Graph Theory and the Identity of Indiscernibles

The mathematical field of graph theory has recently been used to provide counterexamples to the Principle of the Identity of Indiscernibles. In response to this, it has been argued that appeal to relations between graphs allows the Principle to survive the counterexamples. In this paper, I aim to show why that proposal does not succeed

Strategies for defending the Principle of Identity of Indiscernibles: a critical survey and a new approach

The Principle of Identity of Indiscernibles (PII) is the focus of much controversy in the history of Metaphysics and in contemporary Physics. Many questions rover the debate about its truth or falsehood, for example, to which objects the principle applies? Which properties can be counted as discerning properties? Is the principle necessary? In other words, which version of the principle is the correct and is this version true? This thesis aims to answer this questions in order to show that PII is a necessarily true principle of metaphysics. To accomplish this task, the reader will find, in this thesis, an encyclopaedical introduction to the history of PII and to the reasons it matters so much, followed by a presentation of the most famous arguments against it and the defences used against these arguments. Then, the reader finds in-depth discussion of the minutiae involved in postulating the principle as to make clear what is in fact being attacked and defended. With these preliminaries solved, a deeper analysis of these defences is presented aiming to discover which is the most appropriate example to use against the attacks to the principle. This analysis allowed a classification of these defences in four families with different strategies within them. Finally, with these defensive strategies at hand we are able to confront alleged counterexamples to PII in Mathematics with the intention to test these defences

Grades of individuality. A pluralistic view of identity in quantum mechanics and in the sciences

This paper offers a critical assessment of the current state of the debate about the identity and individuality of material objects. Its main aim, in particular, is to show that, in a sense to be carefully specified, the opposition between the Leibnizian ‘reductionist’ tradition, based on discernibility, and the sort of ‘primitivism’ that denies that facts of identity and individuality must be analysable has become outdated. In particular, it is argued that—contrary to a widespread consensus— ‘naturalised’ metaphysics supports both the acceptability of non-qualitatively grounded (both ‘contextual’ and intrinsic) identity and a pluralistic approach to individuality and individuation. A case study is offered that focuses on non-relativistic quantum mechanics, in the context of which primitivism about identity and individuality, rather than being regarded as unscientific, is on the contrary suggested to be preferable to the complicated forms of reductionism that have recently been proposed. More generally, by assuming a plausible form of anti-reductionism about scientific theories and domains, it is claimed that science can be regarded as compatible with, or even as suggesting, the existence of a series of equally plausible grades of individuality. The kind of individuality that prevails in a certain context and at a given level can be ascertained only on the basis of the specific scientific theory at hand

Taxonomias para os argumentos e contra-argumentos no debate sobre o princípio de identidade dos indiscerníveis

Este artigo visa apresentar uma taxonomia original dos argumentos mais difundidos contra o Princípio de Identidade dos Indiscerníveis ao longo da história da Filosofia, mas focando em versões defendidas no século XX e XXI; bem como uma taxonomia das respostas mais efetivas para esses argumentos usados no início do século XXI com uma breve avaliação sobre quais são as mais efetivas para cada argumento de ataque. O leitor também encontrará uma bibliografia atualizada sobre os debates envolvendo esses argumentos e contra-argumentos nas seções correspondentes. Palavras-chave: Virtudes epistêmicas. História da Filosofia. Louis Rougier. Liberalismo

The ontology of haecceities

This thesis deals with the Problem of Distinction, i.e. what explains the distinction of two substances, especially when they are qualitatively indiscernible? It argues that the best solution to this problem is an ontology of haecceities, properties like “being identical with X” which is unique for X and responsible for its individuation. This is achieved in two steps. In the first half of the thesis (Chapters 2 to 5), the nature of the Problem of Distinction is clarified and Principles of Evaluations of the solution to the Problem of Distinction are set out. Then based on these Principles, the thesis argues against the main extant non-haecceity solutions to the Problem of Distinction including the Spacetime Points Solution, Bare Particularism, Trope Theory, and the Universal Bundle Theory. In the second half of the thesis (Chapters 6 to 9), it develops a novel ontology of haecceities. A Haecceity Mereology with three rules is proposed. According to this ontology, the reality is constituted by two fundamental kinds of properties, universals and haecceities. An individual substance is a special mereological sum of a haecceity and its correspondent universals. Hence, there are two distinct substances because of the distinction of two haecceities. Besides solving the Problem of Distinction, the ontology of haecceities also explains many other things such as the unity of substances. Further, we argue that, although our knowledge of substances is epistemically fallible, the relationship between a haecceity and its correspondent universals is metaphysically necessary

