Abstract
In conclusion of the previous chapter, we argued that the strong involvement of probabilities in the formalism of QM and the fact that one is not bound to introducing (formally explicit) hidden variables λ justifies to reconsider knowledge. We also briefly mentioned that there are further reasons in QIT to consider quantum states as being concerned with knowledge.
Author’s note: I owe the contrast between ‘making sense’ and a mere ‘coming to terms’ to Markus Schrenk (private communication).
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Notes
- 1.
Cf. Nielsen and Chuang (2010, p. 87); the proof is quite straightforward.
- 2.
…who, however, was not so comfortable with this “Deliberate About-Face of the Epistemological Viewpoint” (cf. Schrödinger 1935b, p. 157 ff.).
- 3.
Zeh (2012, p. 19) points out that the ‘founding fathers’, especially those who contributed to the ‘Copenhagen’ tradition, were driven, in their interpretive efforts, by their respective world views, not necessarily even by well worked-out philosophies. To some extent this is certainly correct and to some extent it even emphasizes our point; that one might seek for answers consulting sources outside physics. But one should also caution against attributing a false systematic value to the insight. For one can equally localize the reasons for endorsing any of the ontological interpretations discussed in Chap. 6 in strong ‘realistic’ intuitions that may in turn be influenced by a naïvely realist ‘world view’. To infer from this (which Zeh does not, at least not overtly) the inferiority of any of the respective views would simply mean to confound the context of their discovery with the context of their justification.
- 4.
The origin of the term is not unambiguously clear, but folklore has it that it stems from the bad reputation of seventeenth century dutch bookmakers (cf. Hájek 2009a, p. 174).
- 5.
- 6.
Of course convictions of independence go into the very formulation of such a quantum state. Note also that the N systems could be investigated in temporal succession, i.e. that our concern here is not with a box of interacting particles or the like.
- 7.
To see the latter, just consider that both n ± lie in the x-z plane, so the azimuthal angle φ is zero; a trigonometric consideration then gives \(\cos {}(\frac {\pi }{2} - \theta ) = \pm \frac {\sqrt {3}}{2} \Leftrightarrow \theta = \pm \frac {\pi }{3}\). Using (2.19), one obtains two matrices
, each with (obvious) eigenvalues ± 1 respectively and + 1-eigenvectors 
(in the standard z-spin basis). To avoid confusion, note that |n
−〉≠ |−n
+〉, i.e. the two are not related as spin-up-π∕3 and spin-down-π∕3. - 8.
This point is also significantly clarified in Mermin (2012, p. 8).
- 9.
This is sometimes assumed as an axiom in doxastic logics (e.g. Kraus and Lehmann 1988).
- 10.
Author’s note: I am indebted to Chris Timpson for helping me sort this issue out.
- 11.
Cf. Schurz (2014, p. 80 ff.) for a general overview of purported solutions and their problems. Schurz’s own proposal does provide an optimality-based justification for induction on the object-level under certain epistemological background assumptions—which, however, means that object-induction might still do pretty baldy but that (even under the respective, favorable circumstances) we just have no better alternative. Arnold (2010), moreover, assesses some general limitations to Schurz’s solution when applied to the meta-level of prediction methods, which is where cleverly adapted (meta-)inductive practices are proven, for a whole range of possible scenarios, to have the same long-run success rates as the best of all other epistemically accessible prediction methods (e.g. Schurz 2009).
- 12.
German original: “in der Quantenmechanik sind Aussagen über das, was ‘wirklich’ ist, Aussagen über das Objekt, verboten, sie handeln nur von der Relation Objekt-Subjekt—und zwar offenbar in einem noch viel einschneidenderen Sinn, als dies schließlich von jeder Naturbeschreibung gilt.”
- 13.
German original: “Man möchte darum schließen, daß das Lichtquant jederzeit einen ganz bestimmten Ort und einen ganz bestimmten Impuls besitzt—eine Auffassung, die wir doch eigentlich längst als zu hart und paradox verlassen haben.”
- 14.
German: “Notverordnung”
- 15.
- 16.
Somewhat ironically, Fuchs (2010, p. 7) also happily refers back to Pierce’s claims of theories as instruments, despite his strong reluctance to the label.
- 17.
Cf. however Fuchs (2010, p. 20) for a quite different characterization of the project (which is partially his).
- 18.
