Editing Quantum logic (section)

== History and modern criticism ==
In his classic 1932 treatise ''[[Mathematical Foundations of Quantum Mechanics]]'', [[John von&nbsp;Neumann]] noted that [[projection (mathematics)|projection]]s on a [[Hilbert space]] can be viewed as propositions about physical observables; that is, as potential ''yes-or-no questions'' an observer might ask about the state of a physical system, questions that could be settled by some measurement.{{sfn|von&nbsp;Neumann|1932}}  Principles for manipulating these quantum propositions were then called ''quantum logic'' by von&nbsp;Neumann and Birkhoff in a 1936 paper.{{sfn|Birkhoff|von&nbsp;Neumann|1936}}

[[George Mackey]], in his 1963 book (also called ''Mathematical Foundations of Quantum Mechanics''), attempted to axiomatize quantum logic as the structure of an [[orthocomplemented lattice|ortho&shy;complemented lattice]], and recognized that a physical observable could be ''defined'' in terms of quantum propositions.  Although Mackey's presentation still assumed that the ortho&shy;complemented lattice is the [[Lattice (order)|lattice]] of [[closed set|closed]] [[linear subspace]]s of a [[separable space|separable]] Hilbert space,{{sfn|Mackey|1963}} [[Constantin Piron]], Günther Ludwig and others later developed axiomatizations that do not assume an underlying Hilbert space.<ref>Piron:
* C. Piron, "Axiomatique quantique" (in French), ''Helvetica Physica Acta'' vol.&nbsp;37, 1964.  DOI:&nbsp;[http://doi.org/10.5169/seals-113494 10.5169/seals-113494].
* {{harvnb|Piron|1976}}.
Ludwig:
* Günther Ludwig, "[https://link.springer.com/content/pdf/10.1007/BF01653647.pdf Attempt of an Axiomatic Foundation of Quantum Mechanics and More General Theories]"&nbsp;II, ''Commun. Math. Phys.'', vol.&nbsp;4, 1967.  pp.&nbsp;331-348.  
* {{harvnb|Ludwig|1954}}
</ref>

Inspired by [[Hans Reichenbach]]'s then-recent defence of [[general relativity]], the philosopher [[Hilary Putnam]] popularized Mackey's work in two papers in 1968 and 1975,{{sfn|Maudlin|2005}} in which he attributed the idea that anomalies associated to quantum measurements originate with a failure of logic itself to his coauthor, physicist [[David Finkelstein]].{{sfn|Putnam|1969}}  Putnam hoped to develop a possible alternative to [[Hidden-variable theory|hidden variables]] or [[wavefunction collapse]] in the problem of [[quantum measurement]], but [[Gleason's theorem]] presents severe difficulties for this goal.{{sfn|Maudlin|2005}}{{sfn|Wilce}}  Later, Putnam retracted his views, albeit with much less fanfare,{{sfn|Maudlin|2005}} but the damage had been done.  While Birkhoff and von&nbsp;Neumann's original work only attempted to organize the calculations associated with the [[Copenhagen interpretation]] of quantum mechanics, a school of researchers had now sprung up, either hoping that quantum logic would provide a viable hidden-variable theory, or obviate the need for one.<ref>{{wikicite |reference=T.&nbsp;A. Brody, "On Quantum Logic", ''Foundations of Physics'', vol.&nbsp;14, no.&nbsp;5, 1984.  pp.&nbsp;409-430.|ref={{harvid|Brody|1984}}}}</ref>  Their work proved fruitless, and now lies in poor repute.{{sfn|Bacciagaluppi|2009}}

Most philosophers would agree that quantum logic is not a competitor to [[classical logic]]. It is far from evident (albeit true<ref>{{harvnb|Dalla&nbsp;Chiara|Giuntini|2002|p=94}}: "Quantum logics are, without any doubt, logics. As we have seen, they satisfy all the canonical conditions that the present community of logicians require in order to call a given abstract object a logic."</ref>) that quantum logic is a ''logic'', in the sense of describing a process of reasoning, as opposed to a particularly convenient language to summarize the measurements performed by quantum apparatuses.{{sfn|Maudlin|2005|p=159-161}}{{sfn|Brody|1984}} In particular, some modern [[philosopher of science|philosophers of science]] argue that quantum logic attempts to substitute metaphysical difficulties for unsolved problems in physics, rather than properly solving the physics problems.{{sfn|Brody|1984|pp=428-429}}  [[Tim Maudlin]] writes that quantum "logic 'solves' the [[measurement problem|[measurement] problem]] by making the problem impossible to state."{{sfn|Maudlin|2005|p=174}}

Quantum logic remains in use among logicians{{sfn|Dalla&nbsp;Chiara|Giuntini|2002}} and interests are expanding through the recent development of [[quantum computing]], which has engendered a proliferation of new logics for formal analysis of quantum protocols and algorithms (see also {{slink||Relationship to other logics}}).{{sfn|Dalla&nbsp;Chiara|Giuntini|Leporini|2003}}  The logic may also find application in (computational) linguistics.