In Metaphysics A, Aristotle offers some objections to Plato’s theory of Forms to the effect that Plato’s Forms would not be explanatory in the right way, and seems to suggest that they might even make the explanatory project worse. One interesting historical puzzle is whether Aristotle can avoid these same objections to his own theory of universals. The concerns Aristotle raises are, I think, cousins of contemporary concerns about the usefulness and explanatoriness of abstract objects, some of which (...) have recently been receiving attention in the philosophy of mathematics. After discussing Aristotle’s objections and their contemporary cousins, the paper discusses some of the main available lines of response to these sorts of challenges, before concluding with an examination of whether these responses could assist Plato or Aristotle in responding to these challenges. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The (...) main reason for producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

A debated topic in Avicennan psychology is whether for Avicenna abstraction is a metaphor for emanation or to be taken literally. This issue stems from the deeper philosophical question of whether humans acquire intelligibles externally from an emanation by the Active Intellect, which is a separate substance, or internally from an inherently human cognitive process, which prepares us for an emanation from the Active Intellect. I argue that the tension between thesedoctrines is only apparent. In his logical works Avicenna limns (...) an account where through the internal human process of abstraction accidents accruing to an essence existing in matter are extracted, thus preparing the essence for new accidents emanating externally from the Active Intellect, which make the essence something conceptualized in the intellect. This study, then, outlines the epistemological and metaphysical framework presented in the logical works that underpins Avicenna’s theory of abstraction presented in his psychological works. (shrink)

A debated topic in Avicennan psychology is whether for Avicenna abstraction is a metaphor for emanation or to be taken literally. This issue stems from the deeper philosophical question of whether humans acquire intelligibles externally from an emanation by the Active Intellect, which is a separate substance, or internally from an inherently human cognitive process, which prepares us for an emanation from the Active Intellect. I argue that the tension between thesedoctrines is only apparent. In his logical works Avicenna limns (...) an account where through the internal human process of abstraction accidents accruing to an essence existing in matter are extracted, thus preparing the essence for new accidents emanating externally from the Active Intellect, which make the essence something conceptualized in the intellect. This study, then, outlines the epistemological and metaphysical framework presented in the logical works that underpins Avicenna’s theory of abstraction presented in his psychological works. (shrink)

In this paper, we consider the relative significance of concrete and abstract features for the identity and persistence of a group. The theoretical background for our analysis is the position according to which groups are realizations of structures. Our main argument is that the relative significance of the abstract features with respect to the significance of concrete features can vary across different types of groups. The argumentation will be backed by introducing the examples in which we show that (...) this difference in significance can affect the identity and persistence of the group. (shrink)

The link between the high-order metaphysics and abstractions, on the one hand, and choice in the foundation of set theory, on the other hand, can distinguish unambiguously the “good” principles of abstraction from the “bad” ones and thus resolve the “bad company problem” as to set theory. Thus it implies correspondingly a more precise definition of the relation between the axiom of choice and “all company” of axioms in set theory concerning directly or indirectly abstraction: the principle of abstraction, (...) axiom of comprehension, axiom scheme of specification, axiom scheme of separation, subset axiom scheme, axiom scheme of replacement, axiom of unrestricted comprehension, axiom of extensionality, etc. (shrink)

This is Francesco Orilia's book review of Edward N. Zalta's 1983 book, Abstract Objects: An Introduction to Axiomatic Metaphysics.

Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time. This book provides a comprehensive critical assessment of the (...) problems raised by abstract entities and the debates about existence, truth, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between platonists who accept abstract entities and nominalists who deny abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality: arguments for platonism and their connections to semantics, science, and metaphysical explanation the abstract–concrete distinction and views about the nature of abstract reality epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities. arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation nominalist options that seek to dispense with abstract entities. Including chapter summaries, annotated further reading, and a glossary, _Entities_ is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities. (shrink)