Why ‘only half the battle’? Because immediately the question arises: ‘The probability of…these NQMCs being true? Appropriate to future experience? Assertible…?’
- 19.
‘It’ here refers to the agent. Healey wishes to include also non-conscious ‘agents’.
- 20.
Point of clarification: a subjunctive conditional has the (schematic) natural language-form ‘if it were the case that x, then y would be the case as well’. A subjunctive counterfactual has a false antecedent (x is not the case), whereas subjunctive conditionals in general may also express epistemic uncertainty as to the truth of the antecedent. Note also that Lewis (1973, p. 4) cites a case where the expression is not (or at least not overtly) subjunctive but still a counterfactual conditional.
- 21.
For historical details on Peirce’s role in the development of pragmatism e.g. Kenny (2007, p. 34 ff.). Burch (2014, p. 8), in particular, argues that “even when Peirce calls himself a ‘realist’ or is called by others a ‘realist,’ it must be kept in mind that Peirce was always a realist of the Kantian ‘empirical’ sort and not a Kantian ‘transcendental realist.’” We identified Kant as a specific kind of internal realist in interlude I, so the connections run quite deep.
- 22.
Davies (2006, p. 23) equally refers to the understanding of a sentence as an explication of what it is to know its meaning. Since knowledge implies truth on most conceptions, we may take it that a sentence has to have a meaning in order for a competent speaker to understand it. Here is Quine (1939, p. 703, emphasis in original): “The noun ‘Pegasus’ is meaningful. If asked its meaning, we could reply with a translation into other words: ‘the winged horse captured by Bellerophon.’”
- 23.
E.g. Kant (1781, pp. 26 and 34–35): “Space does not represent any quality of objects by themselves, or objects in their relation to one another”; “time is no longer objective, if we remove the sensuous character of our intuitions, […] and speak of things in general.”
- 24.
Cf. also Beller (2000) for historical details on Einstein’s life-long exposure to Kantian thought.
- 25.
Cf. also Allison (2015, ch. 7) on this point.
- 26.
Mittelsteadt makes no mention of Friedman or Reichenbach or of the difficulties with the synthetic a priori and d’Espagnat’s tenet (II). But his aim is to show how “objects can be constituted as new entities by means of invariance properties of the theories in question.” (Mittelstaedt 2009, p. 847; my emphasis – FB) Since this is understood by him as an execution of the “Kantian way of reasoning” (p. 851), he seems to unconsciously appeal to a relativized a priori.
- 27.
10 is the number of independent parameters needed to specify the elements of the group: 3 rotational, 1 time- and 3 space-translational, and 3 for velocity-shifts (e.g. Ballentine 2000, p. 68).
- 28.
Lattices are algebraic structures, certain of which (‘Boolean’ ones) can be understood as an abstract formulation of propositional logic. Lattices, interpreted thus, are basically sets of propositions which allow for combination by material implication, dis-, and conjunction. A complemented lattice has a negation and a Boolean one additionally allows for the usual distribution laws between disjunction and conjunction. Orthogonal projectors on a Hilbert space can be used to construct a non-Boolean qua non-distributive lattice in virtue of non-commutativity, and so define a non-classical ‘quantum logic’. Cf. Redhead (1987, p. 176) for an elementary introduction and Piron (1976) or Bub (1997) for more detailed treatments.
- 29.
In principle the fact that the scaling transformations only form a semigroup (do not all have inverses) introduces a subtlety; but that much of the literature suppresses the ‘semi’ can at least be seen as evidence for the fact that these scaling transformations are typically viewed as similarly important for the theory as are proper transformation groups.
- 30.
- 31.
E.g. Healey (2007, p. 5 ff.) for the following.
- 32.
This ‘coming to terms’ is certainly reminiscent of Friederich’s (2015) therapeutic approach to QM (therapeutic in the sense of Wittgenstein (1968)), whereby one is ‘cured’ from the OP by viewing QM (very roughly) as an activity that is constituted by certain rules (state assignment, decoherence mechanism, Born rule,…) and proceeds without problem. In Boge (2016a, p. 6), it was argued though, that this still raises the question why exactly that activity results, when one applies the rules; and for that reason we here pursue a quite different course. Friederich’s own turn to the block universe to make sense of EPRB-correlations (his p. 143 ff.) and his defense of the in-principle possibility of sharp values for all observables (in the sense of hidden variables; his p. 161 ff.) may serve as evidence that his therapy has not really worked on himself—both considerations would otherwise be obsolete.
