Awareness is a two-place determinable relation some determinates of which are seeing, hearing, etc. Abstractobjects are items such as universals and functions, which contrast with concrete objects such as solids and liquids. It is uncontroversial that we are sometimes aware of concrete objects. In this paper I explore the more controversial topic of awareness of abstractobjects. I distinguish two questions. First, the Existence Question: are there any experiences that make their subjects aware (...) of abstractobjects? Second, the Grounding Question: if an experience makes its subject aware of an abstract object, in virtue of what does it do so? I defend the view that intuitions, specifically mathematical intuitions, sometimes make their subjects aware of abstractobjects. In defending this view, I develop an account of the ground of intuitive awareness. (shrink)
This paper is concerned with neo-Fregean accounts of reference to abstractobjects. It develops an objection to the most familiar such accounts, due to Bob Hale and Crispin Wright, based upon what I call the 'proliferation problem': Hale and Wright's account makes reference to abstractobjects seem too easy, as is shown by the fact that any equivalence relation seems as good as any other. The paper then develops a response to this objection, and offers an (...) account of what it is for abstracta to exist that is Fregean in spirit but more robust than familiar views. (shrink)
Philosophers have defended various views about abstractobjects by appealing to metaphysical considerations, considerations regarding mathematics or science, and, not infrequently, intuitions about natural language. This book pursues the question of how and whether natural language allows for reference to abstractobjects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues (...) for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstractobjects such as properties, numbers, propositions, and degrees is considerably more marginal than generally held. (shrink)
In this paper, the author derives the Dedekind-Peano axioms for number theory from a consistent and general metaphysical theory of abstractobjects. The derivation makes no appeal to primitive mathematical notions, implicit definitions, or a principle of infinity. The theorems proved constitute an important subset of the numbered propositions found in Frege's Grundgesetze. The proofs of the theorems reconstruct Frege's derivations, with the exception of the claim that every number has a successor, which is derived from a modal (...) axiom that (philosophical) logicians implicitly accept. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct Frege's conception of numbers and logical objects. (shrink)
The Platonic theist Peter van Inwagen argues that God cannot create abstractobjects. Thus, the quantifier ‘everything’ in traditional statements of the doctrine of creation should be appropriately restricted to things that can enter into causal relations and abstractobjects cannot: ‘God is the creator of everything distinct from himself…that can enter into causal relations.’ I respond to van Inwagen arguing that he has provided no good reason for thinking abstractobjects must be uncreated. (...) And if this is the case, then there is no good reason to think that God cannot create abstractobjects. (shrink)
TABLE OF CONTENTS Introduction: Art, Metaphysics, & The Paradox of Standards (Christy Mag Uidhir) GENERAL ONTOLOGICAL ISSUES 1. Must Ontological Pragmatism be Self-Defeating? (Guy Rohrbaugh) 2. Indication, Abstraction, & Individuation (Jerrold Levinson) 3. Destroying Artworks (Marcus Rossberg) INFORMATIVE COMPARISONS 4. Artworks & Indefinite Extensibility (Roy T. Cook) 5. Historical Individuals Like Anas platyrhynchos & ‘Classical Gas’ (P.D. Magnus) 6. Repeatable Artworks & Genericity (Shieva Kleinschmidt & Jacob Ross) ARGUMENTS AGAINST & ALTERNATIVES TO 7. Against Repeatable Artworks (Allan Hazlett) 8. How (...) to be a Nominalist & a Fictional Realist (Ross Cameron) 9. Platonism vs. Nominalism in Musical Ontology (Andrew Kania) ABSTRACTA ACROSS THE ARTS 10. Reflections on the Metaphysics of Sculpture (Hud Hudson) 11. Installation Art & Performance: A Shared Ontology (Sherri Irvin) 12. What Type of ‘Type’ is a Film? (David Davies) 13. Musical Works: A Metaphysical Mash-Up (Joseph Moore) . (shrink)
In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambigu-ity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argu-ment’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstractobjects are arguments?
This book offers an historically-informed critical assessment of Dummett's account of abstractobjects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.