Physical reality as an explanatory model is an abstraction of the mind. Every perceptual system is a user interface, like the dashboard of an aeroplane or the desktop of a computer. We do not see or otherwise perceive reality but only interface with reality. The user interface concept is a starting point for a critical dialogue with those epistemic theories that present themselves as veridical and take explanatory abstractions as ontological primitives. At the heart of any scientific model are assumptions (...) about which things exist, how they are related, and how we can know them. Scientific models take our knowledge beyond ordinary experience toward explanatory abstractions. The main problem with veridical models lies in why we cannot express our theories and the explanatory abstractions associated with them other than through classical perceptual interface symbols. This study analyses the limits, possibilities and constraints of explanatory abstractions. (shrink)

First, I offer a short overview on the classical occidental philosophy as propounded by the ancient Greeks and the natural philosophies of the last 2000 years until the dawn of the empiricist logic of science in the twentieth century, which wanted to delimitate classical metaphysics from empirical sciences. In contrast to metaphysical concepts which didn’t reflect on the language with which they tried to explain the whole realm of entities empiricist logic of science initiated the end of metaphysical theories (...) by reflecting on the preconditions for foundation and justification of sentences about objects of investigation, i.e. a coherent definition of language in general, which was not the aim of classical metaphysics. Unexpectedly empiricist logic of science in the linguistic turn failed in the physical and mathematical reductionism of language and its use in communication, as will be discussed below in further detail. Nevertheless, such reflection on language and communication also introduced this vocabulary into biology. Manfred Eigen and bioinformatics, later on biolinguistics, used ‘language’ applied linguistic turn thinking to biology coherent to the logic of science and its formalisable aims. This changed significantly with the birth of biosemiotics and biohermeneutics. At the end of this introduction it will be outlined why and how all these approaches reproduced the deficiencies of the logic of science and why the biocommunicative approach avoids their abstractive fallacies. (shrink)

Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars are the very alphabet of being. The concept of an abstract particular has been repeatedly attacked in the literature. Opponents and proponents of trope theory alike have levelled their criticisms at the abstractness of tropes and the associated act of abstraction. In this paper I defend the concept (...) of a trope qua abstract particular by rejecting arguments that purport to show that tropes should not be understood as abstract and by arguing that the abstractness of tropes plays an indispensable role in one of our more promising trope-theoretic analyses of universals and of concrete objects. (shrink)

_Metaphysics: A Contemporary Introduction_ is for students who have already completed an introductory philosophy course and need a fresh look at the central topics in the core subject of metaphysics. It is essential reading for any student of the subject. This Fourth Edition is revised and updated and includes two new chapters on Parts and Wholes, and Metaphysical Indeterminacy or vagueness. This new edition also keeps the user-friendly format, the chapter overviews summarizing the main topics, concrete examples to clarify (...) difficult concepts, annotated further reading at the end of each chapter, endnotes, and a full bibliography. Topics addressed include: the problem of universals the nature of abstract entities the problem of individuation the nature of modality identity through time the nature of time the nature of parts and wholes the problem of metaphysical indeterminacy the Realism/anti-Realism debate. Wherever possible, Michael J. Loux and Thomas M. Crisp relate contemporary views to their classical sources in the history of philosophy. As experienced teachers of philosophy and important contributors to recent debates, Loux and Crisp are uniquely qualified to write this book. (shrink)

It is maintained that abstract objects are literally entia rationis: their being lies in being conceived and their nature is inextricably entangled with the operation of minds.

It is maintained that abstract objects are literally entia rationis: their being lies in being conceived and their nature is inextricably entangled with the operation of minds.

