The Diamond Sutra is one of the earliest and most treasured of the Perfection of Wisdom Sutras and had a wide influence on the development of Zen Buddhism. There has been, in recent years, great interest in one particular form of sentences that repeatedly occur in the sutra, sentences of the form “A is not A, therefore it is A”. These sentences display what has been called the “logic of not” or the “logic of affirmation-in-negation”. They are of special interest (...) since they do not only encapsulate one of the central insights of Zen Buddhism, that of nonduality, but at the same time seem to go against one of the most orthodox laws of logic in Western philosophy, the law of identity. This paper discusses the interpretation of these “diamond sentences” by the Vietnamese Zen monk Thich Nhat Hanh. I present Thich Nhat Hanh’s interpretation of the diamond sentences in terms of interbeing and go on to argue that and explain how, on his interpretation, the validity of the law of identity is indeed rejected. Finally, I spell out consequences for formulating a “logic of Zen” and for a related debate about the validity of the law of non-contradiction in Zen. (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)

Ruth Boeker offers a new perspective on Locke’s account of persons and personal identity by considering it within the context of his broader philosophical project and the philosophical debates of his day. Her interpretation emphasizes the importance of the moral and religious dimensions of his view. By taking seriously Locke’s general approach to questions of identity, Boeker shows that we should consider his account of personhood separately from his account of personal identity over time. On this basis, she argues that (...) Locke endorses a moral account of personhood, according to which persons are subjects of accountability, and that his particular thinking about moral accountability explains why he regards sameness of consciousness as necessary for personal identity over time. In contrast to some Neo-Lockean views about personal identity, Boeker argues that Locke’s account of personal identity is not psychological per se, but rather his underlying moral, religious, metaphysical, and epistemic background beliefs are relevant for understanding why he argues for a consciousness-based account of personal identity. Taking his underlying background beliefs into consideration not only sheds light on why many of his early critics do not adopt Locke’s view, but also shows why his view cannot be as easily dismissed as some of his critics assume. -/- . (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)

Stage theorists invoke the idea of counterpart relations to make sense of how objects are able to persist despite their claim that an object is identical with a single instantaneous stage. According to stage theorists, an object persists if and only if it has a later counterpart that bears the appropriate counterpart relation of identity to it. Whilst objects can and do persist, stages cannot and do not. This seems to amount to a refutation of Leibniz’s law. Stage theorists think (...) that the nature of the counterpart relation invoked depends on how it is that the object is referred to. In this paper, I argue that the context sensitivity that they invoke here gives stage theorists a response to the Leibniz’s Law Problem. (shrink)

Numerical identity is standardly considered to be a relation between things. This means that two things are identical if they are only one thing. It is not only Wittgenstein who finds this claim rather odd. Another possibility is to understand identity as a relation between names which denote the same thing; or as a relation between the senses of those names which are modes of presentation of the same thing. Or identity statements can be considered as expressions of the fact (...) that there is exactly one thing that has certain characteristics. These conceptions are, in fact, closely interlinked. There are some rather straightforward proposals on how to give these approaches a formal pattern in relative harmony with classical logic. What is important to emphasize and keep in mind is the specific character of identity and essential dissimilarities between identity and relations of objects in logic. (shrink)

This article is a plea for a realist view of deliberative bodies against a nominalist view. They cannot be reduced to the changing collection of the individuals who compose it. The deliberative bodies are real collective entities insofar as we are able to precise their criteria of identity. These are the differentiation between an interior and an exterior linked by functions or ends; thus these collective entities are adaptive systems. There are three kinds of such adaptive systems: technical systems, organisms (...) and human organizations. The specificity of human organizations is related to the nature of the relations between parties, which are normative, and to the way their ends are determined. Deliberative bodies are organizations of which the specific characteristics have been listed. The mode of being of these collective entities is adverbial. This means that the existence of a deliberative body is subordinated to the nature of the activity of its members and to the manner they are oriented toward its instituted ends. (shrink)

