This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers such as 'whole', (...) 'together', and 'alone', nominal and adverbial quanitfiers ranging over parts, and expressions of completion such as 'completely' and 'partly'. (shrink)

ObjectiveThis paper explores the interrelation among the concepts of identity, individuality and indiscernibilty, primarily from the standpoint of contemporary western analytic ontology and logic.MethodI review, compare and evaluate the classical and the alternative approaches to identity. In this regard, I focus on the issue whether these purportedly alternative approaches do really provide us with alternative conceptions of identity, or they are considering some other forms of equivalence relations weaker than the relation of identity. Arguments for and against the Principles of (...) Indiscernibility of Identicals and Identity of Indiscernibles are delineated to unravel the connection between identity and indiscernibility. Various attempts to provide the definition of identity in terms of indiscernibility have also been evaluated.FindingsI argue that it is a verbal issue whether we use the term ‘identity’, when analysed in terms of indiscernibility, or ‘congruence’, but the underlying metaphysical issues are not simple. If identity is analysed in terms of indiscernibility, stipulation of one’s philosophical understanding of property and possession of properties in the concerned logic and ontology should be made in clear terms to avoid confusion. But there can also be ontological and logical frameworks where numerical identity and difference are not qualitatively explicable.ConclusionA pluralist stance, at least at the phenomenal level, is proposed to be maintained with regard to the explanation of the phenomenon of identity. This pluralist stance has also been proposed as a plausible metatheoretical framework of metaphysical debates. (shrink)

The Christian doctrine of the Trinity poses a serious philosophical problem. On the one hand, it seems to imply that there is exactly one divine being; on the other hand, it seems to imply that there are three. There is another well-known philosophical problem that presents us with a similar sort of tension: the problem of material constitution. We argue in this paper that a relatively neglected solution to the problem of material constitution can be developed into a novel solution (...) to the problem of the Trinity. (shrink)

Mereotopology is today regarded as a major tool for ontological analysis, and for many good reasons. There are, however, a number of open questions that call for an answer. Some are philosophical, others have direct applicative import, but all are crucial for a proper assessment of the strengths and limits of mereotopology. This paper is an attempt to put sum order in this area.

The object of this paper is to show why recent research in the psychology of deductive and probabilistic reasoning does not have.

In recent decades, a view of identity I call Sortalism has gained popularity. According to this view, if a is identical to b, then there is some sortal S such that a is the same S as b. Sortalism has typically been discussed with respect to the identity of objects. I argue that the motivations for Sortalism about object-identity apply equally well to event-identity. But Sortalism about event-identity poses a serious threat to the view that mental events are token identical (...) to physical events: A particular mental event m is identical with a particular physical event p only if there is a sortal S such that m and p are both Ss. If there is no such sortal, the doctrine of token-identity is not true. I argue here that we have no good reason for thinking that there is any such sortal. (shrink)

According to Zhiyi 智顗 (538–597), the founder of the Chinese Buddhist Tiantai school 天台宗, “one object is all objects;” hence, all objects are profoundly interconnected. In this paper, I critically examine Zhiyi’s metaphysics of objects as presented in the historical Tiantai texts and subsequently develop a contemporary and accessible thesis of interconnectedness by integrating Zhiyi’s views with resources from contemporary analytic philosophy, particularly relative identity. By drawing on Zhiyi’s insights and incorporating contemporary philosophical ideas, I also illustrate how historical Chinese (...) Buddhism and contemporary analytic metaphysics can be mutually informing. (shrink)

A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. (...) Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory. (shrink)

It is widely assumed that the identity relation is, among other things, transitive. Some have proposed that the identity relation might hold between objects contingently or occasionally. If, on those proposals, identity is shown to not be transitive, then there is reason to reject such proposals. One such argument attempts to show that the identity relation on such proposals violates transitivity in cases of ‘simultaneous’ fissions and fusion. I argue that, even in those cases, contingent identity and occasional identity are (...) transitive. (shrink)