- 33.
NB: ‘external’ is here meant, as the quote makes explicit, in the ‘sensuously external sense’. Kant (1781, p. 22) famously declared space and time “pure forms of intuition”, and ‘external objects’ are meant here as objects situated in space and time. When we have talked about an ‘external reality’ above (and when we do so below), we thereby meant what Kant (1781, p. 372) means by “something […] transcendentally […] outside us[…].” (my emphasis—FB).
- 34.
There are, in fact, also attempts more recent than Berkeley’s (who in the end, to recall, merely replaced the external world by an all-perceiving god anyways; e.g. §66 of the Principles) of constructing the impression of a mind-independent world purely out of “interacting conscious agents” (Hoffman and Prakash 2014, p. 1), and with the ambitious aim to “show that […] the quantum free […] wave function […] is identical in form to the harmonic functions that characterize the asymptotic dynamics of conscious agents […].” (ibid.) While certainly interesting, these results have at best a preliminary character though, and rest, among other things, on questionable (formal) notions of what counts as a ‘conscious agent’.
- 35.
We have used the term ‘nature’ here to emphasize the dynamical character (usually associated with the term) that this punishment has, within experienced reality. We have also used ‘nature’ above as a synonym for ‘mind-independent reality’ though, and d’Espagnat (1987, p. 527) equally identifies the use of this word as an indicator that his colleagues who otherwise decree versions of phenomenalism do endorse realist intuitions after all. But we have been careful to separate the dynamical content of ‘nature’ (which is within experience) from its strong metaphysical realist content (which expresses the conviction that the source of this punishment is external). We are silent, in other words, about the (non-)spatiotemporality of a mind-independent reality here, in contrast to Kant.
- 36.
Cf. also Allison (2004, chapter 3), for a detailed discussion of this problem.
- 37.
An interesting proposal along somewhat similar lines is defended by Gebharter A, Retzlaff N (A new proposal how to handle counterexamples to Markov causation à la Cartwright, or: fixing the chemical factory, unpublished manuscript), who introduce what they call “common cause triggered non-causal dependencies”. The suggestion is to take, in the EPRB case, the quantum state as a common cause of the two subsequent detection events, but not of the correlated values. The correlated values are then rather explained in terms of a different, nomological dependency that does not allow for the kind of intervention that a causal connection would.
- 38.
- 39.
In a quite similar vein, Camilleri and Schlosshauer (2015, p. 74) understand decoherence as “only the last step in a long line of attempts to undergird (or supplant) Bohr’s doctrines by an explicit dynamical and physical account”, noting that “[s]uch approaches were already pursued by a number of Bohr’s followers […]in the 1960s, who, far from seeing it as an invalidation of Bohr’s basic insight, regarded it as providing a justification of his views.”
- 40.
It has sometimes been argued that Kant was not even well-acquainted with Berkeley’s writings when he wrote the first edition of the Critique, but there is also good historical evidence to the contrary (cf. Turbayne 1955).
- 41.
Cf. also da Costa and French (2003, p. 18 ff.) for considerations on partial truth.
- 42.
Cf. Button (2013, pp. 9 and 18 ff.), for a brief discussion of the relation between correspondence theories and truthmaking.
- 43.
Consider, in this connection, the understanding of time as “only an approximate concept” which “emerges from the separation into […] different subsystems” (Kiefer 2009, p. 6) in some approaches to quantum gravity or the fact that treating GR as “an effective theory seriously involves rethinking physics without spactime” (Markopoulou 2009, p. 148).
- 44.
This view, of course, gains direct support from the debate on cognitive impenetrability of preception; Müller-Lyer illusions are an impressive, simple example (e.g. Pylyshyn 1999, p. 344).
- 45.
Langton (1998) e.g. provides a book-length investigation of this aspect of Kant’s internal realism.
, each with (obvious) eigenvalues ± 1 respectively and + 1-eigenvectors 
(in the standard z-spin basis). To avoid confusion, note that |n
−〉≠ |−n
+〉, i.e. the two are not related as spin-up-π∕3 and spin-down-π∕3.References
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Boge, F.J. (2018). Reconsidering Knowledge, or, Coming to Terms With Quantum Mechanics. In: Quantum Mechanics Between Ontology and Epistemology. European Studies in Philosophy of Science, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-95765-4_7
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