What is a concept? Philosophers have given many different answers to this question, reflecting a wide variety of approaches to the study of mind and language. Nonetheless, at the most general level, there are two dominant frameworks in contemporary philosophy. One proposes that concepts are mental representations, while the other proposes that they are abstractobjects. This paper looks at the differences between these two approaches, the prospects for combining them, and the issues that are involved in the (...) dispute. We argue that powerful motivations have been offered in support of both frameworks. This suggests the possibility of combining the two. Unlike Frege, we hold that the resulting position is perfectly coherent and well worth considering. Nonetheless, we argue that it should be rejected along with the view that concepts are abstractobjects. (shrink)
The ideas of fixed points (Kripke in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 53–81, 1975; Martin and Woodruff in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 47–51, 1984) and revision sequences (Gupta and Belnap in The revision theory of truth. MIT, London, 1993; Gupta in The Blackwell guide to philosophical logic. Blackwell, London, pp 90–114, 2001) have been exploited to provide solutions to the semantic paradox and have achieved admirable (...) success. This happy situation naturally encourages one to look for other philosophical areas of their further applications where paradoxical results seem to follow from intuitively acceptable principles. In this paper, I propose to extend the use of these ideas to give two new treatments of abstractobjects. Sections 1 and 2 below check several abstractionist theories and their main defects. Section 3 shows how the two ideas can be applied to generate consistent theories of abstractobjects without any ad hoc restriction on any principle. (shrink)
Book Information Knowledge, Cause, and AbstractObjects: Causal Objections to Platonism. Knowledge, Cause, and AbstractObjects: Causal Objections to Platonism Colin Cheyne , Dordrecht: Kluwer Academic Publishers , 2001 , xvi + 236 , £55 ( cloth ) By Colin Cheyne. Dordrecht: Kluwer Academic Publishers. Pp. xvi + 236. £55.
In this paper, the author shows how one can independently prove, within the theory of abstractobjects, some of the most significant claims, hypotheses, and background assumptions found in Kripke's logical and philosophical work. Moreover, many of the semantic features of theory of abstractobjects are consistent with Kripke's views — the successful representation, in the system, of the truth conditions and entailments of philosophically puzzling sentences of natural language validates certain Kripkean semantic claims about natural (...) language. (shrink)
It is not a common practice to postulate meaning entities treated as objects of some kind. The paper demonstrates two ways of introducing meaning-objects in two logics of natural language, Tichy’s Transparent Intensional Logic and Zalta’s Intensional Logic of AbstractObjects. Tichy’s theory belongs to the Fregean line of thinking, with what he calls ‘constructions’ as Fregean senses, and ‘determiners’ as object-like meaning entities constructed by the senses. Zalta’s theory belongs to Meinongian logics and he postulates (...) a rich realm of abstract Meinongian objects to play the role of meanings. The paper analyses the mechanisms of reference in both conceptions and it offers a comparison of the mediating meaning-objects and the framework designed to expose this mediation in both theories. An attempt is made to expose how the treatment of the meaning entities depends upon the theory of meaning which is assumed. (shrink)
Review of G. Duke: Dummett onObjects References G. Frege. Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, 100, 25–50, 1892. Translated in G.Frege, Collected Papers on Mathematics, Logic and Philosophy, edited by B. McGuinness. Oxford, Basil Blackwell, 157–77. G. Frege. Die Grundlagen der Arithmetik. Breslau, Verlag von W. Koebner, 1884. Translated by J.L. Austin as The Foundations of Arithmetic, Oxford, Basil Blackwell, second revised edition 1953. M. Dummett. Frege: Philosophy of Language. London, Duckworth, 1973. M. Dummett. Frege: Philosophy (...) of Mathematics. London: Duckworth, 1991. B. Hale. AbstractObjects. Oxford: Basil Blackwells, 1987. B. Hale. Dummett's critique of Wright's attempt to resuscitate Frege. Philosophia Mathematica 2 (2):122–47 , 1994 http://dx.doi.org/10.1093/philmat/2.2.122 B. Hale and C. Wright. The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics. Oxford, Oxford University Press, 2001. B. Hale and C. Wright. The Metaontology of Abstraction. In D. Chalmers, D. Manley & R. Wasserman, editors, Metametaphysics: New essays on the Foundations of Ontology. Oxford, Clarendon Press, 178–213, 2009. C. Wright. Frege’s Conception of Numbers as Objects. Scots Philosophical Monographs. Aberdeen, Aberdeen University Press, 1983. (shrink)