In English, some common nouns, like 'dog', can combine with determiners like 'a' and 'many', but not with 'much', while other nouns, like 'water', can be used together with 'much', but not with 'a' and 'many'. These common nouns have been respectively called count nouns (CNs) and mass nouns (MNs). How do children learn to use CNs and MNs in the appropriate contexts? Gaining a better understanding of this is the goal of this paper. To do so, it is important (...) to first get clear on the nature of the distinction between CNs and MNs. Is it a grammatical distinction? Does the distinction apply to nouns, to their senses, or only to their occurrences within noun phrases (NPs)? Showing that the count-mass distinction really is grammatical and applies to nouns is the matter of my first part. Then the question occurs as to whether the distinction corresponds to a systematic difference in the sense of count and mass expressions. If it does, children's acquisition of the distinction may simply follow from their ability to learn the senses of these expressions and determiners. In a second part, I thus discuss various semantic characterizations that have been proposed, and make explicit the exceptions from which they suffer. Now, understanding the sense of an expression is interpreting it correctly as it occurs in an utterance. Formal characterizations of our interpretations help to clarify what is involved in learning and understanding these expressions. In my third part, I examine several formal characterizations with the purpose to specify what would be an adequate representation of the interpretations of mass and count nominal expressions. The understanding gained in these first three parts is used to identify what abilities are exercised by children when they acquire the count-mass distinction. The picture that emerges differs from earlier views of the acquisition in several respects. I thus describe these views and highlight the differences between them and my own proposal. In a final, fifth part, I critically examine the experimental evidence that proponents of some of the accounts of the acquisition of the count-mass distinction have cited in their favor. (shrink)

This essay examines an argument of perennial importance against naive Leibnizian absolute identity theory, originating with Ruth Barcan in 1947 (Barcan, R. 1947. ?The identity of individuals in a strict functional 3 calculus of second order?, Journal of Symbolic Logic, 12, 12?15), and developed by Arthur Prior in 1962 (Prior, A.N. 1962. Formal Logic. Oxford: The Clarendon Press), presented here in the form offered by Nicholas Griffin in his 1977 book, Relative Identity (Griffin, N. 1977. Relative Identity. Oxford: The Clarendon (...) Press). The objection considers the property of being necessarily identical to a specific object a as a counterexample to Leibnizian identity conditions, and more particularly to the indiscernibility of identicals, when it is only contingently true that a=b. The inquiry eliminates necessity and reference to a specifically designated object as responsible for the counterexample, leaving only identity. The requirements for an exact reinterpretation of Leibniz's Law in light of counterexamples involving converse intentional properties and the family of properties suggested by the property of being necessarily identical to a where a=b (or an equivalent definite descriptor variation) is only logically contingently true, are formalized in a more powerful, counterexample-resistant version of Leibniz's Law that does not succumb to relative identity as a necessary alternative motivated by desperation over the failure of the absolute identity principle. (shrink)

In English, some common nouns, like "cat", can be used in the singular and in the plural, while others, like "wate"r, are invariable. Moreover, nouns like "cat" can be employed with numerals like "one" and "two" and determiners like "a", "many" and "few", but neither with "much" nor "little". On the contrary, nouns like "milk" can be used with determiners like "much" and "little", but neither with "a", "one" nor "many". These two types of nouns constitute two morphosyntactic sub-classes of (...) English common nouns; cf. for instance Gillon (1992). They have been respectively called count nouns and mass nouns. In many languages, notably Romance and Germanic languages, one can similarly identify two morphosyntactic subclasses of common nouns, nouns of one class admitting singular and plural number, and nouns of the other being invariable in grammatical number. The question we want to address in this paper is one in lexical semantics: Is there anything characteristic about the meaning of a count noun? (shrink)