In his interesting article, Michael Burke (1996) offers a novel solution to the puzzle of Tibbles, the cat, a solution he says, which is based on Aristotelian essentialism. In what follows I argue that, despite its ingenuity, Burke’s solution can be seen to be too implausible to be accepted once we extend it to a variant of the puzzle Burke himself suggests. The conclusion must be that one of the other solutions to the puzzle must be correct. Or, perhaps, that (...) there is no correct solution and that we should simply (to use a Wittgensteinian turn of phrase) ‘say what we like as long as we are clear about the facts.’. (shrink)

Examples suggest that one and the same A may be different Bs, and hence that there is some sort of incompleteness in the unqualified statement that x and y are the same which needs to be eliminated by answering the question “the same what?” One way to make this more precise is by appeal to Geach's idea that identity is relative. In this paper I evaluate Geach's relative identity thesis.

An influential thesis in contemporary philosophy of mind is that subjectivity is best conceived as inner awareness of qualia. has argued that this unique subjective awareness generates a paradox which resists empirical explanation. On account of this “paradox of subjective duality,” Levine concludes that the hardest part of the hard problem of consciousness is to explain how anything like a subjective point of view could arise in the world. Against this, I argue that the nature of subjective thought is not (...) correctly characterized as inner awareness, that a non-paradoxical approach to the first-person perspective is available, and that the problem about subjectivity should be distinguished from the perennial problem of qualia or phenomenal properties. (shrink)

In this paper, I defend Peter Geach’s theory of Relative Identity against the charge that it cannot make sense of basic semantic notions.

In §54 of the Grundlagen, Frege advances an interesting proposal on how to distinguish among different sorts of concepts, only some of which he thinks can be associated with number. This paper is devoted to an analysis of the two criteria he offers, isolation and non-arbitrary division. Both criteria say something about the way in which a concept divides its extension; but they emphasize different aspects. Isolation ensures that a concept divides its extension into discrete units. I offer two construals (...) of this: isolation as discreteness, i.e. absence of overlap, between the objects to be counted; and isolation as the drawing of conceptual boundaries. Non-arbitrary division concerns the internal structure of the units we count: it makes sure that we cannot go on dividing them arbitrarily and still find more units of the kind. Non-arbitrary division focuses not only on how long something can be divided into parts of the same kind; it also speaks to the way in which these divisions are made, arbitrarily or non-arbitrarily, as well as to the compositional structure of the objects divided. (shrink)

Among the philosophical accounts of reference, Quine’s The Roots of Reference stands out in offering an integrated account of the acquisition of linguistic reference and object individuation. Based on a non-referential ability to distinguish bodies, the acquisition of sortals and quantification are crucial steps in learning to refer to objects. In this article, we critically re-assess Quine’s account of reference. Our critique will proceed in three steps with the aim of showing that Quine effectively presupposes what he sets out to (...) explain, namely, reference to objects. We are going to argue that sortals do not individuate, that bodies are already objects, and that the acquisition of variables presupposes a notion of identity. The result is diagnostic of a central desideratum for any theory of reference: an explanation of spatiotemporal object individuation. (shrink)

We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism is the philosophical background of the semantic system.

We propose a new intensional semantics for modal-tense second-order languages with sortal predicates. The semantics provides a variable-domain interpretation of the second-order quantifiers. A formal logical system is characterized and proved to be sound and complete with respect to the semantics. A contemporary variant of conceptualism as a theory of universals is the philosophical background of the semantics. Justification for the variable-domain interpretation of the second-order quantifiers presupposes such a conceptualist framework.

In this paper I will argue against a view that I call foundationalism about persistence-conditions. The core of this view is that composite physical objects have their specific persistence-conditions in virtue of these conditions being fulfilled by the object’s physical constituents at various times. I will provide two arguments – the argument from the possibility of instantaneous objects and the argument from the presence of persistence-conditions – which show that this view is untenable. These arguments will also point towards a (...) more adequate understanding of what it means for an object to have certain persistence-conditions. I will expound this understanding and suggest, on its basis, an unorthodox, hylomorphist account of the persistence-conditions of objects. (shrink)