Book reviewed:;Jerrold J. Katz, Language and OtherObjects;Book reviewed:;Jerrold J. Katz, Language and Other Abstract Objects;Book reviewed:;Jerrold J. Katz, Language and Other Abstract Objects;Book reviewed:;Jerrold J. Katz, Language and Other Abstract Objects;Book reviewed:;Jerrold J. Katz, Language and Other Abstract Objects;Book reviewed:;Jerrold J. Katz, Language and Other Abstract Objects;Book reviewed:;Jerrold J. Katz, Language and Other Abstract Objects;Book reviewed:;Jerrold J. Katz, Language and Other Abstract Objects;Book reviewed:;Jerrold J. Katz, Language and Other Abstract Objects;Book reviewed:;Jerrold J. (...) Katz, Language and Other Abstract Objects. (shrink)

Metaphysics of Science is the philosophical study of key concepts that figure prominently in science and that, prima facie, stand in need of clarification. It is also concerned with the phenomena that correspond to these concepts. Exemplary topics within Metaphysics of Science include laws of nature, causation, dispositions, natural kinds, possibility and necessity, explanation, reduction, emergence, grounding, and space and time. Metaphysics of Science is a subfield of both metaphysics and the philosophy of science—that is, it (...) can be allocated to either, but it exhausts neither. Unlike metaphysics simpliciter, Metaphysics of Science is not primarily concerned with metaphysical questions that may already arise from everyday phenomena such as what makes a thing (a chair, a desk) the very thing it is, what its identity criteria are, out of which parts is it composed, whether it remains the same if we exchange a couple of its parts, and so forth. Nor is it concerned with the concrete entities (superstrings, molecules, genes, and so forth) postulated by specific sciences; these issues are the subject matter of the special philosophies of science (for example, of physics, of chemistry, of biology). Metaphysics of Science is concerned with more abstract and general concepts that inform all of these sciences. Many of these concepts are interwoven with each other. For example, metaphysicians of science inquire whether dispositionality, lawhood, and causation can be accounted for in nonmodal terms; whether laws of nature presuppose the existence of natural kinds; and whether the properties of macrolevel objects supervene on dispositional or nondispositional properties. This article surveys the scope (section 1), historical origin (section 2), exemplary subject matters (section 4), and methodology (section 5) of Metaphysics of Science, as well as the motivation that drives it (section 3). (shrink)

Jonathan Lowe argues that metaphysics should be restored to a central position in philosophy, as the most fundamental form of rational inquiry, whose findings underpin those of all other disciplines. He portrays metaphysics as charting the possibilities of existence, by idetifying the categories of being and the relations of ontological dependency between entities of different categories. He proceeds to set out a unified and original metaphysical system: he defends a substance ontology, according to which the existence of the (...) world s one world in time depends upon the existence of persisting things which retain their identity over time and through processes of qualitative change. And he contends that even necessary beings, such as the abstract objects of mathematics, depend ultimately for their existence upon there being a concrete world of enduring substances. Within his system of metaphysics Lowe seeks to answer many of the deepest and most challenging questions in philosophy. (shrink)

This volume is about abstract objects and the ways we refer to them in natural language. Asher develops a semantical and metaphysical analysis of these entities in two stages. The first reflects the rich ontology of abstract objects necessitated by the forms of language in which we think and speak. A second level of analysis maps the ontology of natural language metaphysics onto a sparser domain--a more systematic realm of abstract objects that are fully analyzed. This (...) second level reflects the commitments of real metaphysics. The models for these commitments assign truth conditions to natural language discourse. Annotation copyright by Book News, Inc., Portland, OR. (shrink)

Metaphysics: An Introduction combines comprehensive coverage of the core elements of metaphysics with contemporary and lively debates within the subject. It provides a rigorous and yet accessible overview of a rich array of topics , connecting the abstract nature of metaphysics with the real world. Topics covered include: Basic logic for metaphysics An introduction to ontologyobjects Material objects Critiques of metaphysics Free Will Time Modality Persistence Causation Social ontology: the metaphysics of race This (...) outstanding book not only equips the reader with a thorough knowledge of the fundamentals of metaphysics but provides a valuable guide to contemporary metaphysics and metaphysicians. Additional features such as exercises, annotated further reading, a glossary and a companion website www.routledge.com/cw/ney will help students find their way around this subject and assist teachers in the classroom. (shrink)

When the works began being translated into English, those abstract Latin words or their cognates were used, thus suggesting a level of jargon and abstraction, and in some cases misleading interpretation, which was not Aristotle's language...

