dorsal/arxiv
View SchemaA Semantic Approach to the Completeness Problem in Quantum Mechanics
| Authors | Claudio Garola, Sandro Sozzo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309221 |
| URL | https://arxiv.org/abs/quant-ph/0309221 |
| DOI | 10.1023/B:FOOP.0000041291.04835.e9 |
| Journal | Foundations of Physics, Vol. 34, No. 8, August 2004 (1249-1266) |
Abstract
The old Bohr-Einstein debate about the completeness of quantum mechanics (QM) was held on an ontological ground. The completeness problem becomes more tractable, however, if it is preliminarily discussed from a semantic viewpoint. Indeed every physical theory adopts, explicitly or not, a truth theory for its observative language, in terms of which the notions of semantic objectivity and semantic completeness of the physical theory can be introduced and inquired. In particular, standard QM adopts a verificationist theory of truth that implies its semantic nonobjectivity; moreover, we show in this paper that standard QM is semantically complete, which matches Bohr's thesis. On the other hand, one of the authors has provided a Semantic Realism (or SR) interpretation of QM that adopts a Tarskian theory of truth as correspondence for the observative language of QM (which was previously mantained to be impossible); according to this interpretation QM is semantically objective, yet incomplete, which matches EPR's thesis. Thus, standard QM and the SR interpretation of QM come to opposite conclusions. These can be reconciled within an integrationist perspective that interpretes non-Tarskian theories of truth as theories of metalinguistic concepts different from truth.
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"abstract": "The old Bohr-Einstein debate about the completeness of quantum mechanics (QM)\nwas held on an ontological ground. The completeness problem becomes more\ntractable, however, if it is preliminarily discussed from a semantic viewpoint.\nIndeed every physical theory adopts, explicitly or not, a truth theory for its\nobservative language, in terms of which the notions of semantic objectivity and\nsemantic completeness of the physical theory can be introduced and inquired. In\nparticular, standard QM adopts a verificationist theory of truth that implies\nits semantic nonobjectivity; moreover, we show in this paper that standard QM\nis semantically complete, which matches Bohr\u0027s thesis. On the other hand, one\nof the authors has provided a Semantic Realism (or SR) interpretation of QM\nthat adopts a Tarskian theory of truth as correspondence for the observative\nlanguage of QM (which was previously mantained to be impossible); according to\nthis interpretation QM is semantically objective, yet incomplete, which matches\nEPR\u0027s thesis. Thus, standard QM and the SR interpretation of QM come to\nopposite conclusions. These can be reconciled within an integrationist\nperspective that interpretes non-Tarskian theories of truth as theories of\nmetalinguistic concepts different from truth.",
"arxiv_id": "quant-ph/0309221",
"authors": [
"Claudio Garola",
"Sandro Sozzo"
],
"categories": [
"quant-ph"
],
"doi": "10.1023/B:FOOP.0000041291.04835.e9",
"journal_ref": "Foundations of Physics, Vol. 34, No. 8, August 2004 (1249-1266)",
"title": "A Semantic Approach to the Completeness Problem in Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0309221"
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