Reflection on the self's way of being "in" consciousness yields two arguments for a theory of self-reference not based in any way all all on self-cognition. First, I show that one theory of self-reference predicts an experience of the self because the theory inadequately analyzes the semantical facts about indexicality. I construct a dilemma for this cognitivism, which it cannot get out of, for it requires even solitary self-reference to be based on some original self-knowledge, which is not available. I (...) describe my "kinetic model" of unspoken self-reference, and I show how it fits the facts of four forms of consciousness, all of which presuppose self-reference, rather than yield it. Second, a speaker uses the first person pronoun in sentences because she is aware of the unmediated role in agency of the beliefs she would express, and not because she is aware of herself in their content. The cognitive model, in contrast, succumbs to a vicious regress and is exposed as an obstacle to an understanding of consciousness. (shrink)

Michael Dummett is a leading contemporary philosopher whose work on the logic and metaphysics of language has had a lasting influence on how these subjects are conceived and discussed. This volume contains some of the most provocative and widely discussed essays published in the last fifteen years, together with a number of unpublished or inaccessible writings. Essays included are: "What is a Theory of Meaning?," "What do I Know When I Know a Language?," "What Does the Appeal to Use Do (...) for the Theory of Meaning?," "Language and Truth," "Truth and Meaning," "Language and Communication," "The Source of the Concept of Truth," "Mood, Force, and Convention," "Frege and Husserl on Reference," "Realism," "Existence," "Does Quantification Involve Identity?," "Could there be Unicorns?," "Causal Loops," "Common Sense and Physics," "Testimony and Memory," "What is Mathematics About?," "Wittgenstein on Necessity: Some Reflections," and "Realism and Anti-Realism." Serving well as a companion to Dummett's other collections, the essays in this volume are not forbiddingly technical or specialized, and have relevance to many areas of analytic philosophy. (shrink)

A conceptual theory of the referential and predicable concepts used in basic speech and mental acts is described in which singular and general, complex and simple, and pronominal and nonpronominal, referential concepts are given a uniform account. The theory includes an intensional realism in which the intensional contents of predicable and referential concepts are represented through nominalized forms of the predicate and quantifier phrases that stand for those concepts. A central part of the theory distinguishes between active and deactivated referential (...) concepts, where the latter are represented by nominalized quantifier phrases that occur as parts of complex predicates. Peter Geach's arguments against theories of general reference in Reference and Generality are used as a foil to test the adequacy of the theory. Geach's arguments are shown to either beg the question of general as opposed to singular reference or to be inapplicable because of the distinction between active and deactivated referential concepts. (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)

Peter Geach famously holds that there is no such thing as absolute identity. There are rather, as Geach sees it, a variety of relative identity relations, each essentially connected with a particular monadic predicate. Though we can strictly and meaningfully say that an individual a is the same man as the individual b, or that a is the same statue as b, we cannot, on this view, strictly and meaningfully say that the individual a simply is b. It is difficult (...) to find anything like a persuasive argument for this doctrine in Geach's work. But one claim made by Geach is that his account of identity is the account most naturally aligned with Frege's widely admired treatment of cardinality. And though this claim of an affinity between Frege's and Geach's doctrines has been challenged, the challenge has been resisted. William Alston and Jonathan Bennett, indeed, go further than Geach to argue that Frege's doctrine implies Geach's. If Alston and Bennett are right, then those who favor a broadly Fregean treatment of cardinality have no choice but to adopt Geach's doctrine of relative identity. And because contemporary set-theoretic accounts of cardinality are essentially Fregean in all respects relevant to this issue (see §11 below), it follows from Alston and Bennett's claim that virtually every standard modern treatment of cardinality requires a 'relativized' treatment of identity. The purpose of this paper is to argue against the implication claimed by Alston and Bennett. Despite some superficial similarities between Frege's treatment of cardinality and Geach's treatment of identity, the two doctrines are fundamentally opposed. Frege's account of cardinality, and its set-theoretic descendants, are all inconsistent with the claim that identity is 'relative' in Geach's sense. (shrink)