An Analysis of Persistence

‘Something persists iff it exists at more than one time’ asserts Lewis. How things persist takes two forms: ‘something perdures iff it persists by having different temporal parts, or stages, at different times’ whereas ‘it endures iff it persists by being wholly present at more than one time. Lewis’ words show insight although some of their import has been overlooked. The debate has been articulated mainly around the interplay between theories of time and persistence, oblivious of the evidence that Lewis’ definitions embed philosophically ubiquitous and crucial notions like existence (and identity) which deserves to be investigated. In addition, the inquiry has often moved from time to persistence: e.g. teasing out the features that a specific view of time had which yielded a specific theory of persistence, whereas as it has recently been urged the relationship between views of time and persistence might be more relaxed: any theory of time could fit with any theory of persistence. This thesis is an exploration of persistence, time, and existence (and to a lesser extent identity) to make sense of whether and how the first could affect the others. The investigation is restricted to material objects (though little depends upon this), and to how and why the intuitions and common sense considerations in the background of perdurance, the theory of persistence I sympathise with, motivate a specific theory of time, i.e. eternalism; and finally how both afford a specific notion of existence, to wit a view of existence a là Quine, according to which existence is delimited by true uses of the existential quantifier. Thus, the direction of investigation will be from persistence, via time, to existence. The reason for this is that change is an undeniable datum of experience for which we have robust intuitions and common sense considerations, whilst time, although pervasive, is so in an elusive way which is hard to pin down. The thesis is divided into three parts which mirror the three main topics spelt out above. In the first part, a case of a persisting object will be used to show that our common sense thinking and intuitions harbour a predicament: it appears plausible to believe that there is a fact of the matter whether an object is or is not one and the same although we may not be able pin down the reason why. This will be clarified without supposing these intuitions and common sense considerations to be inviolable. The focus will be on two main contenders, perdurance and endurance, and what discriminates between them: the notion of temporal parts. Their centrality makes it decisive to understand what temporal parts are and what they do. It will be argued that whilst the debate has reached a stalemate in attempting to define temporal parts, the notion rests upon a robust basis of intuitions and common sense considerations which draw upon our ordinary understanding of parts in space, and this is sufficient to give a working grasp of them as well as the potential for a definition which stands scrutiny. It has also been argued that temporal parts are decisive in solving some puzzling situations; therefore I will examine one of these, the long-standing problem of change, and show that there is a sense in which it might not be a genuine metaphysical problem. Leibniz’s Law is a law of logic and it is best formulated accordingly; whereas the way it is used to generate the problem of change is metaphysically loaded. The problem of change as a metaphysical problem is thus deflated but, it will be argued, there are better, more intuitive, ways of motivating perdurance. The intelligibility and possibility of temporal parts, and hence perdurantism, has been shown to rely on the thought that reality is four-dimensional, so that in addition to the three spatial dimensions in which reality uncontentiously extends, there is a fourth, time, along which similarly reality extends. In the second part I shall consider if what philosophers have said about this stands scrutiny. Philosophers have argued that space and time share some decisive features (the similarity thesis); it might be hoped that investigating what they have said will clarify whether and how time could be so considered. I will argue that such an investigation will leave the space/time analogy wanting, and therefore I shall endeavour to venture a tentative picture of time which could accommodate the similarity thesis as well as a view of time as extended. I will then take a brief look into the current debate in the philosophy of time and tease out what the different theories of time are really about, their basic assumptions which are supposed to make manifest how each view sees time and what they try to defend as basic features of it. I will make clear why perdurance’s four-dimensional view of reality is most appealing if combined with an eternalist view of time according to which every time co-exists; both four-dimensionalism and eternalism sharing the assumption that time is a dimension through which things extend. In the third part, I unveil the nexus between perdurance, eternalism, and the notion of existence. I argue that perdurance’s basic assumption that reality is four-dimensional which is shared by eternalism, motivates a view of existence a là Quine, since it guarantees an existentially closed domain of existents, which is what perdurance and eternalism imply. The overall conclusion is that once unpacked, perdurance, eternalism, and a view of existence a là Quine fit together in a way in which each one motivates the others. Each has intuitions and assumptions that it tries to preserve and defend; intuitions and assumptions which might not be preserved if the theories are combined differently

Homotopy Type Theory and Structuralism

I explore the possibility of a structuralist interpretation of homotopy type theory (HoTT) as a foundation for mathematics. There are two main aspects to HoTT's structuralist credentials. First, it builds on categorical set theory (CST), of which the best-known variant is Lawvere's ETCS. I argue that CST has merit as a structuralist foundation, in that it ascribes only structural properties to typical mathematical objects. However, I also argue that this success depends on the adoption of a strict typing system which undermines the metaphysical seriousness of this structuralism. Homotopy type theory adds to CST a distinctive theory of identity between sets, which arguably allows its objects to be seen as ante rem structures. I examine the prospects for such a view, and address many other interpretive problems as they arise

Properties and powers

This thesis concerns the relation between the fundamental properties and the powers they confer. The views considered are introduced in terms of their acceptance or rejection of the quiddistic thesis. Essentially the quiddistic thesis claims that properties confer the powers they do neither necessarily nor sufficiently. Quidditism is the view that accepts the quiddistic thesis. The other two views to be considered, the pure powers view and the grounded view reject the quiddistic thesis. The pure powers view supports its denial of the quiddistic thesis with the claim that properties consist in conferring the powers they do; the possession of a property just is the possession of a power. The grounded view, the positive view of this thesis, rejects the idea that properties are constituted by conferring the causal powers they do. Rather on the grounded view, it is the natures of the fundamental properties that metaphysically explain why they confer the powers they do

Humean Metaphysics and the Philosophy of Science

Humeanism is often taken to be a prime example of metaphysics which has failed to be sufficient attention to contemporary science. I argue that these claims have been made too hastily: there are moves available to Humeans which bring the account closer to scientific practice while still preserving the spirit of the view. The thesis comprises two parts. In the first half, I deal with the Best System Account of laws, and consider how it ought to treat initial conditions. From there, I turn to the question of whether Humean laws can explain events. This has recently been a topic of renewed interest in the literature and I disentangle the various claims philosophers have made on behalf of Humeanism. From these, I identify three promising responses to the argument that Humean explanations are circular. In the second half of the thesis, I consider how the Humean approach to laws can be extended to cover symmetry principles when the latter are understood as laws of laws. In response to a problem concerning properties and language, I suggest that the account go language-relative. The result of this is a regularity-based approach that can incorporate both laws and their symmetries into a single unified framework. Finally, I draw upon some examples from biology to indicate how the account can deal with the special sciences