In section 3 of his paper ‘Three-valued logic’, Hilary Putnam deals with Reichenbach's attempt to interpret quantum mechanics on the basis of three-valued logic, and he uses some arguments of his own in order to show that this attempt is ‘a move in the direction of simplifying the whole system of laws’ (171). I believe that the Reichenbach–Putnam procedure cannot be defended and that it leads to undesirable consequences. There are the reasons for my belief: THREE-VALUED LOGIC AND CONTACT-ACTION Putnam asserts (a) that ‘the laws of quantum mechanics … are logically incompatible with’ the principle of contact-action ‘if ordinary two-valued logic is used’; and (b) that ‘adopting a three-valued logic permits one to preserve both the laws of quantum mechanics and the principle that no causal signal travels with infinite speed’. Assuming for a moment that (a) and (b) give a correct statement of Reichenbach's position (which they do not – see section 3) and that (a) is true we can at once say that adopting the procedure suggested in (b) would violate one of the most fundamental principles of scientific methodology, namely, the principle to take refutations seriously. The statement that there is no velocity greater than the velocity of light is a well-corroborated statement of physics. If, as is asserted in (a), quantum mechanics implies the negation of that statement, we should consider it as refuted and look for a better theory. This is what has in fact happened.
In section 3 of his paper ‘Three-valued logic’, Hilary Putnam deals with Reichenbach's attempt to interpret quantum mechanics on the basis of three-valued logic, and he uses some arguments of his own in order to show that this attempt is ‘a move in the direction of simplifying the whole system of laws’ (171). I believe that the Reichenbach–Putnam procedure cannot be defended and that it leads to undesirable consequences. There are the reasons for my belief: THREE-VALUED LOGIC AND CONTACT-ACTION Putnam asserts (a) that ‘the laws of quantum mechanics … are logically incompatible with’ the principle of contact-action ‘if ordinary two-valued logic is used’; and (b) that ‘adopting a three-valued logic permits one to preserve both the laws of quantum mechanics and the principle that no causal signal travels with infinite speed’. Assuming for a moment that (a) and (b) give a correct statement of Reichenbach's position (which they do not – see section 3) and that (a) is true we can at once say that adopting the procedure suggested in (b) would violate one of the most fundamental principles of scientific methodology, namely, the principle to take refutations seriously. The statement that there is no velocity greater than the velocity of light is a well-corroborated statement of physics. If, as is asserted in (a), quantum mechanics implies the negation of that statement, we should consider it as refuted and look for a better theory. This is what has in fact happened.
‘A Philosopher Looks at Quantum Mechanics’ (Putnam [1965]) explained why the interpretation of quantum mechanics is a philosophical problem in detail, but with only the necessary minimum of technicalities, in the hope of making the difficulties intelligible to as wide an audience as possible. When I wrote it, I had not seen Bell ([1964]), nor (of course) had I seen Ghirardi et al. ([1986]). And I did not discuss the ‘Many Worlds’ interpretation. For all these reasons, I have decided to make a similar attempt forty years later, taking account of additional interpretations and of our knowledge concerning non-locality. (The Quantum Logical interpretation proposed in Putnam [1968] is not considered in the present paper, however, because Putnam [1994b] concluded that it was unworkable.) Rather than advocate a particular interpretation, this paper classifies the possible kinds of interpretation, subject only to the constraints of a very broadly construed scientific realism. Section 7 does, however, argue that two sorts of interpretation—ones according to which a ‘collapse’ is brought about by the measurement (e.g. the traditional ‘Copenhagen’ interpretation), and the Many Worlds interpretation or interpretations—should be ruled out. The concluding section suggests some possible morals of a cosmological character. 1. Background 2. Scientific realism is the premise of my discussion 3. What ‘quantum mechanics’ says—and some problems 4. Other interpretations of quantum mechanics 5. The problem of Einstein's bed 6. Classification of the possible kinds of interpretation 7. Which interpretations I think we can rule out 8. The ‘moral’ of this discussion
In this essay, I offer a critical evaluation of Hilary Putnam's writings on epistemology and philosophy of science, in particular his engagement with interpretative problems in quantum mechanics. I trace the development of his thinking from the late 1960s when he adopted a strong causal-realist position on issues of meaning, reference, and truth, via the "internal realist" approach of his middle-period writings, to the various forms of pragmatist, naturalized, or "commonsense" epistemology proposed in his latest books. My contention is that Putnam's retreat from a full-fledged realist outlook has been prompted in large part by his belief that it cannot possibly be reconciled with the implications of quantum mechanics for our understanding of processes and events in the subatomic domain. However, I suggest, this response should be seen as premature given the range of as-yet unresolved problems with quantum mechanics on the orthodox (Copenhagen) interpretation and also the existence of an alternative account - David Bohm's hidden-variables theory - which perfectly matches the established predictive-observational results while providing a credible realist ontology. I also examine Putnam's case for adopting a nonstandard (three-valued) "quantum logic" in relation to the thinking of other philosophers - Michael Dummett among them - who have espoused a more global or doctrinaire version of anti-realism. I conclude that Putnam's early (causal-realist) position is by no means untenable in light of the various arguments that he now takes as counting decisively against it.