What is metaphysics? Metaphysics: A Basic Introduction in a Christian Key gives a simplified answer to this daunting question. Born under the shadow of the Parthenon by Aristotle and his contemporaries, metaphysics eventually enjoyed its heyday in the medieval era and is finding a resurgence today in modernity. This book explores the perennial question of being and its uptake in the world of Christian theology. Donald Wallenfang leads the reader through five navigable chapters that feature the most (...) basic themes of metaphysics: the question of being, first principles, causality, cosmology, and morality. The abstract tendencies of metaphysics are brought down to earth with reference to the gospel of Jesus and the relevance of metaphysics for daily living. Altogether, the reader will be inspired to think toward the whole by asking questions that penetrate beneath the surface of things. Beauty, truth, and goodness will be unveiled to the degree that we accompany Jesus the metaphysician along his itinerary of being given. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Breakdown of C i M phy " artes an eta sacs RICHARD A. WATSON WITHIN CARTESIANISMthere arose many problems deriving from conflicts between Cartesian principles. Inadequate attempts to solve these problems were crucial reasons for the breakdown of Cartesian metaphysics in the late seventeenth and early eighteenth centuries. The major difficulties derived from the acceptance of a dualism of substances seated in a system which included (...) epistemological and causal likeness principles plus an ontological framework in which the categories of substance and modification were exhaustive. The major solutions involved either denying the likeness principles or altering the ontological framework. The first led to unintelligibility ; the second, culminating in Hume, opened the way to non-Cartesian metaphysics. The first section of this study contains a characterization of late seventeenth -century Cartesian metaphysics. The second is an exposition of Foucher 's four major criticisms of this system. In the third section, monistic solutions suggested in Descartes and by Spinoza, Foucher, Leibniz, and Locke are considered; in the fourth, the dualistic solutions of the orthodox Cartesians Rohault, R~gis, Desgabets, La Forge, Le Grand, and Arnauld; and in the fifth, the occasionalist solution of Malebranche. The sixth section is an analysis of these orthodox and occasionalist solutions, showing how each ultimately fails because of dependence upon the ontology of substance and modification. The seventh section is a consideration of Berkeley and Hume in the Cartesian context. A consideration of their systems as offering solutions to Cartesian problems illuminates in new light both the systems and the problems. In broad terms, this study moves from a consideration of problems arising from an ontology of two substances, to a consideration of problems arising from the ontological pattern of substance and modification. The Cartesians were concerned with relationships between two substances, but they saw no difficulties connected with the relationship between a substance and its modifications (or properties). Berkeley's treatment (deriving from Male- [177] 178 HISTORY OF PHILOSOPHY branche) of the relationships between mind and idea, and between mind and notion, is illuminated by a consideration of the extent to which he took these relationships for granted in the Cartesian way, and of the extent to which he saw difficulties in the relationship between substance and modification. The Berkeleian solution to Cartesian problems, like that of Malebranche before him, was not successful; Malebranche belittled, and Berkeley denied the dualism of substances, but neither philosopher could break entirely with the ontological pattern of substance and modification. The final breakdown of Cartesian metaphysics came with Hume, who, in providing the culmination of a most important trend in modern philosophy, opened the way to new metaphysics and became the father of contemporary philosophy. I A model late seventeenth-century Cartesian metaphysical system. The last grand expositor of the Cartesian philosophy was Antoine Le Grand who in 1694 published An Entire Body of Philosophy. The characterization of the late seventeenth-century Cartesian system given below follows Le Grand's exposition more closely than others, but it also incorporates elements from those of Rohault, R6gis, Desgabets, La Forge, Malebranche, and Arnauld.1 None of these philosophers professed a system of exactly the sort this characterization pictures, nor is it implied here that they do. The guide and rationale for drawing from them such a model Cartesianism is the polemical writing of Simon Foucher. Foucher's series of attacks upon Cartesianism (of which the second is his criticism of Malebranche of 1675, Critique de la Rdcherche de la veritd) give clearly the most important objections against Cartesian metaphysics.2The system outlined below, while more com1Le Grand, Antoine, An Entire Body of Philosophy According to the Principles of the Famous Renate des Cartes (London, 1694); Rohault, Jacques, Traitd de physique (Paris, 1671); R6gis, Pierre-Sylvain, Syst~me de philosophie, contenant la logique, la mdtaphysique, la physique et la morale (Lyon, 1690); Desgabets, Robert, Critique de la Critique de la Recherche de la veritd, oCt l'on decouvre le chemin qui conduit aux connoissances solides. Pour servir de rdsponse gtla Lettre d'un academicien (Paris, 1675); La Forge, Louis de, Traitd de l'dme humaine, de ses facultds et fonctions et de son union avec le corps, d'apr~s les principes de... (shrink)