Traditionally, this puzzle has been solved in various ways. Aristotle, for example, distinguished between “accidental” and “essential” changes. Accidental changes are ones that don't result in a change in an objects' identity after the change, such as when a house is painted, or one's hair turns gray, etc. Aristotle thought of these as changes in the accidental properties of a thing. Essential changes, by contrast, are those which don't preserve the identity of the object when it changes, such as when (...) a house burns to the ground and becomes ashes, or when someone dies. Armed with these distinctions, Aristotle would then say that, in the case of accidental changes, (1) and (2) are both false—a changing thing can really change one of its “accidental properties” and yet literally remain one and the same thing before and after the change. (shrink)

Sortal concepts are at the center of certain logical discussions and have played a significant role in solutions to particular problems in philosophy. Apart from logic and philosophy, the study of sortal concepts has found its place in specific fields of psychology, such as the theory of infant cognitive development and the theory of human perception. In this monograph, different formal logics for sortal concepts and sortal-related logical notions are characterized. Most of these logics are intensional in nature and possess, (...) in addition, a bidimensional character. That is, they simultaneously represent two different logical dimensions. In most cases, the dimensions are those of time and natural necessity, and, in other cases, those of time and epistemic necessity. Another feature of the logics in question concerns second-order quantification over sortal concepts, a logical notion that is also represented in the logics. Some of the logics adopt a constant domain interpretation, others a varying domain interpretation of such quantification. Two of the above bidimensional logics are philosophically grounded on predication sortalism, that is, on the philosophical view that predication necessarily requires sortal concepts. Another bidimensional logic constitutes a logic for complex sortal predicates. These three sorts of logics are among the important novelties of this work since logics with similar features have not been developed up to now, and they might be instrumental for the solution of philosophically significant problems regarding sortal predicates. The book assumes a modern variant of conceptualism as a philosophical background. For this reason, the approach to sortal predicates is in terms of sortal concepts. Concepts, in general, are here understood as intersubjective realizable cognitive capacities. The proper features of sortal concepts are determined by an analysis of the main features of sortal predicates. Posterior to this analysis, the sortal-related logical notions represented in the above logics are discussed. There is also a discussion on the extent to which the set-theoretic formal semantic systems of the book capture different aspects of the conceptualist approach to sortals. These different semantic frameworks are also related to realist and nominalist approaches to sortal predicates, and possible modifications to them are considered that might represent those alternative approaches. (shrink)

P.T. Geach has maintained (see, e.g., Geach (1967/1968)) that identity (as well as dissimilarity) is always relative to a general term. According to him, the notion of absolute identity has to be abandoned and replaced by a multiplicity of relative identity relations for which Leibniz's Law - which says that if two objects are identical they have the same properties - does not hold. For Geach relative identity is at least as good as Frege's cardinality thesis which he takes to (...) be strictly connected with relative identity - according to which an ascription of cardinality is always relative to a concept which specifies what, in any particular case, counts as a unit. The idea that there is a close connection between relative identity and Frege's cardinality thesis has been issued again quite recently by Alston and Bennett in (1984). In their opinion, Frege's cardinality thesis is not only similar to relative identity - as Geach maintains - but it implies it. Moreover, they agree with Geach in claiming that a commitment to Frege's cardinality thesis forces a parallel commitment to relative identity. Against Geach, Alston and Bennett we will claim that (Tl): "Frege's cardinality thesis is similar to relative identity" is false and that therefore (T2) "Frege's cardinality thesis implies relative identity" is false as well. (shrink)

Cet ouvrage est consacre a l'etude de la distinction linguistique entre noms massifs (lait, mobilier, desordre, amour...) et noms comptables (chat, equipe, combat, chose...). Les premiers sont normalement invariables, tandis que les seconds s'emploient librement au singulier et au pluriel. Apres avoir etabli qu'il s'agit bien d'une distinction morpho-syntaxique, l'ouvrage discute la possibilite de caracteriser semantiquement cette distinction. Les recherches existantes ne tiennent compte, essentiellement, que des noms s'appliquant au domaine materiel. Ce travail, au contraire, examine en detail aussi bien (...) les noms concrets qu'abstraits. Il propose de redefinir les proprietes souvent attribuees aux noms massifs (references distributive et cumulative), grace, notamment, a une nouvelle notion de partie. Concernant les noms comptables, il montre qu'aucune propriete purement semantique n'est necessaire pour qu'un nom soit de ce type. L'ouvrage se termine par l'analyse des conversions (emplois massifs des noms comptables, et vice versa), et du role qu'y jouent les facteurs pragmatiques. (shrink)

The following considerations are to be seen in the framework of nontraditional theory of predication (NTP), which stems in its basic features from Sinowjew (cf. Sinowjew 1970, Sinowjew/Wessel 1975), and which is described in detail in Wessel 1989.

