Discusses Armstrong's and Roman Ingarden's ontology, criticises substance ontology, and defends tropes and a field ontology.

This volume portrays the Polish or Lvov-Warsaw School, one of the most influential schools in analytic philosophy, which, as discussed in the thorough introduction, presented an alternative working picture of the unity of science.

This thesis explores attempts to characterise the structure of reality. Three notions stand out: Lewisian naturalness, Sider’s ‘structure’, and grounding, where the latter has become the most popular way to characterise the structure of reality in the contemporary literature. I argue that none of these notions, as they are currently understood, are suited for limning the metaphysical structure of reality. In the first part of the thesis I argue that, by the lights of the relevant theories, both naturalness and structure (...) fall short of the theoretical role carved out for those posits. In the second part of the thesis I present two challenges to the ‘orthodox’ conception of grounding. The first contests the standard assumption that grounding is asymmetric, both by citing what I take to be best described as symmetric instances of grounding, and by developing and arguing for a new theory of metaphysical structure – ‘metaphysical interdependence’ – which takes grounding to be nonsymmetric. The second challenge concerns the relationship between grounding and explanation, and leads to a dilemma for the grounding theorist. My proposed resolution to the dilemma is to adopt an antirealist approach to grounding, which I further motivate and develop in the final chapter. (shrink)

Brentano's theory of consciousness has garnered a surprising amount of attention in recent philosophy of mind. Here I argue for a novel interpretation of Brentano's theory that casts it as more original than previously appreciated and yet quite plausible upon inspection. According to Brentano's theory, as interpreted here, a conscious experience of a tree is a mental state that can be simultaneously thought of, or framed, equally accurately as an awareness of a tree or an awareness of an awareness of (...) a tree. (shrink)

In his excellent book, Four-Dimensionalism: An Ontology of Persistence and Time (Sider, 2001), Theodore Sider defends a version of four-dimensionalism which he calls the ‘stage-theory’. This paper focuses on Sider's argument from vagueness and argues that, due to the problematic nature of the argument from vagueness, Sider’s case in favor of four-dimensionalism is in the end not successful.

This paper addresses questions of universality related to ontological engineering, namely aims at substantiating (negative) answers to the following three basic questions: (i) Is there a ‘universal ontology’?, (ii) Is there a ‘universal formal ontology language’?, and (iii) Is there a universally applicable ‘mode of reasoning’ for formal ontologies? To support our answers in a principled way, we present a general framework for the design of formal ontologies resting on two main principles: firstly, we endorse Rudolf Carnap’s principle of logical (...) tolerance by giving central stage to the concept of logical heterogeneity, i.e. the use of a plurality of logical languages within one ontology design. Secondly, to structure and combine heterogeneous ontologies in a semantically well-founded way, we base our work on abstract model theory in the form of institutional semantics, as forcefully put forward by Joseph Goguen and Rod Burstall. In particular, we employ the structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining a general concept of heterogeneous, distributed, highly modular and structured ontologies, called hyperontologies. Moreover, we distinguish, on a structural and semantic level, several different kinds of combining and aligning heterogeneous ontologies, namely integration, connection, and refinement. We show how the notion of heterogeneous refinement can be used to provide both a general notion of sub-ontology as well as a notion of heterogeneous equivalence of ontologies, and finally sketch how different modes of reasoning over ontologies are related to these different structuring aspects. (shrink)

