Vincenzo Fano

Quantum mechanics is often credited for having clearly shown that the whole is something over and above the sum of its parts. We want to assess whether this is really the case, and if so, in what sense. We argue that there is indeed a sense in which this is true. Our argument is that even a weak realistic interpretation of quantum mechanics renders a particular metaphysical principle about property instantiation, that we label Property Compositional Determinateness, untenable. Yet there is another metaphysical principle about composition that is usually maintained to imply that composition of parts exhausts the whole they are part of, namely Mereological Extensionalism. In this case, contrary to widespread agreement, we argue that quantum mechanics does not provide any reason, either direct or indirect, to abandon such principle.

A draft of a possible comparison between the use made of mathematics in classical field theories and in quantum mechanics is presented. Hilbert’s space formalism, although not only elegant and powerful but intuitive as well, does not give us a spatio-temporal representation of physical events. The picture of the electromagnetic field as an entity which is real in itself– i.e., as a wave without support – fostered by the emergence of special relativity can be seen as the first step, favored by many physicists and philosophers, of a gradual “escape” from intuition into a purely mathematical representation of the external world. After the introduction, in recent theoretical physics, of fiber bundle formalism the classical notion of field acquires a new spatio-temporal intuitiveness. This intuitiveness is clearly foreshadowed in the Kantian and Meinongian analysis of the notion of magnitude. At the end of the paper we show that, contrary to what happens in quantum mechanics, mathematics plays a truly explicative role in general relativity, without any loss of spatio-temporal intuitiveness.

Abstract: It seems that from an epistemological point of view comparative probability has many advantages with respect to a probability measure. It is more reasonable as an evaluation of degrees of rational beliefs. It allows the formulation of a comparative indifference principle free from well known paradoxes. Moreover it makes it possible to weaken the principal principle, so that it becomes more reasonable. But the logical systems of comparative probability do not admit an adequate probability updating, which on the contrary is possible for a probability measure. Therefore we are faced with a true epistemological dilemma between comparative and quantitative probability.

We present a new thought experiment that raises a threat for Minimal Physicalism, i.e. the thesis according to which mental properties supervene on physical properties. Our proposal is an example of the so called hard problems in philosophy of mind, in particular the problem of maximal consciousness. We do not however presuppose anything about its very nature apart from the minimal, weak assumption that it is determined by first order mental properties. We argue that either Minimal Physicalism is unable to give an adequate account of the new thought experiment we present or has to explain the fact that two numerically distinct but physically indistinguishable individuals have different maximal consciousness due to their spatial location. We contend that this last conclusion is strongly at variance with our contemporary scientific image of the world.