The analytical philosophy of the last hundred years has been heavily influenced by a doctrine to the effect that the key to the correct understanding of reality is captured syntactically in the ‘Fa’ (or, in more sophisticated versions, in the ‘Rab’) of standard first order predicate logic. Here ‘F’ stands for what is general in reality and ‘a’ for what is individual. Hence “f(a)ntology”. Because predicate logic has exactly two syntactically different kinds of referring expressions—‘F’, ‘G’, ‘R’, etc., and ‘a’, (...) ‘b’, ‘c’, etc.—so reality must consist of exactly two correspondingly different kinds of entity: the general (properties, concepts) and the particular (things, objects). We describe the historical influence of this view, and also show how standard first-order predicate logic can be used for the logical formalization of a more adequate “six category ontology”, which recognizes, at the level of both particulars and universals, not only things or objects but also events and qualities. (shrink)

Once we assume that objects are bundles of tropes, we want to know how the latter cohere. Are they held together by a substratum, are they linked by external relations or do they cling to one another by internal relations? This paper begins by exploring the reasons for eliminating the first two suggestions. Defending that the third option can be made plausible, it advances the following thesis: Maintaining that tropes are held in a compresence by appropriately qualified internal relations avoids (...) the consequence that such properties will be essential to the object. The specific targets of the second part of the paper include, first, a more precise description of the notion of a cohesive internal relation, and second, an explanation of how alteration is possible in an object the particular properties of which hold together by qualified internal relations. (shrink)

For over 20 years, Jaegwon Kim’s Causal Exclusion Argument has stood as the major hurdle for non-reductive physicalism. If successful, Kim’s argument would show that the high-level properties posited by non-reductive physicalists must either be identical with lower-level physical properties, or else must be causally inert. The most prominent objection to the Causal Exclusion Argument—the so-called Overdetermination Objection—points out that there are some notions of causation that are left untouched by the argument. If causation is simply counterfactual dependence, for example, (...) then the Causal Exclusion Argument fails. Thus, much of the existing debate turns on the issue of which account of causation is appropriate. In this paper, however, I take a bolder approach and argue that Kim’s preferred version of the Causal Exclusion Argument fails no matter what account one gives of causation. Any notion of causation that is strong enough to support the premises of the argument is too strong to play the role required in the logic of the argument. I also consider a second version of the Causal Exclusion Argument, and suggest that although it may avoid the problems of the first version, it begs the question against a particular form of non-reductive physicalism, namely emergentism. (shrink)

The development of a defensible and fecund notion of emergence has been dogged by a number of threshold issues neatly highlighted in a recent paper by Jaegwon Kim. We argue that physicalist assumptions confuse and vitiate the whole project. In particular, his contention that emergence entails supervenience is contradicted by his own argument that the ‘microstructure’ of an object belongs to the whole object, not to its constituents. And his argument against the possibility of downward causation is question-begging and makes (...) false assumptions about causal sufficiency. We argue, on the contrary, for a rejection of the deeply entrenched assumption, shared by physicalists and Cartesians alike, that what basically exists are things (entities, substances). Our best physics tells us that there are no basic particulars, only fields in process. We need an ontology which gives priority to organization, which is inherently relational. Reflection upon the fact that all biological creatures are far-from-equilibrium systems, whose very persistence depend upon their interactions with their environment, reveals incoherence in the notion of an ‘emergence base’. (shrink)

In considering the nature of properties four controversial decisions must be made. (1) Are properties universals or tropes? (2) Are properties attributes of particulars, or are particulars just bundles of properties? (3) Are properties categorical (qualitative) in nature, or are they powers? (4) If a property attaches to a particular, is this predication contingent, or is it necessary? These choices seem to be in a great degree independent of each other. The author indicates his own choices.

The identity of indiscernibles states that indiscernible objects must be identical. Many philosophers have held that the PII turns out to be either true but trivial, or non-trivial but false, depending on how the notion of discernibility is spelled out. In this paper, I propose and defend an account of this notion which aims to yield a minimally non-trivial and yet plausible version of the PII. I argue moreover that this version of the principle is immune to a number of (...) well-known and recent objections to the PII. (shrink)

In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.