This book is a survey of the most important developments in Austrian philosophy in its classical period from the 1870s to the Anschluss in 1938. Thus it is intended as a contribution to the history of philosophy. But I hope that it will be seen also as a contribution to philosophy in its own right as an attempt to philosophize in the spirit of those, above all Roderick Chisholm, Rudolf Haller, Kevin Mulligan and Peter Simons, who have done so much (...) to demonstrate the continued fertility of the ideas and methods of the Austrian philosophers in our own day. For some time now, historians of philosophy have been gradually coming to terms with the idea that post-Kantian philosophy in the German-speaking world ought properly to be divided into two distinct traditions which we might refer to as the German and Austrian traditions, respectively. The main line of the first consists in a list of personages beginning with Kant, Fichte, Hegel and Schelling and ending with Heidegger, Adorno and Bloch. The main line of the second may be picked out similarly by means of a list beginning with Bolzano, Mach and Meinong, and ending with Wittgenstein, Neurath and Popper. As should be clear, it is the Austrian tradition that has contributed most to the contemporary mainstream of philosophical thinking in the Anglo-Saxon world. For while there are of course German thinkers who have made crucial contributions to the development of exact or analytic philosophy, such thinkers were outsiders when seen from the perspective of native German philosophical culture, and in fact a number of them found their philosophical home precisely in Vienna. When, in contrast, we examine the influence of the Austrian line, we encounter a whole series of familiar and unfamiliar links to the characteristic concerns of more recent philosophy of the analytic sort. As Michael Dummett points out in his Origins of Analytic Philosophy, the newly fashionable habit of referring to analytic philosophy as "Anglo-American" is in this light a "grave historical distortion". If, he says, we take into account the historical context in which analytic philosophy developed, then such philosophy "could at least as well be called "Anglo-Austrian" (1988, p. 7). Much valuable scholarly work has been done on the thinking of Husserl and Wittgenstein, Mach and the Vienna Circle. The central axis of Austrian philosophy, however, which as I hope to show in what follows is constituted by the work of Brentano and his school, is still rather poorly understood. Work on Meinong or Twardowski by contemporary philosophers still standardly rests upon simplified and often confused renderings of a few favoured theses taken out of context. Little attention is paid to original sources, and little effort is devoted to establishing what the problems were by which the Austrian philosophers in general were exercised -- in spite of the fact that many of these same problems have once more become important as a result of the contemporary burgeoning of interest on the part of philosophers in problems in the field of cognitive science. (shrink)

The ancient puzzle of Dion and Theon has given rise to a surprising array of apparently implausible views. For example, in order to solve the puzzle, several philosophers have been led to deny the existence of their own feet, others have denied that objects can gain and lose parts, and large numbers of philosophers have embraced the thesis that distinct objects can occupy the same space, having all their material parts in common. In this paper, I argue for an alternative (...) approach: I claim that human beings have ordinary parts—hands, heads, feet, and so on—but no extraordinary parts, such as ‘foot-complements’, the existence of which is essential to the puzzle. I rebut three objections to this approach: an objection that it is unacceptably metaphysically arbitrary, an objection that the view is incompatible with versions of the puzzle involving decapitation, and an objection concerning masses of matter. If we can believe that there are such things as hands and feet without involving ourselves in paradox, and without accepting large numbers of co-located material objects that share all their material parts, then that is what we should do. My view is the only known alternative which allows this. (shrink)

In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if according to fragment (...) B 6 such a possibility requires the existence of “the smallest”, while according to the general principle stated in fragment B 3 there is not “the smallest” but always only “a smaller”? This paper showcases the perplexity of these two questions but deals only with the former. The answer follows from Anaxagoras’ being a thoroughgoing infinitist in the way in which no Greek physicist was: the principle of space isotropy operative in geometry is extended to physics as well. So any two parts of the original mixture are similar to each other not only in view of the smaller-larger relation but also because each contains everything that the other one contains. This in effect means that at the stage of maximal possible heterogeneity each part of any part contains infinitely many heterogeneous parts of any kind whatsoever. So, neither can there be homogeneous parts in view of any qualitative property, nor can there be predominance in quantity of parts of any kind that would make some property manifest. (shrink)

Are there atoms in the constitution of things? Or is everything made of atomless ‘gunk’ whose proper parts have proper parts? Anaxagoras is the first gunk lover in the history of metaphysics. For him gunk is not only a theoretical possibility that cannot be ruled out in principle. Rather, it is a view that follows cogently from his metaphysical analysis of the physical world of our experience. What is distinctive about Anaxagoras’s take on gunk is not only what motives the (...) view, but also the particular type of gunk that he develops. It is qualitative gunk, rather than material gunk. Anaxagoras’s ontology was developed before matter was ‘invented’. It includes quality tropes only; they are gunky. The resulting metaphysical view – a world of qualitative gunk – is new, in the sense of being hitherto unexplored; and yet, it is derived from Anaxagoras’s writings. Drawing on Anaxagoras’s insights, this paper offers a sketch of what qualitative gunk ontology l.. (shrink)

Online collection of papers by Devitt, Dretske, Guarino, Hochberg, Jackson, Petitot, Searle, Tye, Varzi and other leading thinkers on philosophy and the foundations of cognitive Science. Topics dealt with include: Wittgenstein and Cognitive Science, Content and Object, Logic and Foundations, Language and Linguistics, and Ontology and Mereology.

