{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:55:55Z","timestamp":1740149755200,"version":"3.37.3"},"reference-count":79,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,5,24]],"date-time":"2018-05-24T00:00:00Z","timestamp":1527120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"Extensions of the Kochen\u2013Specker theorem use quantum logics whose classical interpretation suggests a true-implies-value indefiniteness property. This can be interpreted as an indication that any view of a quantum state beyond a single context is epistemic. A remark by Gleason about the ad hoc construction of probability measures in Hilbert spaces as a result of the Pythagorean property of vector components is interpreted platonically. Unless there is a total match between preparation and measurement contexts, information about the former from the latter is not ontic, but epistemic. This is corroborated by configurations of observables and contexts with a truth-implies-value indefiniteness property.<\/jats:p>","DOI":"10.3390\/e20060406","type":"journal-article","created":{"date-parts":[[2018,5,24]],"date-time":"2018-05-24T11:54:01Z","timestamp":1527162841000},"page":"406","source":"Crossref","is-referenced-by-count":11,"title":["New Forms of Quantum Value Indefiniteness Suggest That Incompatible Views on Contexts Are Epistemic"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6554-2802","authenticated-orcid":false,"given":"Karl","family":"Svozil","sequence":"first","affiliation":[{"name":"Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10\/136, 1040 Vienna, Austria"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,24]]},"reference":[{"key":"ref_1","first-page":"885","article-title":"Measures on the closed subspaces of a Hilbert space","volume":"6","author":"Gleason","year":"1957","journal-title":"J. Math. Mech."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mermin, D.N. (2007). Quantum Computer Science, Cambridge University Press.","DOI":"10.1017\/CBO9780511813870"},{"key":"ref_3","unstructured":"Halmos, P.R. (1958). Finite-Dimensional Vector Spaces, Springer. Undergraduate Texts in Mathematics."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Svozil, K. (1993). Randomness & Undecidability in Physics, World Scientific.","DOI":"10.1142\/1524"},{"key":"ref_5","first-page":"407","article-title":"Partition Logics, Orthoalgebras and Automata","volume":"68","author":"Svozil","year":"1995","journal-title":"Helv. Phys. Acta"},{"key":"ref_6","unstructured":"Svozil, K. (1998). Quantum Logic, Springer."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s10773-005-7052-0","article-title":"Logical equivalence between generalized urn models and finite automata","volume":"44","author":"Svozil","year":"2005","journal-title":"Int. J. Theor. Phys."},{"key":"ref_8","unstructured":"Engesser, K., Gabbay, D.M., and Lehmann, D. (2009). Contexts in quantum, classical and partition logic. Handbook of Quantum Logic and Quantum Structures, Elsevier."},{"key":"ref_9","first-page":"276","article-title":"Generalized event structures and probabilities","volume":"Volume 6","author":"Burgin","year":"2016","journal-title":"Information and Complexity"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Svozil, K. (2018). Physical [A]Causality. Determinism, Randomness and Uncaused Events, Springer.","DOI":"10.1007\/978-3-319-70815-7"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF02034335","article-title":"Commutators and decompositions of orthomodular lattices","volume":"6","author":"Chevalier","year":"1989","journal-title":"Order"},{"key":"ref_12","unstructured":"Shannon, C.E., and McCarthy, J. (1956). Gedanken-Experiments on Sequential Machines. Automata Studies, Princeton University Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1741","DOI":"10.1007\/BF00676288","article-title":"Automaton partition logic versus quantum logic","volume":"34","author":"Schaller","year":"1995","journal-title":"Int. J. Theor. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Schaller, M., and Svozil, K. (1996). Automaton logic. Int. J. Theor. Phys., 35.","DOI":"10.1007\/BF02302381"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1007\/BF01889696","article-title":"Generalized urn models","volume":"20","author":"Wright","year":"1990","journal-title":"Found. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1119\/1.2205879","article-title":"Staging quantum cryptography with chocolate balls","volume":"74","author":"Svozil","year":"2006","journal-title":"Am. J. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.tcs.2014.09.019","article-title":"Non-contextual chocolate ball versus value indefinite quantum cryptography","volume":"560","author":"Svozil","year":"2014","journal-title":"Theor. Comput. Sci."},{"key":"ref_18","unstructured":"Svozil, K. (arXiv, 2000). On generalized probabilities: Correlation polytopes for automaton logic and generalized urn models, extensions of quantum mechanics and parameter cheats, arXiv."},{"key":"ref_19","first-page":"225","article-title":"On the Theory of Probabilities","volume":"152","author":"Boole","year":"1862","journal-title":"Philos. Trans. R. Soc. Lond."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF02903286","article-title":"Constructive generalization of Bell\u2019s inequalities","volume":"64","author":"Froissart","year":"1981","journal-title":"Il Nuovo Cimento B"},{"key":"ref_21","first-page":"329","article-title":"Some results and problems on quantum Bell-type inequalities","volume":"8","year":"1993","journal-title":"Hadron. J. Suppl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1556","DOI":"10.1063\/1.527066","article-title":"The range of quantum probabilities","volume":"27","author":"Pitowsky","year":"1986","journal-title":"J. Math. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1093\/bjps\/45.1.95","article-title":"George Boole\u2019s \u2018Conditions of Possible Experience\u2019 and the Quantum Puzzle","volume":"45","author":"Pitowsky","year":"1994","journal-title":"Br. J. Philos. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0097-3165(71)90015-X","article-title":"Orthomodular lattices admitting no states","volume":"10","author":"Richard","year":"1971","journal-title":"J. Comb. Theory Ser. A"},{"key":"ref_25","unstructured":"Fukuda, K. (2017, July 01). cdd and cddplus Homepage, cddlib Package cddlib-094h, 2000. Available online: http:\/\/www.inf.ethz.ch\/personal\/fukudak\/cdd_home\/."},{"key":"ref_26","unstructured":"Marlow, A.R. (1978). The state of the pentagon. A nonclassical example. Mathematical Foundations of Quantum Theory, Academic Press."},{"key":"ref_27","unstructured":"Kalmbach, G. (1983). Orthomodular Lattices (London Mathematical Society Monographs), Academic Press."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Beltrametti, E.G., and Ma\u00e7zy\u0144ski, M.J. (1995). On the range of non-classical probability. Rep. Math. Phys., 36.","DOI":"10.1016\/0034-4877(96)83620-2"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"020403","DOI":"10.1103\/PhysRevLett.101.020403","article-title":"Simple Test for Hidden Variables in Spin-1 Systems","volume":"101","author":"Klyachko","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Bub, J., and Stairs, A. (2009). Contextuality and Nonlocality in \u2018No Signaling\u2019 Theories. Found. Phys., 39.","DOI":"10.1007\/s10701-009-9307-8"},{"key":"ref_31","unstructured":"Bub, J., and Stairs, A. (arXiv, 2010). Contextuality in Quantum Mechanics: Testing the Klyachko Inequality, arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Badzia\u0327g, P., Bengtsson, I., Cabello, A., Granstr\u00f6m, H., and Larsson, J.A. (2011). Pentagrams and Paradoxes. Found. Phys., 41.","DOI":"10.1007\/s10701-010-9433-3"},{"key":"ref_33","unstructured":"Kochen, S., and Specker, E.P. (1965). Logical Structures arising in quantum theory. The Theory of Models, Proceedings of the 1963 International Symposium at Berkeley, North Holland."},{"key":"ref_34","first-page":"59","article-title":"The Problem of Hidden Variables in Quantum Mechanics","volume":"17","author":"Kochen","year":"1967","journal-title":"J. Math. Mech."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Redhead, M. (1990). Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics, Clarendon Press.","DOI":"10.1119\/1.16032"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/S1355-2198(03)00035-2","article-title":"Betting on the outcomes of measurements: A Bayesian theory of quantum probability","volume":"34","author":"Pitowsky","year":"2003","journal-title":"Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/1-4020-4876-9_10","article-title":"Quantum Mechanics as a Theory of Probability","volume":"Volume 72","author":"Demopoulos","year":"2006","journal-title":"Physical Theory and Its Interpretation"},{"key":"ref_38","unstructured":"Belinfante, F.J. (1973). A Survey of Hidden-Variables Theories, Pergamon Press, Elsevier."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1086\/289140","article-title":"Quantum logic, realism, and value definiteness","volume":"50","author":"Stairs","year":"1983","journal-title":"Philos. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"(1993). Getting contextual and nonlocal elements-of-reality the easy way. Am. J. Phys., 61, 443\u2013447.","DOI":"10.1119\/1.17239"},{"key":"ref_41","unstructured":"Pt\u00e1k, P., and Pulmannov\u00e1, S. (1991). Orthomodular Structures as Quantum Logics. Intrinsic Properties, State Space and Probabilistic Topics, Kluwer Academic Publishers, Springer. Fundamental Theories of Physics."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1002\/mana.19911540113","article-title":"The pasting constructions for orthomodular posets","volume":"154","author":"Navara","year":"1991","journal-title":"Math. Nachr."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1119\/1.17551","article-title":"Comment on Getting contextual and nonlocal elements-of-reality the easy way","volume":"62","author":"Johansen","year":"1994","journal-title":"Am. J. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1119\/1.17488","article-title":"Comment on Getting contextual and nonlocal elements-of-reality the easy way","volume":"62","author":"Vermaas","year":"1994","journal-title":"Am. J. Phys."},{"key":"ref_45","unstructured":"Cabello, A., Portillo, J.R., Sol\u00eds, A., and Svozil, K. (arXiv, 2013). Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories, arXiv."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.ins.2008.06.012","article-title":"Quantum Scholasticism: On Quantum Contexts, Counterfactuals, and the Absurdities of Quantum Omniscience","volume":"179","author":"Svozil","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1088\/0143-0807\/15\/4\/004","article-title":"A simple proof of the Kochen-Specker theorem","volume":"15","author":"Cabello","year":"1994","journal-title":"Eur. J. Phys."},{"key":"ref_48","unstructured":"Cabello, A. (1996). Pruebas Algebraicas de Imposibilidad de Variables Ocultas en Mec\u00e1nica Cu\u00e1ntica. [Ph.D. Thesis, Universidad Complutense de Madrid]."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1023\/A:1026646229896","article-title":"Greechie diagrams of small quantum logics with small state spaces","volume":"37","author":"Tkadlec","year":"1998","journal-title":"Int. J. Theor. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"5380","DOI":"10.1063\/1.531710","article-title":"Greechie diagrams, nonexistence of measures in quantum logics and Kochen\u2013Specker type constructions","volume":"37","author":"Svozil","year":"1996","journal-title":"J. Math. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"102201","DOI":"10.1063\/1.4931658","article-title":"A variant of the Kochen-Specker theorem localising value indefiniteness","volume":"56","author":"Abbott","year":"2015","journal-title":"J. Math. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Pitowsky, I. (1982). Substitution and Truth in Quantum Logic. Philos. Sci., 49.","DOI":"10.1086\/289067"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2981","DOI":"10.1103\/PhysRevLett.68.2981","article-title":"Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories","volume":"68","author":"Hardy","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1103\/PhysRevLett.71.1665","article-title":"Nonlocality for two particles without inequalities for almost all entangled states","volume":"71","author":"Hardy","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"2755","DOI":"10.1103\/PhysRevLett.79.2755","article-title":"Ladder Proof of Nonlocality without Inequalities: Theoretical and Experimental Results","volume":"79","author":"Boschi","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Cabello, A., and Garc\u00eda-Alcaine, G. (1995). A hidden-variables versus quantum mechanics experiment. J. Phys. A Math. Gen. Phys., 28.","DOI":"10.1088\/0305-4470\/28\/13\/016"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0375-9601(96)00134-X","article-title":"Bell-Kochen-Specker theorem: A proof with 18 vectors","volume":"212","author":"Cabello","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"4109","DOI":"10.1103\/PhysRevA.55.4109","article-title":"No-hidden-variables proof for two spin- particles preselected and postselected in unentangled states","volume":"55","author":"Cabello","year":"1997","journal-title":"Phys. Rev. A"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"062116","DOI":"10.1103\/PhysRevA.88.062116","article-title":"Hardy\u2019s paradox for high-dimensional systems","volume":"88","author":"Chen","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"180404","DOI":"10.1103\/PhysRevLett.111.180404","article-title":"Simple Hardy-Like Proof of Quantum Contextuality","volume":"111","author":"Cabello","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1063\/1.532334","article-title":"Infinite and finite Gleason\u2019s theorems and the logic of indeterminacy","volume":"39","author":"Pitowsky","year":"1998","journal-title":"J. Math. Phys."