Tomasz Bigaj

Spacetime substantivalists insist that spatiotemporal points are fundamental entities and thus are ontologically independent from the physical objects occupying these points.This chapter argues that the best metaphysical option for the substantivalist is to adopt a radical version of structural essentialism, according to which participation in a certain relational structure is both a necessary and sufficient condition of identity for the elements characterized by this structure.It comparesthe author’sproposed variant of essentialism with some alternative conceptions, such as Tim Maudlin’s metric essentialism and David Glick’s Minimal Structural Essentialism. It discusses how the author’sRadical Structural Essentialism deals with the challenge of the hole argument as well as some less well-known challenges, such as the problem of contingent counterfactuals regarding the material contents of spacetime, and the ‘mole’ argument. Later the chapter explains why the structure consisting of the metric tensor is a genuinely relational structure, and itdefend the claim that in order to preserve the identity of its elements the actual structure may be merely embeddable in (and not necessarily isomorphic with) an alternative structure.

This article concerns the problem of identity and individuality of quantum particles. It has been suggested that ensembles of indistinguishable particles (e.g. electrons) can be treated in the way that is analogous to the way we refer to continuous matter using so-called mass terms (such as “water”). In the article I give several arguments against interpreting quantum predicates as mass terms. While the ontological interpretation of quantum objects as mass density fields determined by their wave functions is not uncommon in quantum mechanics (it features e.g. in the GRW interpretation of quantum theory), it is controversial to treat fragments of these fields as representing genuine entities picked out by quantum predicates. I point out that proper parts of electron matter-fields do not possess the same kinds of properties as whole electrons. Also, there are some measurable properties of ensembles of particles that cannot be recovered by describing a homogenized distribution of mass density. This problem affects both entangled and non-entangled states. In conclusion I opt for an approach (known as heterodoxy) according to which it is possible to individuate same-type particles momentarily using symmetric projectors.

According to quantifier generalism, all facts about the world can be expressed in a language devoid of proper names, whose only referential expressions are variables bound by quantifiers. This paper considers and repels some of the recently raised objections against this position. The central part of the paper presents a critical analysis of the claim advanced by Ted Sider that quantifier generalism is inevitably holistic and therefore requires unusually strong expressive resources when applied to infinite domains. Using an example of arithmetic, it is shown that there is a simple generalistic description of natural numbers that does not resort to any infinitary conjunctions or quantifiers. Such generalistic accounts also exist in many cases involving continua (such as descriptions of matter distribution in a continuous space). Moreover, these accounts are arguably superior to their individualistic counterparts due to their parsimony. In addition to that, Sider’s argument alleging that generalism cannot account for the difference between non-isomorphic models of arithmetic is repelled.

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.

This book analyzes metaphysical consequences of the quantum theory of many particles with respect to the fundamental notions of identity, individuality and discernibility. The main focus is on the proper interpretation of the quantum formalism in relation to the role of permutation invariance and the adequate representation of the properties of individual subsystems. Two main approaches to the issue of the individuation of quantum particles are distinguished and thoroughly discussed. These approaches differ radically with respect to their metaphysical consequences – while one of them implies the complete indiscernibility of quantum particles of the same kind, the other one restores the possibility of discerning individual particles by their properties. We connect the problem of quantum individuation and discernibility with an analysis of the concept of quantum entanglement, and we also discuss identity over time and in counterfactual scenarios.

This book contains a non-specialist introduction to modern physics and its formal and conceptual apparatus, with an emphasis on its philosophical aspects. It presents the development of the most important concepts and problems of physics, from ancient astronomical theories, through Newtonian mechanics, thermodynamics, the theory of electromagnetism, to both theories of relativity and quantum mechanics. It discusses in detail related philosophical questions, such as the issue of determinism and predictability, the dispute over the nature of time and space, the ontological status of physical fields, and the testing and acceptance of empirical theories. The book can be useful to students of philosophy interested in the philosophical aspects of physical sciences, and to students of natural sciences who want to supplement their specialist knowledge with philosophical issues.

The debate between individualism and generalism (qualitativism) concerns, inter alia, the question of whether qualitative identity implies numerical identity. One important argument against the affirmative answer to this question is based on an analysis of cases known as symmetry-breaking indeterministic processes, including the case of a collapsing tower. Generalism implies that all processes of that kind are deterministic, contrary to our snap judgment. This article contains a multifaceted analysis of the above argument against generalism, taking into account its metaphysical, scientific and modal aspects. It is suggested that the intuition of indeterminism regarding the considered cases can be explained by a distinct phenomenon of indeterminacy affecting the diachronic identity of participating objects. It is also observed that both individualism and generalism are unable to formulate a theory which could make definite predictions that are more specific than the ones made in purely qualitative language. This strongly suggests that the purported indeterminism of the considered scenarios is not genuine. Finally, the modal analysis shows how generalism is capable of expressing the idea of alternative possibilities without violating the fundamental assumption of determinism. This approach is based on the Lewisian counterpart semantics for quantified modal logic with same-world counterparts.

Boris Kment formulates two challenges to anti-haecceitism: one based on the concept of chance, and the other involving counterfactuals. In this paper I refute the chance-based argument by appropriately reformulating its premises in a non-individualistic language. Regarding the argument from counterfactuals I consider three strategies of defense. The strategy that is ultimately accepted as most promising is a revamped approach based on the distinction between possible worlds and possibilities. I counter Kment’s claim that the introduction of fine-grained possibilities within possible worlds is haecceitism in disguise. My conclusion is that anti-haecceitism survives the criticism, and is an overall more attractive position than its competitor.

The debate between individualism and generalism (qualitativism) concerns the status of individualistic facts and their relations with qualitative facts. It is argued that a proper definition of individualistic facts should be a modal one, and moreover that it requires the assumption of haecceitism for its adequacy, contrary to the common belief. Consequently, the positions of individualism and generalism are dependent upon the more fundamental stances of haecceitism and anti-haecceitism in the metaphysics of modality de re.

In this article we undertake a diagnosis of the state of ontology as it is currently practiced in Poland. We point to the strengths of Polish ontology and the aspects that should be improved in order for Polish ontology to flourish further.We cover different styles of thinking in Polish ontology, as well as different methodologies. We address threads influencing Polish ontology, both substantive, as well as those of an organizational, cultural and institutional nature. Apart from the ontologists, this paper also includes the opinions of scholars from the hard sciences, which allows us to shed light on Polish ontology from outside the philosophical community. The article presents concrete steps that could improve and strengthen Polish ontology in the future.We also present here thirty examples of important contributions to ontology by Polish ontologists.

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.

The main goal of the paper is to revisit the concept of a symmetry for relational structures in light of the ontological position dubbed “essentialist structuralism”. It is argued that the standard definition of the notion of a symmetry commits us to the existence of non-qualitative, haecceitistic differences between possible worlds. An alternative notion of symmetry is developed, based on the distinction between essential and contingent structures. It is claimed that this new concept is better suited for the doctrine of structuralism, and moreover it offers a new perspective on some well-known problems in the foundation of physical theories, such as the problem of permutation invariance in quantum mechanics and diffeomorphism invariance in general relativity.

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.

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.