Whenever an object constitutes, makes up or composes another object, the objects in question share a striking number of properties. This paper is addressed to the question of what might account for the intimate relation and striking similarity between constitutionally related objects. According to my account, the similarities between constitutionally related objects are captured at least in part by means of a principle akin to that of strong supervenience. My paper addresses two main issues. First, I propose independently plausible principles (...) by means of which to delineate, in a non-ad-hoc, non-stipulative and non-circular fashion, those properties which can be expected to be shared among constitutionally related objects in virtue of their being so related from those which in general cannot be expected to be shared, or which are shared for other reasons. Secondly,I spell out in detail the nature of the supervenience-principle at work in this context. My account thus aims at isolating, in a methodologically responsible fashion, the particular sort of restricted indiscernibility principle which is a component of the constitution-relation. (shrink)

In this paper, I consider the philosophical consequences of one tradition in Trinitarian theology, which emphasizes that each of the persons of the Trinity is wholly God. I pay special attention to Leftow’s claim that the persons of the Godhead must be divine in the same sense of the word ‘divine’ as the Godhead itself. I argue that the existing philosophical account of the Trinity which best captures this view is what I have termed the ‘Strong Theory of Relative Identity,’ (...) first proposed Peter Geach. I then develop what I take to be the most pressing objection to this account of the Trinity, namely that it cannot be supplemented with a coherent model-theoretic semantics. I end with a suggestion for responding to this objection. (shrink)

Anderson-like ontological proofs, studied in this paper, employ contingent identity, free principles of quantification of the 1st order variables and classical principles of quantification of the 2nd order variables. All these theories are strongly complete wrt. classes of modal structures containing families of world-varying objectual domains of the 1st order and constant conceptual domains of the 2nd order. In such structures, terms of the 1st order receive only rigid extensions, which are elements of the union of all 1st order domains. (...) Terms of the 2nd order receive extensions and intensions. Given a family of preselected world-varying objectual domains of the 2nd order, non-rigid extensions of the 2nd order terms belong always to a preselected domain connected with a given world. Rigid intensions of the 2nd order terms are chosen from among members of a conceptual domain of the 2nd order, which is the set of all functions from the set of worlds to the union of all 2nd order preselected domains such that values of these functions at a given world belong to a preselected domain connected with this world. (shrink)

This paper is a modification of Nicola Guarino and Christopher Welty's conception of the subsumption relation. Guarino and Welty require that that whether one property may subsume the other should depend on the modal metaproperties of those properties. I argue that the part of their account that concerns the metaproperty carrying a criterion of identity is essentially flawed. Subsequently, I propose to constrain the subsumption relation not, as Guarino and Welty require, by means of incompatible criteria of absolute identity but (...) by means of incompatible criteria of relative identity. After discussing the benefits of applying relative identity in ontological investigations I provide a formal framework in which to prove a counterpart of the identity criteria constraint. (shrink)

We shall distinguish between sortal predication and standard predication. The former kind of predication necessarily involves sortal concepts but the latter, as it is customarily viewed, does not. It is generally thought that the only essential occurrence of a concept in a standard predication is the concept being predicated. In this paper, we shall put forward an alternative view. We shall propose to understand standard predication as a cognitive act essentially requiring sortal concepts. We shall call this view conceptual predication (...) sortalism and ground it on the basis of epistemic-semantic reasons. Concepts are understood as intersubjectively realizable capacities or abilities that fulfill particular cognitive roles, such as those of classification, categorization, individuation, and referring. (shrink)