Mereology, the theory of parts and wholes, is sometimes used as a framework for categorisation because it is regarded as ontologically innocent in the sense that the mereological fusion of some entities is nothing over and above the entities. In this paper it is argued that an adequate answer to the question of whether the thesis of the ontological innocence of mereology holds relies crucially on the underlying theory of reference. It is then shown that upholding the thesis comes at (...) high costs, viz. at the cost of a quite strong logical background theory or at paradoxical ways of predicating and counting. (shrink)

Suppose we believe that a property F is coextensive with moral permissibility. F may be, for example, the property of having the best consequences, if we are Consequentialists, or that of conforming to a universalisable maxim, if we are Kantians, and so on. This may raise the following problem. It is plausible that permissibility is “closed under implication”: any act that is implied by a permissible act must itself be permissible. Yet, in some cases, F might not be closed under (...) implication. If that is so, then F cannot be coextensive with permissibility. Maximalism has been proposed as a solution to this problem. A “maximal” act is one not implied by any other act. Maximalism restricts the claim that F is coextensive with permissibility to maximal acts only. A non-maximal act may be permissible without being F if it is implied by a maximal act that is F. The general aim of this paper is to investigate these issues by considering the formal structure of acts, or the “act-implication” relation. Discussions of Maximalism have tended to assume implicitly that acts have structure of some sort, but there has been little careful attention given to this structure. I aim to show that, by thinking about structure, we can provide a stronger defence of Maximalism. (shrink)

I show how existing concepts of supervenience relate to two more fundamental ontological relations: determination and dependence. Determination says that the supervenient properties of a thing are a function of its base properties, while dependence says that having a supervenient property implies having a base property. I show that most varieties of supervenience are either determination relations or determination relations conjoined with dependence relations. In the process of unpacking these connections I identify limitations of existing concepts of supervenience and provide (...) ways of overcoming them. What results is a more precise, flexible, and powerful set of tools for relating sets of properties than current concepts of supervenience provide. I apply these tools to a recalcitrant problem in the physicalism literature – the problem of extras. (shrink)

Constituent ontologies maintain that the properties of an object are either parts or something very much like parts of that object. Recently, such a view has been criticized as leading to a bizarre and problematic form of substance dualism and implying the existence of impossible objects. After briefly presenting constituent and relational ontologies, I respond to both objections, arguing that constituent ontology does not yield either of these two consequences and so is not shown to be an unacceptable ontological framework.

The problem of the many threatens to show that, in general, there are far more ordinary objects than you might have thought. I present and motivate a solution to this problem using many-one identity. According to this solution, the many things that seem to have what it takes to be, say, a cat, are collectively identical to that single cat.

A scientific explanatory project, part-whole explanation, and a kind of science, part-whole science are premised on identifying, investigating, and using parts and wholes. In the biological sciences, mechanistic, structuralist, and historical explanations are part-whole explanations. Each expresses different norms, explananda, and aims. Each is associated with a distinct partitioning frame for abstracting kinds of parts. These three explanatory projects can be complemented in order to provide an integrative vision of the whole system, as is shown for a detailed case study: (...) the tetrapod limb. My diagnosis of part-whole explanation in the biological sciences as well as in other domains exploring evolved, complex, and integrated systems (e.g., psychology and cognitive science) cross-cuts standard philosophical categories of explanation: causal explanation and explanation as unification. Part-whole explanation is itself one essential aspect of part-whole science. (shrink)

Two kinds of explanation might be put forward. The first goes like this: the necessary connection between the location of a whole and the location of its parts holds because the location of the whole is nothing but the collective location of its parts. The second style of explanation goes like this: the connection holds because what it is for a material whole to have something as a part, is (perhaps among other things) for the whole to contain the part.

