Tomasz Bigaj

The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying Łukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form "X will be the case at time t" is true (resp. false) at time t, then this sentence must be already true (resp. false) at present. However, it is easy to see that this principle is violated in Lukasiewicz's original calculus (as the cases of the law of excluded middle and the law of contradiction show). Nevertheless it is possible to construct (either with the help of the notion of "supervaluation", or purely algebraically) a different three-valued, semi-classical sentential calculus, which would properly incorporate Łukasiewicz's initial intuitions. Algebraically, this calculus has the ordinary Boolean structure, and therefore it retains all classically valid formulas. Yet because possible valuations are no longer represented by ultrafilters, but by filters (not necessarily maximal), the new calculus displays certain non-classical metalogical features (like, for example, nonextensionality and the lack of the metalogical rule enabling one to derive "p is true or q is true" from" 'p ∨ q' is true"). The second part analyses whether the proposed calculus could be useful in formalizing inferences in situations, when for some reason (epistemological or ontological) our knowledge of certain facts is subject to limitation. Special attention should be paid to the possibility of employing this calculus to the case of quantum mechanics. I am going to compare it with standard non-Boolean quantum logic (in the Jauch-Piron approach), and to show that certain shortcomings of the latter can be avoided in the former. For example, I will argue that in order to properly account for quantum features of microphysics, we do not need to drop the law of distributivity. Also the idea of "reading off" the logical structure of propositions from the structure of Hilbert space leads to some conceptual troubles, which I am going to point out. The thesis of the paper is that all we need to speak about quantum reality can be acquired by dropping the principle of bivalence and extensionality, while accepting all classically valid formulas.

In this paper I discuss some metaphysical consequences of an unorthodox approach to the problem of the identity and individuality of “indistinguishable” quantum particles. This approach is based on the assumption that the only admissible way of individuating separate components of a given system is with the help of the permutation-invariant qualitative properties of the total system. Such a method of individuation, when applied to fermionic compositions occupying so-called GMW-nonentangled states, yields highly implausible consequences regarding the number of distinct components of a given composite system. I specify the problem in detail, and I consider several strategies of solving it. The preferred solution of the problem is based on the premise that spatial location should play a privileged role in identifying and making reference to quantum-mechanical systems.

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.

Three basic positions regarding the nature of fundamental properties are: dispositional monism, categorical monism and the mixed view. Dispositional monism apparently involves a regress or circularity, while an unpalatable consequence of categorical monism and the mixed view is that they are committed to quidditism. I discuss Alexander Bird's defence of dispositional monism based on the structuralist approach to identity. I argue that his solution does not help standard dispositional essentialism, as it admits the possibility that two distinct dispositional properties can possess the same stimuli and manifestations. Moreover, Bird's argument can be used to support the mixed view by relieving it of its commitment to quidditism. I briefly analyse an alternative defence of dispositional essentialism based on Leon Horsten's approach to the problem of circularity and impredicativity. I conclude that the best option is to choose Bird's solution but amend the dispositional perspective on properties. According to my proposal, the essences of dispositions are determined not directly by their stimuli and manifestations but by the role each property plays in the structure formed by the stimulus/manifestation relations.