Many philosophers are baffled by necessity. Humeans, in particular, are deeply disturbed by the idea of necessary laws of nature. In this paper I offer a systematic yet down to earth explanation of necessity and laws in terms of invariance. The type of invariance I employ for this purpose generalizes an invariance used in meta-logic. The main idea is that properties and relations in general have certain degrees of invariance, and some properties/relations have a stronger degree of invariance than others. (...) The degrees of invariance of highly-invariant properties are associated with high degrees of necessity of laws governing/describing these properties, and this explains the necessity of such laws both in logic and in science. This non-mysterious explanation has rich ramifications for both fields, including the formality of logic and mathematics, the apparent conflict between the contingency of science and the necessity of its laws, the difference between logical-mathematical, physical, and biological laws/principles, the abstract character of laws, the applicability of logic and mathematics to science, scientific realism, and logical-mathematical realism. (shrink)

Universals are usually considered to be universal properties. Since tropes are particular properties, if there are only tropes, there are no universals. However, universals might be thought of not only as common properties, but also as common aspects (“determinable universals”) and common wholes (“concrete universals”). The existence of these two latter concepts of universals is fully compatible with the assumption that all properties are particular. This observation makes possible three different trope theories, which accept tropes and no universals, tropes and (...) determinable universals and tropes and concrete universals. (shrink)

Dans cet article je présente une analyse critique de l’approche habituelle de l’identité mathématique qui a son origine dans les travaux de Frege et Russell, en faisant un contraste avec les approches alternatives de Platon et Geach. Je pose ensuite ce problème dans un cadre de la théorie des catégories et montre que la notion d’identité ne peut pas être « internalisée » par les moyens catégoriques standards. Enfin, je présente deux approches de l’identité mathématique plus spécifiques: une avec la (...) fibration catégorielle et l’autre avec des catégories supérieures faibles. (shrink)

Dans cet article je présente une analyse critique de l’approche habituelle de l’identité mathématique qui a son origine dans les travaux de Frege et Russell, en faisant un contraste avec les approches alternatives de Platon et Geach. Je pose ensuite ce problème dans un cadre de la théorie des catégories et montre que la notion d’identité ne peut pas être « internalisée » par les moyens catégoriques standards. Enfin, je présente deux approches de l’identité mathématique plus spécifiques: une avec la (...) fibration catégorielle et l’autre avec des catégories supérieures faibles. (shrink)

This paper is an articulation and defense of a trope-bundle theory of material objects. After some background remarks about objects and tropes, I start the main defense in Section III by answering a charge frequently made against the bundle theory, namely that it commits a conceptual error by saying that properties are parts of objects. I argue that there’s a general and intuitive sense of “part” in which properties are in fact parts of objects. This leads to the question of (...) qualitative unity: in virtue of what are certain properties unified as parts of an object? In Section IV I defend an account of unity for complex material objects. It turns on the thesis that the properties of such objects are structural properties. After addressing some objections, I turn in Section V to the question of unity for simple material objects. Here a different and more radical account is needed, for simples, since they do not have structural properties, are not subsumed by the account of Section IV. I defend the view that a simple object just is a simple property, so that identity delivers the desired unity. (shrink)

Trope theory is the view that the world is a world of abstract particular qualities. But if all there is are tropes, how do we account for the truth of propositions ostensibly made true by some concrete particular? A common answer is that concrete particulars are nothing but tropes in compresence. This answer seems vulnerable to an argument (first presented by F. H. Bradley) according to which any attempt to account for the nature of relations will end up either in (...) contradiction, nonsense, or will lead to a vicious infinite regress. I investigate Bradley’s argument and claim that it fails to prove what it sets out to. It fails, I argue, because it does not take all the different ways in which relation and relata may depend on one another into account. If relations are entities that are distinct from yet essentially dependent upon their relata, the Bradleyan problem is solved. We are then free to say that tropes in compresence are what make true propositions ostensibly made true by concrete particulars. (shrink)