In some sense, survival seems to be an intrinsic matter. Whether or not you survive some event seems to depend on what goes on with you yourself —what happens in the environment shouldn’t make a difference. Likewise, being a person at a time seems intrinsic. The principle that survival seems intrinsic is one factor which makes personal fission puzzles so awkward. Fission scenarios present cases where if survival is an intrinsic matter, it appears that an individual could survive twice over. (...) But it’s well known that standard notions of “intrinsicality” won’t do to articulate the sense in which survival is intrinsic, since ‘personhood’ appears to be a maximal property. We formulate a sense in which survival and personhood (and perhaps other maximal properties) may be almost intrinsic—a sense that would suffice, for example, to ground fission arguments. It turns out that this notion of almost-intrinsicality allows us to formulate a new version of the problem of the many. (shrink)

Worlds where things divide forever ("gunk" worlds) are apparently conceivable. The conceivability of such scenarios has been used as an argument against "nihilist" or "near-nihilist" answers to the special composition question. I argue that the mereological nihilist has the resources to explain away the illusion that gunk is possible.

I consider a grand, yet neglected proposal put forward by Shoemaker—a functionalist theory of all properties. I argue that two possible ways of developing this proposal meet with substantial objections. However, if we are prepared to endorse an ontology of tropes, one of these functionalist analyses can be developed into an original and informative theory of properties.

This paper considers the philosophical interpretation of the concept of svabhāva, sometimes translated as 'inherent existence' or 'own-being', in the Madyamaka school of Buddhist philosophy. It is argued that svabhāva must be understood as having two different conceptual dimensions, an ontological and a cognitive one. The ontological dimension of svabhāva shows it to play a particular part in theories investigating the most fundamental constituents of the world. Three different understandings of svabhāva are discussed under this heading: svabhāva understood as essence, (...) as substance, and as the true nature of phenomena (absolute svabhāva). The cognitive dimension shows svabhāva as playing an important rôle in our everyday conceptualization of phenomena. Svabhāva is here seen as a superimposition (samāropa) which the mind projects onto the world. (shrink)

Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of (...) empty parts, in delivering a balanced and bounded metaphysics of naive space. (shrink)

I argue that the existence of a necessary concrete being can be derived from an exceedingly weak causal principle coupled with two contingent truths one of which falls out of very popular positions in contemporary analytic metaphysics. I then show that the argument resists a great many objections commonly lodged against natural theological arguments of the cosmological variety.

Some philosophers assume that our ordinary parts-whole concepts are intuitive and univocal. Moreover, some assume that mereology—the formal theory of parts-whole relations—adequately captures these intuitive and univocal notions. Lewis, for example, maintains that mereology is “perfectly understood, unproblematic, and certain.” Following his lead, many assume that expressions such as ‘is part of’ are univocal, topic-neutral, and that compositional monism is true. This paper explores the rejection of –. I argue that our ordinary parts-whole expressions are polysemous; they have multiple distinct, (...) but related, interpretations or meanings. I canvass several criteria by which to test for polysemy, and apply these criteria to some of our parts-whole terminology. I also examine some philosophical examples involving abstracta and abstract parts, which give us additional reasons to think that our parts-whole expressions are polysemous and topic-specific. Yet if so, then compositional pluralism is true. (shrink)

It has been argued by some that the argument from vagueness is one of the strongest arguments in favor of the theory of temporal parts. I will neither support nor dispute this claim here. Rather, I will present a version of the argument from vagueness, which – if successful – commits one to the existence of modal parts. I argue that a commitment to the soundness of the argument from vagueness for temporal parts compels one to commit to the soundness (...) of the argument from vagueness for modal parts. I say compels, but not entails; an objection to one of the arguments highlights analogous ways to reject the other, making it difficult to endorse one and reject the other. This would be a significant conclusion, if true, since there are far fewer who currently commit themselves to modal parts than the many who currently commit themselves to temporal parts. (shrink)

