Tomasz Bigaj

The mathematical notion of a permutation of indices in the state description admits different physical interpretations. Two main interpretations analyzed in this paper are: exchange of essences and exchange of haecceities. It is argued that adopting the essentialist approach leads to the conclusion, contrary to the conventional wisdom, that quantum particles of the same type are sometimes discernible by their properties. The indiscernibility thesis can be supported only by the alternative interpretation in terms of primitive thisness.

The main focus of this paper is on the notion of transtemporal identity applied to quantum particles. I pose the question of how the symmetrization postulate with respect to instantaneous states of particles of the same type affects the possibility of identifying interacting particles before and after their interaction. The answer to this question turns out to be contingent upon the choice between two available conceptions of synchronic individuation of quantum particles that I call the orthodox and heterodox approaches. I argue that the heterodox approach offers a better explanation of the known experimental facts regarding particle interactions, and I probe deeper the concepts of synchronic and diachronic identity emerging from this approach.

The aim of this paper is to reconstruct and correct one argument in support of the symmetrization postulate in quantum mechanics. I identify the central premise of the argument as a thesis specifying a particular ontic property of quantum superpositions. The precise form of this thesis depends on some underlying assumptions of a metaphysical character. I compare the exchange degeneracy argument with alternative formal arguments for the symmetrization postulate, and I discuss the role and meaning of labels in the symmetric/antisymmetric representations of the states of many particles.

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

As it is well known, Jan Lukasiewicz invented his three-valued logic as a result of philosophical considerations concerning the problem of determinism and the status of future contingent sentences. In the article I critically analyse the thesis that the sentential calculus introduced by Lukasiewicz himself actually fulfills his philosophical assumptions. I point out that there are some counterintuitive features of Lukasiewicz three-valued logic. Firstly, there is no clear explanation for adopting specific truth-tables for logical connectives, such as conjunction, disjunction and first of all implication. Secondly, it is by no means clear, why certain classical logical principles should be invalid for future contingents. And thirly, I show that within Lukasiewicz logic it is possible to construct a „paradoxical” sentence, namely a conditional which changes in time its logical value from truth to falsity. This fact obviously contradicts Lukasiewicz's philosophical reading of his three truth values, according to which true sentences are already positively determined, false sentences are negatively determined, and possible sentences are neither positively, nor negatively determined. Above-mentioned facts justify in my opinion the thesis that Lukasiewicz's three-valued logic does not satisfy his philosophical intuitions. For this purpose more appropriate seems to be sentential calculus based on the so-called supervaluation. It is three-valued, non-extentional calculus, which nevertheless preserves all tautologies of the classical logic. At the end of the article I consider the possibility of introducing to this calculus modal operators

The author presents and critically analyses different accounts of causal relation given by the main representants of Lvov-Warsaw School in philosophy. Although there are considerable differences between particular approaches to this problem, it is possible at least to distinguish the key questions, analysed and anwsered by these philosophers. Among them are such questions as: how to define „causal relation”, what are its formal features, what is the space-time localization of the effect and the cause, what are causal laws

This is an attempt to formulate (along the line of H. Field's nominalization program) purely qualitative versions of two theories of space time: Galilean and Minkowskian theories. The starting point is to present qualitative theory for affine geometry, which is based only on one primitive predicate: „between”. Then it is shown that with the help of this predicate whole mathematical structure of affine geometry can be reconstructed as a simple definitional extension. As a next step it is shown in details how the same procedure can be carried out for both theories mentioned above

This is a response to a critical review of my book Non-locality and Possible Worlds (Ontos Verlag, Frankfurt 2006) by Witold Strawiński. I present arguments why counterfactual conditionals are needed in the description of quantum-mechanical phenomena, and in particular in the analysis of the condition of locality. I rebut arguments against my choice of the relation of similarity between possible worlds offered by W. Strawiński and M. Dickson. In the later part of the article I address some other issues raised by my critics, such as the problem of the truth value of the antecedents of true counterfactuals, the problem of the semantic relation between sentences and events, and various shortcomings of my formulations of the condition of locality. In my response to the specific criticism of the definition of free-choice events, I agree with the charge that my definition is satisfied by all actual events. I present a correction to the definition which uses the distinction between actual events and merely possible events