Reichenbach's interpretation of quantum mechanics has been narrowly reduced to the advocacy of a three-valued logic. His interpretation rests, though, on the same rich epistemological framework that shapes his influential analysis of space-time theories. Different interpretations of the quantum formalism, with their conflicting ontologies and causes, emerge in this view as “equivalent descriptions”. One casualty of the conventionalist approach is the measurement problem. I give reasons for why Reichenbach's view on the nature of interpretations of quantum theory cannot be defended.
The book investigates the ontology and logic of quantum physics. The first part discusses the relationship of theory and observation and different views on the ontological status of scientific theories. It introduces the fundamentals of quantum mechanics and some of its interpretations and their compatibility with various ontological positions. In the second part, implications of quantum mechanics on classical logic, especially on the distributive law and bivalence, as discussed by Garrett Birkhoff & John von Neumann (1936) and Hilary Putnam (1968), and their counterarguments are reconstructed and discussed. It is concluded that classical logic is sufficient for dealing with quantum mechanical propositions.
In order to solve the problem of which is the real logic of Quantum Mechanics (QM), we suggest to study the mutual relationships between the physical theory (as a whole, that is both its experimental part and its theoretical part), its mathematics and its logic. That results to be a more general problem than what is considered by traditional studies on Quantum Logic (QL). These studies focus attention on the problem of the relationship between the experimental part of the physical theory and only its mathematics, from which logic is then derived. The new approach, that we suggest, generalises the interpretation that one of us (A. D.) successfully tested on the foundations of classical physical theories. The foundations of a theory are interpreted in terms of two options on the kind of mathematics, either classical one or constructive one, and the kind of logic, either classical logic or intuitionistic logic. It is remarkable that each theory making use of intuitionistic logic – i. e. L. Carnot’s classical mechanics, S. Carnot’s thermodynamics, Lobacevskij’s non-Euclidean geometry is organised in order to solve an universal problem (expressed by a double negated sentence), rather than in an entirely deductive way; hence, a non-classical logic does not belong exclusively to QM. From an historical and foundational analysis about QM, we conclude that in QM it is the law of double negation and not modular law (introduced by Birkhoff and von Neumann without giving physical evidence to it) which fails, i. e. which represents the true difference between Classical Logic (CL) and QL. We have looked for previous works on QL supporting our suggestion; in the past Destouches-Fevrier (1948), Fine (1974), Bell-Hallett (1981), Gauthier (1983), Adelman-Corbett (1995) already defended this thesis on the relevance of double negation law for QL. Under this light, QL results to have the same logic of a classical theory organised in a problematic manner. Hence, QM has to be referred to intuitionistic logic, in the same way every theory which is developed around a fundamental problem, expressed by a double negated sentence, does. In particular, by following the founder of intuitionism, Brouwer, we reject the identification of intuitionistic logic with an entirely deductive system; rather, the logical system of QL, as a theory, is organised in such a way to put a crucial problem to be solved. In agreement with this kind of organisation, among the several QM formulations we choose Heisenberg’s formulation, which was ignored by previous authors on QL. This formulation is aimed to solve the problem of quantum measurement, that originates the uncertainty methodological principle. Moreover, it is remarkable that it makes use of an operational mathematics (discrete matrices only). We interpret its characteristic arguing about its principal problem through double negated sentences; it results to be a moving from arguments belonging to non-classical logic expressed by a double negated sentence to the recognition of a suitable mathematics for QM formulation. In sum, QL shows how it is possible to state the relationship between QM and mathematics. This point has been almost ignored by the most traditional approaches to QL, which rather drew it from an a priori mathematics of QM (commonly, Hilbert space). As a verification of our approach, we show that even both Lobachevskij’s geometry and S. Carnot’s thermodynamics argued in order to achieve mathematical formulas expressing the content of the basic double negated sentences of respective theory. In the same way the recent book on QM by T. F. Jordan formalised his matrix mechanics. 1. Logic in classical physics and in Quantum Mechanics An historical analysis of Quantum Mechanics (QM) shows that there were at the origin of the theory two distinct formulations: Matrix Mechanics (Heisenberg, 1925) and Wave Mechanics (Schroedinger, 1926). Although Dirac subsumed these two formulations in a comprehensive mathematical framework (Hilbert space), we think that the organisation of the principles is different in Matrix Mechanics from that in Wave Mechanics, and this difference implies different logics. So we think that in order to characterise the logic of QM it is necessary to distinguish between this two formulations. In Matrix Mechanics, Heisenberg’s basic idea was to explain atomic spectra not in terms of atomic orbits (as Old Quantum Theory tried to make), but only by means of the study of experimental data; i. e., frequencies and intensities of light both emitted and absorbed by matter. Through a
There is no such thing as “The Quantum Logical Interpretation of Quantum Mechanics”. Rather, there is a cluster of interpretations, all of which can be described as “quantum logical”. Here I provide a general framework for discussing interpretations of this kind, and then locate various suggestions within it. The presentation owes much to van Fraassen (see, in particular, van Fraassen 1974 ); his “modal interpretation” is one of those I discuss, along with those of Jauch, Putnam and Kochen. I begin by rehearsing some orthodox quantum theory. Within quantum mechanics we deal with a set 0 of measurable quantities, orobservables(position, momentum, components of spin and so on). Experiment can determine the value of an observable for a given system: the values so determined will be real numbers. A maximal amount of information about what the result would be for a given system, whatever experiment we chose to perform on it, is available once we know thestateof the system.