Quantum theory and the mind brain relation

In reductionist biology, mental states are brain states and the brain obeys the laws of a physical world existing independently of and prior to minds. This account is invalidated if the physical laws themselves involve essential reference to mental states.. The quantum theory has usually been presented in a form making such reference. .To remove the need for this, the first step is to accept that quantum theory applies only to fields and to entities embedded in fields. Ehrenfest's theorem then shows how systems obeying Newtonian mechanics, including objects of everyday life, appear as persistent patterns showing none of the indeterminacy associated with features of the underlying field. The theorems of Gleason, Kocken and Specker demand that the quantum theory should leave a degree of indeterminacy in the pattern of the fields it describes. Any interaction of a quantum system with its environment therefore requires a definite selection of a unique pattern of behaviour within the range of indeterminacy. Such interaction is continuous, and there is no role for a mental state in this selection. It would be consistent with the formalism of quantum theory if a localised interaction in a system caused an instantaneous removal of indeterminacy over an arbitrarily large volume, in apparent conflict with the special theory of relativity. This conflict is not removed by any appeal to the effects of mental states.. However, a consistent interpretation of quantum systems as fields throws doubt on the claim that the event correlations in the experiments of Aspect and his colllaborators are evidence of causal propagation at speeds greater than that of light

Multivalued Logic, Neutrosophy and Schrodinger equation

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by observation that despite almost eight decades, there is indication that some of those paradoxes known in Quantum Physics are not yet solved. In our knowledge, this is because the solution of those paradoxes requires re-examination of the foundations of logic itself, in particular on the notion of identity and multi-valuedness of entity. The book is also intended for young physicist fellows who think that somewhere there should be a ‘complete’ explanation of these paradoxes in Quantum Mechanics. If this book doesn’t answer all of their questions, it is our hope that at least it offers a new alternative viewpoint for these old questions

Observables and Unobservables in Quantum Mechanics: How the No-Hidden-Variables Theorems Support the Bohmian Particle Ontology

The paper argues that far from challenging—or even refuting—Bohm’s quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to position measurements; and (ii) Bohm’s theory provides a clear and coherent explanation of the measurement outcome statistics based on an ontology of particle positions, a law for their evolution and a probability measure linked with that law. What the no-hidden-variables theorems teach us is that (i) one cannot infer the properties that the physical systems possess from observables; and that (ii) measurements, being an interaction like other interactions, change the state of the measured system

Existence, actuality and logical pluralism

This work considers data about the intentional nature of human cognition, and traces their consequences for debates in the philosophy and epistemology of logic, and metaphysics. The first part of this work, comprising its first three chapters, investigates the prospect of revising logic in light of de re intentionality, that is, more precisely, in light of the fact that via their cognitive abilities agents can relate to objects that do not exist. We will consider two candidate systems for logical revision, expressions of two forms of logical revisionism, and eventually motivate, from anti-exceptionalist grounds, our preference for one of them. We will start in Ch. 1 by illustrating the anti-exceptionalist methodological framework assumed in this work. Subsequently, in Ch. 2, we will discuss four classically valid principles inadequate to the data of de re intentionality, reject possible attempts, by proponents of so-called realist abstractionist theories of fiction, to deny those data, and present the system P of positive free logic. We will then go on, in Ch. 3, to illustrate the noneist programme of logical revision and a system, N^R, implementing its principles. We will thus argue from anti-exceptionalist grounds that rational theory choice is exercised by choosing N^R. The rest of the chapter is dedicated to defend a realist account about the ontological dependency of the non-existent on the existent. Ch. 4 and Ch. 5 are dedicated to refute attempts, by Timothy Williamson, to reduce disagreements about non-existent objects to cases of merely verbal disagreements. In Ch. 4, we take issue with arguments to the extent that logical disputes about `exists' are genuine only if the parties use it in deductively ways. In Ch. 5 we address his scepticism towards the dispute, about merely possible objects, between actualism and possibilism, and find it unwarranted

Systems of quantum logic

According to quantum mechanics, the pure states of a microsystem are represented by vectors in a Hilbert Space. Sentences of the form, "x є L" (where x is the state vector for a system, L a subspace of the appropriate Hilbert space), may be called Q-propositions: such sentences serve to summarise our information about the results of possible experiments on the system. Quantum logic investigates the relations which hold among the Q-propositions about a given physical sys tem. These logical relations correspond to algebraic relations among the subspaces of Hilbert space. The algebra of this set of subspaces is non-Boolean, and may be regarded either as an orthomodular lattice or as a partial Boolean algebra. With each type of structure we can associate a logic. A general approach to the semantics for such a logic is provided in terms of interpretations of a formal language within an algebraic structure; an interpretation maps sentences of the language homomorphically onto elements of the structure. When the structure in question is a Boolean algera, the resulting logic is classical; here we develop a semantics for the logic associated with partial Boolean algebras. Two systems of proof, based on the natural deduction systems of Gentzen, are shown for this logic. With respect to the given sematics, these calculi are sound and weakly complete. Strong completeness is conjectured. Quantum logic deals with the logical relations between sentences, and so is properly called a logic. However, it is the logic appropriate to a limited class of sentences: proposals that it should replace classical logic wherever the latter is used should be viewed with suspicion.Arts, Faculty ofPhilosophy, Department ofGraduat