Many of us think that ordinary objects – such as tables and chairs – exist. We also think that ordinary objects have parts: my chair has a seat and some legs as parts, for example. But once we are committed to the thesis that ordinary objects are composed of parts, we then open ourselves up to a whole host of philosophical problems, most of which center on what exactly the composition relation is. Composition as Identity is the view that the (...) composition relation is the identity relation. While such a view has some advantages, there are many arguments against it. In this essay, I will briefly canvass three different varieties of Composition as Identity, and suggest why one of them should be preferred over the others. Then I will outline several versions of the most common objection against CI. I will suggest how a CI theorist can respond to these charges by maintaining that some of the arguments are invalid. (shrink)

Many of us think that ordinary objects – such as tables and chairs – exist. We also think that ordinary objects have parts: my chair has a seat and some legs as parts, for example. But once we are committed to the (seemingly innocuous) thesis that ordinary objects are composed of parts, we then open ourselves up to a whole host of philosophical problems, most of which center on what exactly the composition relation is. Composition as Identity (CI) is the (...) view that the composition relation is the identity relation. While such a view has some advantages, there are many arguments against it. In this essay, I will briefly canvass three different varieties of Composition as Identity, and suggest why one of them should be preferred over the others. Then I will outline several versions of the most common objection against CI. I will suggest how a CI theorist can respond to these charges by maintaining that some of the arguments are invalid. (In part 2, I show how a CI theorist can maintain that the remaining arguments, while valid, are unsound). (shrink)

Many of us think that ordinary objects – such as tables and chairs – exist. We also think that ordinary objects have parts: my chair has a seat and some legs as parts, for example. But once we are committed to the (seemingly innocuous) thesis that ordinary objects are composed of parts, we then open ourselves up to a whole host of philosophical problems, most of which center on what exactly this composition relation is. Composition as Identity (CI) is the (...) view that the composition relation is the identity relation. While such a view has some advantages, there are many arguments against it. In this essay, I discuss several versions of the most common objection against CI, and show how the CI theorist can maintain that these arguments – contrary their initial intuitive appeal – are nonetheless unsound. (shrink)

Disposition ascription has been discussed a good deal over the last few decades, as has the revisionary metaphysical view of ordinary, persisting objects known as 'fourdimensionalism'. However, philosophers have not merged these topics and asked whether four-dimensional objects can be proper subjects of dispositional predicates. This paper seeks to remedy this oversight. It argues that, by and large, four-dimensional objects are not suited to take dispositional predicates.

In Elder-Vass’s response to my critical discussion of his social ontology, it is maintained (1) that a social object is not identical with but is merely composed of its suitably interrelated parts, (2) that a social object is necessarily indistinguishable in terms of its causal capacities from its interrelated parts, and (3) that ontological individualism lacks an adequate ontological justification. In this reply, I argue that in view of (1) the so-called redescription principle defended by Elder-Vass ought to be reformulated (...) and renamed; that the conjunction of (1) and (2) renders social objects causally redundant; and that ontological individualism can be coherently formulated and theoretically justified within Elder-Vass’s own metaphysics of objects with causal powers. (shrink)

In this paper, we describe the conceptual elusiveness of the notion of function as used in engineering practice. We argue that it should be accepted as an ambiguous notion, and then review philosophical argumentations in which engineering functions occur in order to identify the consequences of this ambiguity. Function is a key notion in engineering, yet is used by engineers systematically in a variety of meanings. First, we demonstrate that this ambiguous use is rational for engineers by considering the role (...) of functions in design methods and by analysing the ambiguity in terms of Kuhn’s notion of methodological incommensurability. Second, we discuss ontological and mereological analyses of engineering functions and describe a proof that subfunctions cannot formally be taken as parts of the functions they decompose. Engineering functions figure sometimes in philosophical work and are then typically taken as having an unambiguous, well-defined meaning. Finally, we therefore revisit work in philosophy of technology on the dual nature of technical artefacts, in philosophy of science on functional and mechanistic explanations, and in philosophy of biology on biological functions, and explore the consequences of the fact that engineering function is an ambiguous notion. It is argued that one of these consequences may be that also the notion of biological function has an ambiguous meaning. (shrink)

I argue that Universalism (the thesis that mereological composition is unrestricted) entails Extensionalism (the thesis that sameness of composition is sufficient for identity) as long as the parthood relation is transitive and satisfies the Weak Supplementation principle (to the effect that whenever a thing has a proper part, it has another part disjoint from the first).

