Why classical logic is privileged: justification of logics based on translatability

In Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation without entering a circle, and their motivation based on intuition is unreliable. On the other hand, logics do not express a priori necessities of thinking because alternative non-classical logics have been developed. Section 2 reflects the controversies about four major kinds of non-classical logics—multi-valued, intuitionistic, paraconsistent and quantum logics. Its purpose is to show that there is no particular domain or reason that demands the use of a non-classical logic; the particular reasons given for the non-classical logic can also be handled within classical logic. The result of Sect. 2 is substantiated in Sect. 3, where it is shown (referring to other work) that all four kinds of non-classical logics can be translated into classical logic in a meaning-preserving way. Based on this fact a justification of classical logic is developed in Sect. 4 that is based on its representational optimality. It is pointed out that not many but a few non-classical logics can be likewise representationally optimal. However, the situation is not symmetric: classical logic has ceteris paribus advantages as a unifying metalogic, while non-classical logics can have local simplicity advantages.

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value (sec. 1). Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, can be translated into classical logic by introducing additional intensional operators into the language (sec. 2–5). Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic.

Quantum Paradigm of the Foldover Magnetic Resonance

The explosive development of quantum magnonics requires considering several previously known effects from a new angle. In this article, we revise the phenomenon of "foldover" (bi-stable) magnetic resonance from the point of view of quantum magnonics. The density of magnons under strong excitation can exceed the critical value for the formation of a magnon Bose condensate. Under these conditions, the effect of quantum transport of magnons should be considered. In particular, the effect of spin superfluidity, discovered earlier in super fluid 3He should lead to spatial redistribution of the precessing magnetization. Our experimental results confirm a significant change in properties of the foldover magnetic resonance in yttrium iron garnet (YIG) due to superfluid magnetization transport. This discovery paves the way for many quantum applications of supermagnonics, such as magnetic Josephson effect, long-distance spin transport, Q-bit, quantum logics, magnetic sensors, and others.

Identifying quantum logics by numerical events

Let S be a set of states of a physical system and let p(s) be the probability of an occurrence of an event when the system is in the state s ∈ S. The function p from S to [0, 1] is called a numerical event, multidimensional probability or, alternatively, S-probability. Given a set of numerical events which has been obtained by measurements and not supposing any knowledge of the logical structure of the events that appear in the physical system, the question arises which kind of logic is inherent to the system under consideration. In particular, does one deal with a classical situation or a quantum one?In this survey several answers are presented. Starting by associating sets of numerical events to quantum logics we study structures that arise when S-probabilities are partially ordered by the order of functions and characterize those structures which indicate that one deals with a classical system. In particular, sequences of numerical events are considered that give rise to Bell-like inequalities. At the center of all studies there are so called algebras of S-probabilities, subsets of these and their generalizations. A crucial feature of these structures is that order theoretic properties can be expressed by the addition and subtraction of real functions entailing simplified algorithmic procedures.The study of numerical events and algebras of S-probabilities goes back to a cooperation of E. G. Beltrametti and M. J. Mączyński in 1991 and has since then resulted in a series of subsequent papers of physical interest the main results of which will be commented on and put in an appropriate context.

Paradoxes in scientific cognition and nonclassical logics

The subject of this research is the scientific paradoxes and such means for its resolution as nonclassical logics. The author defends a thesis that paradoxes often stimulate the scientific development. It is demonstrated that most vividly the problem of paradoxes manifested in crises in the fundamentals of mathematics; the attempts for its resolution in many ways contributes to the emergence of nonclassical logics. It is substantiated that nonclassical logics helped to resolve and explain the paraded occurring in scientific cognition. Comparative analysis is conducted on the capabilities of  three-valued “quantum logics” of Garrett Birkhoff and John von Neumann and “logics of complementarity” of Hans Reichenbach. Potential of the three-valued logics of D. Bochvar and nonclassical systems of A. Zinoviev in resolution and explanation of logical paradoxes, as well as importance of temporary logics of G. H. Wright for the philosophy of science is revealed. Special attention is paid  to the paraconsistent logics. The author determines two points of view in understanding of their essence and value for science and philosophy, which juxtaposition shows that none of them fully complies with the actual state of affairs. The main conclusion consists in the statement that paradoxes of scientific cognition should not be assessed just negatively; they also carry a positive meaning: detection of paradoxes in the theory testifies to the need for their elimination, more detailed research and stricter approach towards development of the theory, which in solution of this task can be accomplished by nonclassical logics.