This paper explores the fundamental ideas that have motivated the idea of emergence and the movement of emergentism. The concept of reduction, which lies at the heart of the emergence idea is explicated, and it is shown how the thesis that emergent properties are irreducible gives a unified account of emergence. The paper goes on to discuss two fundamental unresolved issues for emergentism. The first is that of giving a “positive” characterization of emergence; the second is to give a coherent (...) explanation of how “downward” causation, a central component of emergentism, is able to avoid the problem of overdetermination. (shrink)

In this article, we present a new conception of internal relations between quantity tropes falling under determinates and determinables. We begin by providing a novel characterization of the necessary relations between these tropes as basic internal relations. The core ideas here are that the existence of the relata is sufficient for their being internally related, and that their being related does not require the existence of any specific entities distinct from the relata. We argue that quantity tropes are, as determinate (...) particular natures, internally related by certain relations of proportion and order. By being determined by the nature of tropes, the relations of proportion and order remain invariant in conventional choice of unit for any quantity and give rise to natural divisions among tropes. As a consequence, tropes fall under distinct determinables and determinates. Our conception provides an accurate account of quantitative distances between tropes but avoids commitment to determinable universals. In this important respect, it compares favorably with the standard conception taking exact similarity and quantitative distances as primitive internal relations. Moreover, we argue for the superiority of our approach in comparison with two additional recent accounts of the similarity of quantity tropes. (shrink)

In this article, we propose a new trope nominalist conception of determinate and determinable kinds of quantitative tropes. The conception is developed as follows. First, we formulate a new account of tropes falling under the same determinates and determinables in terms of internal relations of proportion and order. Our account is a considerable improvement on the current standard account (Campbell 1990; Maurin 2002; Simons 2003) because it does not rely on primitive internal relations of exact similarity or quantitative distance. The (...) internal relations of proportion and order hold because the related tropes exist; no kinds of tropes need be assumed here. Second, we argue that there are only pluralities of tropes in relations of proportion and order. The tropes mutually connected by the relations of proportion and order form a special type of plurality, tropes belonging to the same kind. Unlike the recent nominalist accounts, we do not identify kinds of tropes with any further entities (e.g. sets) or abstractions from entities (e.g. pluralities of similar tropes). (shrink)

According to realist structuralism, mathematical objects are places in abstract structures. We argue that in spite of its many attractions, realist structuralism must be rejected. For, first, mathematical structures typically contain intra-structurally indiscernible places. Second, any account of place-identity available to the realist structuralist entails that intra-structurally indiscernible places are identical. Since for her mathematical singular terms denote places in structures, she would have to say, for example, that 1 = − 1 in the group (Z, +). We call this (...) the identity problem and conclude that nominalism is presently the safest route for the structuralist. (shrink)

Nominalism in formal ontology is still the thesis that the only acceptable domain of quantification is the first-order domain of particulars. Nominalists may assert that second-order well-formed formulas can be fully and completely interpreted within the first-order domain, thereby avoiding any ontological commitment to second-order entities, by means of an appropriate semantics called “substitutional”. In this paper I argue that the success of this strategy depends on the ability of Nominalists to maintain that identity, and equivalence relations more in general, (...) is first-order and invariant. Firstly, I explain why Nominalists are formally bound to this first-order concept of identity. Secondly, I show that the resources needed to justify identity, a certain conception of identity invariance, are out of the Nominalist’s reach. (shrink)

The aim of this work is to argue for the idea that processes and process-based entities are to be modelled as relational structures. Relational structures are genuine structures, namely entities not committed to the existence of basic objects. My argument moves from the analysis of Whitehead’s original insight about process-based entities that, despite some residual of substance metaphysics, has the merit of grounding the intrinsic dynamism of reality on the holistic and relational characters of process-based entities. The current model of (...) process ontology requires genuine emergence and this, in turn, requires organizations, i.e., emergence in organizations. Another view about processes rely on a structural specification of processes. I suggest that the two views can be made compatible by the help of a specific sort of structures, namely relational structures. The appeal to the mathematical theory of genuine structures, category theory, reveals the formal plausibility of this convergence. According to this formal approach, genuine structures are essentially dynamic entities for they are relational, namely, as well as organizations, they are not existentially committed to particulars. (shrink)