Este trabajo presenta y discute diferentes intentos recientes para resolver el así llamado «problema de la Trinidad». Las declaraciones dogmáticas han asumido que (a) sólo hay un Dios; (b) que hay tres personas diferentes, el Padre, el Hijo y el Espíritu Santo; y (c) que esas tres personas son un solo Dios. Pero si hay tres personas diferentes y esas tres personas diferentes son Dios, entonces parece que, o bien no hay un único Dios, o no hay realmente tres personas (...) diferentes. Han aparecido cuatro posiciones principales en el debate reciente en Teología Filosófica para resolver este problema: (i) la teoría social de la Trinidad, (ii) la teoría «latina» de la Trinidad, (iii) la teoría de la Trinidad basada en identidades relativas, y (iv) la teoría de la Trinidad basada en relaciones de constitución. Se presentan y discuten críticamente las cuatro posiciones. This work presents and discusses different recent attempts to solve the so-called «problem of the Trinity». The dogmatic declarations have assumed that: (a) there is only one God; (b) that there are three different persons, the Father, the Son, and the Holy Spirit; and (c) that those three persons are just one God. But if there are three different persons and those three different persons are God, then it seems that, either there is not just one God, or there are not really three different persons. There have appeared four main positions in the recent debate in Philosophical Theology to solve this problem: (i) the social theory of the Trinity, (ii) the «latin» theory of the Trinity, (iii) the theory of the Trinity based on relative identity, and (iv) the theory of the Trinity based on relations of constitution. All four positions are presented and critically discussed. (shrink)

According to Zhiyi 智顗 (538–597), the founder of the Chinese Buddhist Tiantai school 天臺宗, “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)

Probability and indeterminism have always been core philosophical themes. This paper aims to contribute to understanding probability and indeterminism in biology. To provide the background for the paper, it will first be argued that an omniscient being would not need the probabilities of evolutionary theory to make predictions about biological processes. However, despite this, one can still be a realist about evolutionary theory, and then the probabilities in evolutionary theory refer to real features of the world. This prompts the question (...) of how to interpret biological probabilities which correspond to real features of the world but are in principle dispensable for predictive purposes. This paper will suggest three possible interpretations. The first interpretation is a propensity interpretation of kinds of systems. It will be argued that backward probabilities in biology do not present a problem for this propensity interpretation. The second interpretation is the frequency interpretation. Third, I will suggest Humean chances are a new interpretation of probability in evolutionary theory. Finally, this paper discusses Sansom’s argument that biological processes are indeterministic because probabilities in evolutionary theory refer to real features of the world. It will be argued that Sansom’s argument is not conclusive, and that the question whether biological processes are deterministic or indeterministic is still with us. (shrink)

In this paper I argue that it is finally time to move beyond the Nagelian framework and to break new ground in thinking about epistemic reduction in biology. I will do so, not by simply repeating all the old objections that have been raised against Ernest Nagel’s classical model of theory reduction. Rather, I grant that a proponent of Nagel’s approach can handle several of these problems but that, nevertheless, Nagel’s general way of thinking about epistemic reduction in terms of (...) theories and their logical relations is entirely inadequate with respect to what is going on in actual biological research practice. (shrink)

This is a copy of my DPhil thesis, the abstract for which is as follows: The first third of this thesis argues for a B-theoretic conception of time according to which all times exist equally and the present is in no way privileged. I distinguish "ontological" A-theories from "non-ontological" ones, arguing that the latter are experientially unmotivated and barely coherent. With regard to the former, I focus mainly on presentism. After some remarks on how to formulate this (and eternalism) non-trivially, (...) I review the non-relativistic case against presentism. I then consider the impact of Special Relativity on the debate, and attempt to deepen this impact by supplying a modal variation on the standard arguments. The middle third of the thesis investigates persistence, contending that both endurance and perdurance are consonant with the eternalism already endorsed. After introducing these theories of persistence, and discussing in particular how best to formulate an eternalist endurance, I proceed to defend the coherence of this combination. The Problem of Change is addressed here. I then respond in some detail to recent allegations of relativistic threats to endurance. The final third of the thesis questions the validity of the endurantist-perdurantist dispute. I criticize two recently proposed translation schemes that aim to show this dispute to be non-substantive. However, the second scheme suggests a doctrine of "Ontological Equivalence" which I develop and consider. I then address the Rotating Discs Argument, using this to launch a discussion of identity, genidentity, and the relationship between them. (shrink)