Peter Simons has argued that the expression ‘the universe’ is not a genuine singular term: it can name neither a single, completely encompassing individual, nor a collection of individuals. (It is, rather, a semantically plural term standing equally for every existing object.) I offer reasons for resisting Simons’s arguments on both scores.

I argue that the conjunction of perdurantism (the view that objects are temporally extended) and universalism (the thesis that any old class of things has a mereological fusion) gives rise to undesired complications when combined with certain plausible assumptions concerning the semantics of tensed statements.

Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., parts lacking proper parts. Standardly, this thesis is characterized by an axiom that says, more simply, that everything has atomic parts. Anthony Shiver has argued that this characterization is satisfied by models that are not atomistic, and is therefore inadequate. I argue that Shiver’s conclusion can and ought to be resisted, for the models in question are atomistic in the intended sense, and even though the standard (...) characterization does not say that everything is composed of atoms, it implies so. If there is a sense in which the relevant models are problematic, it lies elsewhere. (shrink)

We tend to talk about (refer to, quantify over) parts in the same way in which we talk about whole objects. Yet a part is not something to be included in an inventory of the world over and above the whole to which it belongs, and a whole is not something to be included in the inventory over and above its constituent parts. This paper is an attempt to clarify a way of dealing with this tension which may be labeled (...) the Minimalist View: An element in the field of a part-whole relation is to be included in an inventory of the world if and only if it does not overlap any distinct element that is itself included in the inventory. (shrink)

Every criminal act ought to be matched by a corresponding punishment, or so we may suppose, and every punishment ought to reflect a criminal act. We know how to count punishments. But how do we count crimes? In particular, how does our notion of a criminal action depend on whether the prohibited action is an activity, an accomplishment, an achievement, or a state?

There are conflicting intuitions concerning the status of a boundary separating two adjacent entities (or two parts of the same entity). The boundary cannot belong to both things, for adjacency excludes overlap; and it cannot belong to neither, for nothing lies between two adjacent things. Yet how can the dilemma be avoided without assigning the boundary to one thing or the other at random? Some philosophers regard this as a reductio of the very notion of a boundary, which should accordingly (...) be treated a mere façon de parler. In this paper I resist this temptation and examine some ways of taking the puzzle at face value within a realist perspective—treating boundaries as ontologically on a par with (albeit parasitic upon) extended parts. (shrink)

Whether certain objects compose a whole at a given time does not seem to depend on anything other than the character of those objects and the relations between them. This observation suggests a far-reaching constraint on theories of composition. One version of the constraint has been explicitly adopted by van Inwagen and rules out his own answer to the composition question. The constraint also rules out the other well-known moderate answers that have so far been proposed.

Mereotopology is an extension of mereology with some relations of topological nature like contact. An algebraic counterpart of mereotopology is the notion of contact algebra which is a Boolean algebra whose elements are considered to denote spatial regions, extended with a binary relation of contact between regions. Although the language of contact algebra is quite expressive to define many useful mereological relations and mereotopological relations, there are, however, some interesting mereotopological relations which are not definable in it. Such are, for (...) instance, the relation of n-ary contact, internal connectedness and some others. To overcome this disadvantage, we introduce a generalisation of contact algebra, replacing the contact with a binary relation between finite sets of regions and a region, satisfying some formal properties of Tarski consequence relation. The obtained system is called sequent algebra, considered as an algebraic counterpart of a new mereotopology. We develop the topological representation theory for sequent algebras showing in this way certain correspondence between point-free and point-based models of space. As a by-product, we show how one logical relation in nature notion, Tarski consequence relation, may have also certain spatial meaning. (shrink)

