Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...) the other. I suggest that ‘i’ functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this? (shrink)

Structural universals are a kind of complex universal. They have been put to work in a variety of philosophical theories but are plagued with problems concerning their compositional nature. In this article, we will discuss the following questions. What are structural universals? Why believe in them? Can we give a consistent account of their compositional nature? What are the costs of doing so?

Philosophers almost universally believe that concepts of supervenience fail to satisfy the standards for physicalism because they offer mere property correlations that are left unexplained. They are thus compatible with non-physicalist accounts of those relations. Moreover, many philosophers not only prefer some kind of functional-role theory as a physically acceptable account of mind-body and other inter-level relations, but they use it as a form of “superdupervenience” to explain supervenience in a physically acceptable way. But I reject a central part of (...) this common narrative. I argue that functional-role theories fail by the same standards for physicalism because they merely state without explaining how a physical property plays or occupies a functional role. They are thus compatible with non-physicalist accounts of that role-occupying relation. I also argue that one cannot redeploy functional-role theory at a deeper level to explain role occupation, specifically by iterating the role-occupant scheme. Instead, one must use part-whole structural and mechanistic explanations that differ from functional-role theory in important ways. These explanations represent a form of “superduperfunctionalism” that stand to functional-role theory as concepts of superdupervenience stand to concepts of supervenience. (shrink)

Some philosophers have claimed that kinds can be construed as mereologically complex structural properties. This essay examines several strategies aimed at construing a certain class of natural kinds, namely isomeric chemical kinds, in accordance with this view. In particular, the essay examines views which posit structural proper parts in addition to micro-constitutive parts to individuate isomeric chemical kinds. It then goes on to argue that the phenomenon of chirality in stereochemistry gives the proponent of kinds-as-complex-properties evidence for positing the existence (...) of causal-cum-dispositional individuating proper parts, in addition to structural parts, for chemical enantiomeric kinds. (shrink)

The different occurrences of a word in a sentence cannot be identified with the one word type, nor with its many tokens. What then are occurrences of a word? How can one type occur more than once in another type? Is the conception of ‘structural universals’ that leads to these questions incoherent, as Lewis maintained? I argue against the answer Wetzel suggested, which identifies sentences with functions from numbers to expressions, and propose instead that occurrences of one type in another (...) are subtypes with different relative positions in the whole. Types have subtypes as well as tokens. Occurrences in non-symmetrical types like sequences are individuated by their relative positions in the type. Occurrences in a symmetrical whole have different positions but stand in the same relations to the other components. They are numerically different subtypes that do not differ from each other qualitatively. (shrink)

Contemporary theories of universals have two things in common: first, they are unable to account for necessary connections between universals that form a structure. Second, they leave teleology out of their accounts of instantiation. These facts are not unrelated; the reason why contemporary theories have such trouble is they neglect the ancient idea that universals are ends at which nature aims. If we want a working theory of universals, however, we must return to this idea. Despite its unpopularity among realists, (...) teleology is not a disposable eccentricity, and its dismissal is not an improvement on ancient views. (shrink)

The aim of this paper is to elucidate the mereological structure of complex states of affairs without relying on the problematic notion of structural universals. For this task tools from graph theory, lattice theory, and the theory of relational systems are employed. Our starting point is the mereology of similarity structures. Since similarity structures are structured sets, their mereology can be considered as a generalization of the mereology of sets..

This accessible essay treats knowledge and belief in a usable and applicable way. Many of its basic ideas have been developed recently in Corcoran-Hamid 2014: Investigating knowledge and opinion. The Road to Universal Logic. Vol. I. Arthur Buchsbaum and Arnold Koslow, Editors. Springer. Pp. 95-126. http://www.springer.com/birkhauser/mathematics/book/978-3-319-10192-7 .

The work presents the concept of a structural universal and the criticisms that have been leveled against it. A structural universal is a property had by an individual due to the nature of its proper parts and due to the relations obtaining between those parts. Mellor has argued that there is no reason to accept such universal in addition to the basic universals that compose them. David Lewis has argued –on the other hand– that it has not been satisfactorily explained (...) how universals are composed by other universals. The composition by which a structural universal is given cannot be a set-theoretical construction or a mereological sum. Several proposals to explain the nature of structural universals are discussed. Finally it is argued that a structural universal should be understood as a complexion of higher-order universals. (shrink)

This paper rejects metaphysical realism about structural universals as a basis for mathematical realism about numbers, and argues that one construal of structural universals via non-well-founded sets should be resisted by the mathematical realist.

I present in this article a new theory of structural properties or, more precisely, of structural kinds, such as being methane. According to this theory, structural kinds are kinds that are both emergent and sustained in their existence. In the first section, I introduce structural properties and four problems that affect the most widely held conception of them, namely, the pictorial conception. In the second section, I introduce some theses about emergence, powers, emergent powers, relations and structures that I have (...) defended in other works and that constitute the basis on which my theory of structural kinds is built up. In the third section, I eventually develop my theory in full detail and show how it can solve the problems mentioned in the second section. Finally, in the fourth section, I face five objections and briefly compare my account with some other accounts of structural properties. (shrink)

In my article I present David Armstrong's stance on properties, relations, particulars and states of affairs. I introduce this categories to show, at the most general level, his metaphysical system called factualism. My article consists of four parts, in each one I characterize following categories: 1. Properties 2. Relation 3. Particulars 4. States of affairs. I also discuss Armstrong's arguments considering the nature of those categories and their role in his philosophy. Also, I try to emphasis differences between Armstrong's factualism (...) and other contemporary metaphysical positions (Bundle theory and Trop theory). (shrink)

Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calculi with their morphisms is defined and both types of fibring (constrained and unconstrained) are introduced. The introduced morphisms induce a novel notion of translation between logics (...) which preserves metaproperties in a strong sense. Finally, some preservation features are explored. (shrink)

When we begin to investigate the persistence of objects through time, we find immediately that the sort of concerns embodied in Leibniz's Law cause philosophers to divide themselves into the two major camps of Purdurantists and Endurantists. What is required according to each for a given object at a given time to be identified with a given object at another time is held to be dramatically different, even while both often look to the same general sort of indicators for their (...) answers to identity questions: identity or similarity of physical properties, including relational properties like spatial location. I believe, however, that logically prior to the problem of the persistence of objects through time will be questions regarding the composition of objects--we must have coherent notions of what an object is, what it means for parts to compose an object, and what is required for an object to be considered to exist at a single time before we can discuss the continued existence of objects at other times. I believe that posing the problem of temporal gaps for both the Perdurantist and Endurantist to solve can help us uncover reasonable answers to these more basic questions, and thereby help us judge the comparative coherence of the parent theories. Towards this goal, we investigate here some of the assumptions of persistence theories--that Perdurantists are four-dimensionalists and Endurantists are Presentists, for example--before moving on to find reasonable explanations of the composition of objects from within each theory. Important at this stage is clarifying such concepts as parthood and the present. When we at length turn our attention to the problem of gaps, it becomes useful to distinguish two sorts of gaps, each with their own difficulties: a 'gap' as a length of time during which the proper parts of an object are scattered through space, and a 'gap' as a length of time during which the proper parts of an object do not exist in space at all. My contention here is that Perdurantism, paired with four-dimensional spacetime, provides the most coherent answers to the challenges presented throughout. (shrink)