Tomasz Bigaj

General metaphysical arguments have been proposed in favour of the thesis that all dispositions have categorical bases (Armstrong; Prior, Pargetter, Jackson). These arguments have been countered by equally general arguments in support of ungrounded dispositions (Molnar, Mumford). I believe that this controversy cannot be settled purely on the level of abstract metaphysical considerations. Instead, I propose to look for ungrounded dispositions in specific physical theories, such as quantum mechanics. I explain why non-classical properties such as spin are best interpreted as irreducible dispositional properties, and I give reasons why even seemingly classical properties, for instance position or momentum, should receive a similar treatment when interpreted in the quantum realm. Contrary to the conventional wisdom, I argue that quantum dispositions should not be limited to probabilistic dispositions (propensities) by showing reasons why even possession of well-defined values of parameters should qualify as a dispositional property. I finally discuss the issue of the actuality of quantum dispositions, arguing that it may be justified to treat them as potentialities whose being has a lesser degree of reality than that of classical categorical properties, due to the incompatibility relations between non-commuting observables.

In the first section of the chapter, I scrutinize Howard Stein’s 1991 definition of a transitive becoming relation that is Lorentz invariant. I argue first that Stein’s analysis gives few clues regarding the required characteristics of the relation complementary to his becoming—i.e. the relation of indefiniteness. It turns out that this relation cannot satisfy the condition of transitivity, and this fact can force us to reconsider the transitivity requirement as applied to the relation of becoming. I argue that the relation of becoming need not be transitive, as long as it satisfies the weaker condition of “cumulativity”: for a given observer the area of the events that have become real should not diminish as time progresses. I show that there are actually two relations of becoming that meet this weakened condition: Stein’s (transitive) relation of causal past connectibility and the (non-transitive) relation that is the logical complement of the future causal connectibility. In the second part of the chapter I defend Stein’s notion of temporal becoming against the attack that appeals to quantum-mechanical non-locality. I critically evaluate the argument given by Mauro Dorato (1996) that purports to show that space-like separated measurements done on the EPR system have to be mutually determinate. Finally, in order to account for the truth of counterfactual statements that link the space-like separated outcomes, I propose a dynamic conception of becoming, according to which the sphere of determinate events as of a given point may depend on the physical phenomena transpiring at this point.

This is an attempt to defend Field's nominalistic program from the criticism raised by K. Wójtowicz in his article. The author argues for the following theses: (a) that Wójtowicz uses the notion of „mathematical theory” broader than Field does it; (b) that he misinterprets the conception of the „abstract counterparts” of nominalistic statements; (c) and that his general evaluation of Field's program is based on too high methodological standards which he applies to the possible nominalistic versions of empirical theories. The second part of this paper contains an attempt to generalize the results of Field's analysis. The following fact is proved: every open sentence expressible in the language of an empirical theory and being empirically contentful is implicitly definable by the set of certain qualitative predicates. In the case of first-order language this result can be strengthened via Beth's definability theorem, to the theorem stating that every open sentence fulfilling conditions formulated above is definable explicitly with the help of certain nominalistic formula. The philosophical significance of this result is that each mathematized empirical theory for which representation theorem is true, can be translated into purely qualitative version.