Contextuality, Witness of Quantum Weirdness

From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality

“…Finally, we conclude our work in XIII with some openings on the use of contextuality. We took great support from the presentation of Hippolyte Dourdent [41] (for the French readers only) throughout this thesis.…”

“…Specker published in 1960 an article entitled The logic of non-simultaneously decidable propositions [43], which preluded to his famous result, in Dialectica, a journal about scientific and cognition philosophy founded by Gaston Bachelard, Paul Bernays and Ferdinand Gonseth. Gonseth had been the teacher of Specker and an inspirational figure for him [41]. He developed the idea that logic was based on the existence of objects on which propositions apply, against the neo-positivism of the then influential Vienna Circle [44] (see section II F below).…”

“…Ironically, Gonseth deduced from his concept of logical objects the three pillars of classical logical, the law of excluded middle, the law of Non-Contradiction and the law of identity, in the form of the three following conceptions of objects of logic [41]:…”

“…Specker was interested in the logical problems that could emerge when one wished to attribute a truth value to a proposition about the future, such as the famous example introduced by Aristotle: A sea battle will take place tommorow. In order to avoid paradoxes, Aristotle stated that propositions about the future were contingent, that they could only be attributed a truth value when they become actual [41]. The study of Future Contingents has long been linked with the study of counterfactual propositions, propositions of conditional logic based on unverified hypothesis [41].…”

“…In order to avoid paradoxes, Aristotle stated that propositions about the future were contingent, that they could only be attributed a truth value when they become actual [41]. The study of Future Contingents has long been linked with the study of counterfactual propositions, propositions of conditional logic based on unverified hypothesis [41]. Their relations to contextuality are still studied nowadays [49].…”