Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us to abandon (...) classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics. (shrink)

Discussion of the relation between exchange-value and use-value (as defined inCapital I) is clarified by the construction of set-theoretical models of these concepts. Marx argues fallaciously for the independence of exchange-value and use-value. His fallacy is diagnosed as depending upon a mistaken assumption about the impossibility of inferring a certain linear order on a set from a certain (different) partial order on that set.

It is shown that the uncertainty principle has nothing directly to do with the non-localisability of position and momentum for an individual system on the quantum logical view. The product Δ x· Δ p for localisation of the ranges of position and momentum of an individual system→ ∞ , while the quantities Δ X and Δ P in the uncertainty principle $\Delta X\cdot \Delta P\geq \hslash /2$ , must be given a statistical interpretation on the quantum logical view.

It is shown that the lattice-theoretic distributive law does not fail to hold in the two slit-experiment for the general case offinite slit widths and for a position measurement which localizes the observed particle to afinite region of the screen. Comments are made on previous and less general discussions of the case considered.