Joe Sachs has followed up his brilliant translation of Aristotle's Physics with a new translation of Metaphysics. Sachs's translations bring distinguished new light onto Aristotle's works, which are foundational to history of science. Sachs translates Aristotle with an authenticity that was lost when Aristotle was translated into Latin and abstract Latin words came to stand for concepts Aristotle expressed with phrases in everyday Greek language. When the works began being translated into English, those abstract Latin words or (...) their cognates were used, thus suggesting a level of jargon and abstraction, and in some cases misleading interpretation, which was not Aristotle's language or style. These important new translations open up Aristotle's original thought to readers. (shrink)

Book reviewed:Jerrold J. Katz, Language and Other Abstract Objects.

This book does two things. First, it introduces a novel kind of non-factualist view, and it argues that we should endorse views of this kind in connection with a wide class of metaphysical questions, most notably, the abstract-object question and the composite-object question (so, more specifically, the book argues that there’s no fact of the matter whether there are any such things as abstract objects or composite objects—or material objects of any other kind). Second, the book explains how (...) these non-factualist views fit into a general anti-metaphysical view called neo-positivism, and it explains how we could argue that neo-positivism is true. Neo-positivism is (roughly) the view is that every metaphysical question decomposes into some subquestions—call them Q1, Q2, Q3, etc.—such that, for each of these subquestions, one of the following three anti-metaphysical views is true of it: non-factualism, or scientism, or metaphysically innocent modal-truth-ism. These three views can be defined (very roughly) as follows. Non-factualism about a question Q is the view that there’s no fact of the matter about the answer to Q. Scientism about Q is the view that Q is an ordinary empirical-scientific question about some contingent aspect of physical reality, and Q can’t be settled with an a priori philosophical argument. And metaphysically innocent modal-truth-ism about Q is the view that Q asks about the truth value of a modal sentence that’s metaphysically innocent in the sense that it doesn’t say anything about reality and, if it’s true, isn’t made true by reality. (shrink)

This book offers a critical account of the fundamental elements of Leibniz's philosophy, as they manifest themselves in his metaphysics and philosophy of language. Emphasis is placed upon his hitherto neglected doctrine of nominalism, which states that only concrete individuals exist and that there are no such things as abstract entities – no numbers, geometrical figures or other mathematical objects, nor any abstractions such as space, time, heat, light, justice, goodness, or beauty. Using this doctrine as a basis, (...) the book considers the core of Leibniz's metaphysics and philosophy of language, including the well‐known principles of Contradiction, Sufficient Reason, Continuity and Individuation, and the concepts of Possible World, Individual Substance, Truth, and Necessity. (shrink)

Kant’s subject as source of universality and necessity in human understanding is Modern Philosophy's solution to the old problem of the universals, a solution which appeared to supersede once and for all the Aristotelian theory of abstraction. The present paper intends to show how Aquinas's Aristotelian doctrine on abstraction may stand the Kantian challenge and resolve the old problem when three principles are brought into play: 1) the same perfection can subsist in two different modes of being, and thus the (...) universal content of knowledge can be present in the particular reality (Summa, I, 84, 1); 2) things which are really distinct between themselves can be known in their distinction, even when they cannot exist separately (metaphysical distinction justifies gnoseological separation); 3) as Cornelio Fabro suggests, it is artificial to separate in the object of experience the object’s different levels of objectivity (quality, configuration and meaning) and, as a result, human experience could be considered the source not only of sensible content but also of intelligible content. This “defense” of Thomistic abstraction intends to offer an account of knowledge which reunites again epistemology with common sense experience, so that philosophy may no longer be a Platonic abstraction but a meaningful explanation of life. (shrink)