Salmon and Soames argue against nominalism about numbers and sentence types. They employ (respectively) higher-order and first-order logic to model certain natural language inferences and claim that the natural language conclusions carry commitment to abstract objects, partially because their renderings in those formal systems seem to do that. I argue that this strategy fails because the nominalist can accept those natural language consequences, provide them with plausible and non-committing truth conditions and account for the inferences made without committing themselves to (...) abstract objects. I sketch a modal account of higher-order quantification, on which instead of ranging over sets, higher order quantifiers are used to make (logical) possibility claims about which predicate tokens can be introduced. This approach provides an alternative account of truth conditions for natural language sentences which seem to employ higher-order quantification, thus allowing the nominalist to evade Salmon’s argument. I also show how the nominalist can account for the occurrence of apparently singular abstract terms in certain true statements. I argue that the nominalist can achieve this by, first, dividing singular terms into real singular terms (referring to concrete objects) and only apparent singular terms (called onomatoids), introduced for the sake of brevity and simplicity, and then providing an account of nominalistically acceptable truth conditions of sentences containing onomatoids. I develop such an account in terms of modally interpreted abstraction principles and argue that applying this strategy to Soames’s argument allows the nominalists to defend themselves. (shrink)

Mainstream metaphysics has been preoccupied by inquiring into the nature of major kinds of entities, like objects, properties and events, while avoiding minor entities, like shadows or holes. However, one might want to hope that dealing with such minor entities could be profitable for even solving puzzles about major entities. I propose a new ontological puzzle, the Shadow of Constitution Puzzle, incorporating the old puzzle of material constitution, with shadows in the role of the minor entity to guide our approach (...) to the issues involved. I then analyze the standard answers to the original puzzle of constitution, in their role as potential solutions to the new puzzle. Finally, I discuss three views that can solve the proposed puzzle. (shrink)

The signature of the formal language of mereology contains only one binary predicate P which stands for the relation “being a part of”. Traditionally, P must be a partial ordering, that is, ${\forall{x}Pxx, \forall{x}\forall{y}((Pxy\land Pyx)\to x=y)}$ and ${\forall{x}\forall{y}\forall{z}((Pxy\land Pyz)\to Pxz))}$ are three basic mereological axioms. The best-known mereological theory is “general extensional mereology”, which is axiomatized by the three basic axioms plus the following axiom and axiom schema: (Strong Supplementation) ${\forall{x}\forall{y}(\neg Pyx\to \exists z(Pzy\land \neg Ozx))}$ , where Oxy means ${\exists (...) z(Pzx\land Pzy)}$ , and (Fusion) ${\exists x\alpha \to \exists z\forall y(Oyz\leftrightarrow \exists x(\alpha \land Oyx))}$ , for any formula α where z and y do not occur free. In this paper, I will show that general extensional mereology is decidable, and will also point out that the decidability of the first-order approximation of the theory of complete Boolean algebras can be shown in the same way. (shrink)

The signature of the formal language of mereology contains only one binary predicate which stands for the relation “being a part of” and it has been strongly suggested that such a predicate must at least define a partial ordering. Mereological theories owe their origin to Leśniewski. However, some more recent authors, such as Simons as well as Casati and Varzi, have reformulated mereology in a way most logicians today are familiar with. It turns out that any theory which can be (...) formed by using the reformulated mereological axioms or axiom schemas is in a sense a subtheory of the elementary theory of Boolean algebras or of the theory of infinite atomic Boolean algebras. It is known that the theory of partial orderings is undecidable while the elementary theory of Boolean algebras and the theory of infinite atomic Boolean algebras are decidable. In this paper, I will look into the behaviors in terms of decidability of those mereological theories located in between. More precisely, I will give a comprehensive picture of the said issue by offering solutions to the open problems which I have raised in some of my papers published previously. (shrink)

It is customary practice to define ‘x is composed of the ys’ as ‘x is a sum of the ys and the ys are pairwise disjoint ’. This predicate has played a central role in the debate on the special composition question and on related metaphysical issues concerning the mereological structure of objects. In this note we show that the customary characterization is nonetheless inadequate. We do so by constructing a mereological model where everything qualifies as composed of atoms even (...) though some elements in the domain are gunky, i.e., can be divided indefinitely into smaller and smaller proper parts. (shrink)