal, these states are \textit{epistemic} in nature rather than \textit{ontological}, i.e., while the reduced states can be regarded as containing separate pieces of information relative to each component, they cannot be taken as \textit{ontologically separate} states and as such, they do not encode definite values for a complete set of observables pertaining entirely to each component, independently of the state in which the other component might be. Indeed, the entanglement which is present in the antisymmetric state of the compound system causes the states to be ontologically inseparable. Therefore there are no ontologically separate states, and no genuinely monadic properties and hence In other words: strong PII fails not because the monadic properties are the same (i.e., not because PII is false), but because there are no monadic properties at all (i.e., because it simply does not apply). Therefore, weak PII is not the weakest version but rather the unique version of PII applicable to fermions in antisymmetric state.