Tomasz Bigaj

It is commonplace to formalize propositions involving essential properties of objects in a language containing modal operators and quantifiers. Assuming David Lewis’s counterpart theory as a semantic framework for quantified modal logic, I will show that certain statements discussed in the metaphysics of modality de re, such as the sufficiency condition for essential properties, cannot be faithfully formalized. A natural modification of Lewis’s translation scheme seems to be an obvious solution but is not acceptable for various reasons. Consequently, the only safe way to express some intuitions regarding essential properties is to use directly the language of counterpart theory without modal operators.

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.

An important part of the influential Humean doctrine in philosophy is the supervenience principle (sometimes referred to as the principle of separability). This principle asserts that the complete state of the world supervenes on the intrinsic properties of its most fundamental components and their spatiotemporal relations (the so-called Humean mosaic). There are well-known arguments in the literature purporting to show that in quantum mechanics the Humean supervenience principle is violated, due to the existence of entangled states. Recently, however, arguments have been presented to the effect that the supervenience principle can be defended in Bohmian mechanics. The key element of this strategy lies in the observation that according to Bohmian mechanics the fundamental facts about particles are facts about their spatial locations, and moreover, for any proper subsystem of the world its state may non-trivially depend on the spatial configuration of the rest of the universe. Thus quantum-mechanical states of subsystems do not represent their intrinsic properties but rather characterize their relations with the environment. In this paper we point out the worry that this Bohmian strategy --known as Bohumianism-- saves the letter but not the spirit of the Humean doctrine of supervenience, since it prima facie violates another seemingly important Humean principle, which we call Strong Supervenience and whose denial implies the existence of necessary connections among distinct individuals. We argue that the best defense for Bohumians is to question the fundamental existence of complex physical systems and their states by treating any reference to them as a convenient description of the underlying collection of Bohmian particles. We consider several pros and cons of this strategy.

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.

One of the basic assumptions of David Lewis's formal semantics of counterfactuals is that the crucial relation of comparative similarity between possible worlds is a linear ordering.Yet there are arguments that when we take into account relativistic features of space-time, this relationshould be only a partial ordering. The first part of the paper deals with the question of how to formulate appropriatetruth conditions for counterfactuals under the supposition of a partial ordering of possible worlds. Such truthconditions will be put forward, and it will be argued that they are more general than those proposed in recentliterature, because they turn out to be applicable also when the so-called Limit Assumption is not met. The secondpart analyzes two relativistically invariant ways of interpreting spatiotemporal counterfactuals with antecedentsreferring to free-chance point events. After briefly examining key differences between these two approaches,the issue of their extension for a broader class of antecedents will be addressed. Following the approach of Finkelstein, who has proposed a specifically designed similarity relation between possible worlds, servingas a generalization tool in the case of one of the above intuitions, the possibility of a similar extension forthe second interpretation will be considered. The main result of the paper is the theorem to the effect that thegeneralization of the second intuition is impossible to obtain. More specifically, the theorem proved in the paperstates that there is no similarity relation which together with the Lewis-style truth conditions for counterfactualswould imply the second of the above interpretations as a special case. Some consequences of thistheorem for the applicability of the Lewis logic of counterfactuals to quantum phenomena will be briefly mentionedat the end of the paper.

The existence of non-local correlations between outcomes of measurements in quantum entangled systems strongly suggests that we are dealing with some form of causation here. An assessment of this conjecture in the context of the collapse interpretation of quantum mechanics is the primary goal of this paper. Following the counterfactual approach to causation, I argue that the details of the underlying causal mechanism which could explain the non-local correlations in entangled states strongly depend on the adopted semantics for counterfactuals. Several relativistically-invariant interpretations of spatiotemporal counterfactual conditionals are discussed, and the corresponding causal stories describing interactions between parts of an entangled system are evaluated. It is observed that the most controversial feature of the postulated causal connections is not so much their non-local character as a peculiar type of circularity that affects them.

David Lewis’s latest theory of causation defines the causal link in terms of the relation of influence between events. It turns out, however, that one event’s influencing another is neither a necessary nor sufficient condition for its being a cause of that event. In the article one particular case of causality without influence is presented and developed. This case not only serves as a counterexample to Lewis’s influence theory, but also threatens earlier counterfactual analyses of causation by admitting a particularly troublesome type of preemption. The conclusion of the article is that Lewis’s influence method of solving the preemption problem fails, and that we need a new and fresh approach to the cases of redundant causation if we want to hold on to the counterfactual analysis of causation

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 book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world semantics of quantum counterfactuals using David Lewis's famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactuals semantics to strengthen Bell's theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell's theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation.

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 article deals with one particular problem created by the counterfactual analysis of causality à la Lewis, namely the context-sensitivity problem or, as I prefer to call it, the background condition problem. It appears that Lewis’ counterfactual definition of causality cannot distinguish between proper causes and mere causal conditions – i.e. factors necessary for the effect to occur, but commonly not seen as causally efficacious. The proposal is put forward to amend the Lewis definition with a condition, based on the notion of cotenability, which would eliminate the problem. It is shown that the corrected definition of causality leads to the transitivity of the causal relation. Possible objections to the proposed solution, involving the assumption of indeterminism and the preemption cases, are given a thorough consideration.

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

This book contains a concise introduction to one of the most fundamental branches of philosophy, which deals with reality and its nature. Among the topics discussed are such metaphysical questions as "Are we fundamentally free?", "Does time really pass?", "Are there any abstract objects?", "What is causation?", "What are necessary and possible truths?". The book is aimed at absolute beginners, so it does not presuppose any previous knowledge of philosophy from the reader. For those who would like to pursue the subject a bit deeper, the book comes equipped with an extended list of further reading.

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