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.shpsb.2003.10.002","article-title":"Generalizations of Kochen and Specker\u2019s theorem and the effectiveness of Gleason\u2019s theorem","volume":"35","author":"Hrushovski","year":"2004","journal-title":"Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"062109","DOI":"10.1103\/PhysRevA.86.062109","article-title":"Strong Kochen-Specker theorem and incomputability of quantum randomness","volume":"86","author":"Abbott","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"032109","DOI":"10.1103\/PhysRevA.89.032109","article-title":"Value-indefinite observables are almost everywhere","volume":"89","author":"Abbott","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"2316","DOI":"10.1103\/PhysRevD.27.2316","article-title":"Deterministic model of spin and statistics","volume":"27","author":"Pitowsky","year":"1983","journal-title":"Phys. Rev. D"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"3751","DOI":"10.1103\/PhysRevLett.83.3751","article-title":"Finite precision measurement nullifies the Kochen-Specker theorem","volume":"83","author":"Meyer","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1007\/BF01491891","article-title":"Die gegenw\u00e4rtige Situation in der Quantenmechanik","volume":"23","year":"1935","journal-title":"Naturwissenschaften"},{"key":"ref_68","unstructured":"London, F., and Bauer, E. (1983). The Theory of Observation in Quantum Mechanics. Quantum Theory and Measurement, Princeton University Press."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1080\/09500340408233598","article-title":"Quantum information via state partitions and the context translation principle","volume":"51","author":"Svozil","year":"2004","journal-title":"J. Mod. Opt."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1086\/425941","article-title":"Who Invented the \u201cCopenhagen Interpretation\u201d? A Study in Mythology","volume":"71","author":"Howard","year":"2004","journal-title":"Philos. Sci."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1038\/121580a0","article-title":"The quantum postulate and the recent development of atomistic theory","volume":"121","author":"Bohr","year":"1928","journal-title":"Nature"},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Von Neumann, J. (1996). Mathematische Grundlagen der Quantenmechanik, Springer. [2nd ed.].","DOI":"10.1007\/978-3-642-61409-5"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1023\/A:1018820410908","article-title":"A Foundational Principle for Quantum Mechanics","volume":"29","author":"Zeilinger","year":"1999","journal-title":"Found. Phys."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.shpsb.2011.07.001","article-title":"Statistical mechanics and thermodynamics: A Maxwellian view","volume":"42","author":"Myrvold","year":"2011","journal-title":"Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1111\/j.1746-8361.1960.tb00422.x","article-title":"Die Logik nicht gleichzeitig entscheidbarer Aussagen","volume":"14","author":"Specker","year":"1960","journal-title":"Dialectica"},{"key":"ref_76","unstructured":"Kochen, S., and Specker, E.P. (September, January 26). The calculus of partial propositional functions. Proceedings of the 1964 International Congress for Logic, Methodology and Philosophy of Science, Jerusalem, Israel."},{"key":"ref_77","unstructured":"Valentini, A. (2018). The de Broglie-Bohm Pilot-Wave Theory, University of Vienna."},{"key":"ref_78","unstructured":"Ferrari, G.R.F. (2000). The Republic, Cambridge University Press. Cambridge Texts in the History of Political Thought."},{"key":"ref_79","unstructured":"Tkadlec, J. Personal communication."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/6\/406\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T23:46:20Z","timestamp":1720309580000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/6\/406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,24]]},"references-count":79,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["e20060406"],"URL":"https:\/\/doi.org\/10.3390\/e20060406","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,5,24]]}}}