It is widely supposed that every entity falls into one of twocategories: Some are concrete; the rest abstract. The distinction issupposed to be of fundamental significance for metaphysics andepistemology. This article surveys a number of recent attempts to sayhow it should be drawn.

Art and Abstract Objects presents a lively philosophical exchange between the philosophy of art and the core areas of philosophy. The standard way of thinking about non-repeatable (single-instance) artworks such as paintings, drawings, and non-cast sculpture is that they are concrete (i.e., material, causally efficacious, located in space and time). Da Vinci's Mona Lisa is currently located in Paris. Richard Serra's Tilted Arc is 73 tonnes of solid steel. Johannes Vermeer's The Concert was stolen in 1990 and remains missing. (...) Michaelangelo's David was attacked with a hammer in 1991. By contrast, the standard way of thinking about repeatable (multiple-instance) artworks such as novels, poems, plays, operas, films, symphonies is that they must be abstract (i.e., immaterial, causally inert, outside space-time): consider the current location of Melville's Moby Dick, the weight of Yeats' "Sailing to Byzantium", or how one might go about stealing Puccini's La Boheme or vandalizing Mozart's Piano Concerto No. 9. Although novels, poems, and symphonies may appear radically unlike stock abstract objects such as numbers, sets, and propositions, most philosophers of art think that for the basic intuitions, practices, and conventions surrounding such works to be preserved, repeatable artworks must be abstracta. -/- This volume examines how philosophical enquiry into art might itself productively inform or be productively informed by enquiry into abstracta taking place within not just metaphysics but also the philosophy of mathematics, epistemology, philosophy of science, and philosophy of mind and language. While the contributors chiefly focus on the relationship between philosophy of art and contemporary metaphysics with respect to the overlap issue of abstracta, they provide a methodological blueprint from which scholars working both within and beyond philosophy of art can begin building responsible, mutually informative, and productive relationships between their respective fields. (shrink)

Abstract Theories are metaphysically equivalent just if there is no fact of the matter that could render one theory true and the other false. In this paper I argue that if we are judiciously to resolve disputes about whether theories are equivalent or not, we need to develop testable criteria that will give us epistemic access to the obtaining of the relation of metaphysical equivalence holding between those theories. I develop such ?diagnostic? criteria. I argue that correctly inter-translatable theories (...) are metaphysically equivalent, and what we need are ways of determining whether a putative translation is correct or not. To that end I develop a number of tools we can employ to discern whether a translation is a correct one. (shrink)

How can a metaphysics of abstract entities be built upon a metaphysics of time? In this paper, I address the question of how to accommodate abstract entities in a presentist world. I consider both the traditional metaontological approach of unrestricted fundamental quantification and then ontological pluralism. I argue that under the former we need to impose two constraints in the characterization of presentism in order to avoid undesired commitments to abstract entities: we have to characterize (...) presentism as a thesis only about the concrete, and we also need to avoid the widely held distinction between tensed and tenseless senses of existence. Under ontological pluralism, instead, I argue that we can naturally accommodate any view of abstract objects in a presentist world. (shrink)

abstract This paper re‐examines some well‐known and commonly accepted arguments for the non‐individuality of the embryo, due mainly to the work of John Harris. The first concerns the alleged non‐differentiation of the embryoblast from the trophoblast. The second concerns monozygotic twinning and the relevance of the primitive streak. The third concerns the totipotency of the cells of the early embryo. I argue that on a proper analysis of both the empirical facts of embryological development, and the metaphysical importance or (...) otherwise of those facts, all three arguments are found wanting. None of them establishes that the embryo is not an individual human being from the moment of conception. (shrink)