This paper investigates feasible ways of destroying artworks, assuming they are abstractobjects, or works of a particular art-form, where the works of at least this art-form are assumed to be abstracta. If artworks are eternal, mind-independent abstracta, and hence discovered, rather than created, then they cannot be destroyed, but merely forgotten. For more moderate conceptions of artworks as abstractobjects, however, there might be logical space for artwork destruction. Artworks as abstracta have been likened to (...) impure sets (i.e., sets of concrete things, as opposed to pure sets, i.e., sets of nothing but other sets) that have a beginning in time, namely when their members come into being, and an end in time, namely when their members cease to exist. Alternatively, artworks as abstracta have been thought of as types that are created with their first token. Artwork destruction is harder on this account: merely destroying every token might not yet destroy the type. To what extent such similes can be spelt out and made plausible as an ontology of artworks, and what options there are on the different accounts for artwork destruction, is explored in this paper. (shrink)
In this paper, the authors discuss Frege's theory of "logical objects" (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the 'eta' relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstractobjects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the 'eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory (...) of abstractobjects uses unrestricted Comprehension for Logical Objects and banishes encoding (eta) formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstractobjects are described, involving: (a) the theory of extensions, (b) the theory of directions and shapes, and (c) the theory of truth values. (shrink)
Four experiments (E1-E2-E3-E4) investigated whether different acquisition modalities lead to the emergence of differences typically found between concrete and abstract words, as argued by the Words As Tools (WAT) proposal. To mimic the acquisition of concrete and abstract concepts, participants either manipulated novel objects or observed groups of objects interacting in novel ways (training1). In TEST 1 participants decided whether two elements belonged to the same category. Later they read the category labels (training2); labels could be (...) accompanied by an explanation of their meaning. Then participants observed previously seen exemplars and other elements, and were asked which of them could be named with a given label (TEST2). Across the experiments, it was more difficult to form abstract than concrete categories (TEST 1); even when adding labels, abstract words remained more difficult than concrete words (TEST 2). TEST3 differed across the experiments. In E1 participants performed a feature production task. Crucially, the associations produced with the novel words reflected the pattern evoked by existing concrete and abstract words, as the first evoked more perceptual properties. In E2-E3-E4, TEST3 consisted of a color verification task with manual/verbal (keyboard-microphone) responses. Results showed the microphone use to have an advantage over keyboard use for abstract words, especially in the explanation condition. This supports WAT: due to their acquisition modality, concrete words evoke more manual information; abstract words elicit more verbal information. This advantage was not present when linguistic information contrasted with perceptual one. Implications for theories and computational models of language grounding are discussed. (shrink)
Frege suggests that criteria of identity should play a central role in the explanation of reference, especially to abstractobjects. This paper develops a precise model of how we can come to refer to a particular kind of abstract object, namely, abstract letter types. It is argued that the resulting abstract referents are ‘metaphysically lightweight’.
In his latest book, Realistic Rationalism (Cambridge, MA: MIT Press, 1998), Jerrold J. Katz proposes an ontology designed to handle putative counterexamples to the traditional abstract/concrete distinction. Objects like the equator and impure sets, which appear to have both abstract and concrete components, are problematic for classical Platonism, whose exclusive categories of objects with spatiotemporal location and objects lacking spatial or temporal location leave no room for them. Katz proposes to add a “composite” category to (...) Plato’s dualistic ontology, which is supposed to include all those objects with both abstract and concrete components.But every concrete object stands in an indefinite number of relations to abstract ones. Thus, Katz must offer principled criteria describing just those relations that produce a composite object, lest all concrete objects turn out to be composite. The trouble that he has in specifying such a “creative” relationship results from his clinging to the traditional definitions of “abstract” and “concrete.” The substance dualism that results renders the articulation of any relations between abstract and concrete difficult, and a category such as Katz’s “composite objects” impossible. (shrink)
I explicate and defend the claim that, fundamentally speaking, there are no numbers, sets, properties or relations. The clarification consists in some remarks on the relevant sense of ‘fundamentally speaking’ and the contrasting sense of ‘superficially speaking’. The defence consists in an attempt to rebut two arguments for the existence of such entities. The first is a version of the indispensability argument, which purports to show that certain mathematical entities are required for good scientific explanations. The second is a speculative (...) reconstruction of Armstrong's version of the One Over Many argument, which purports to show that properties and relations are required for good philosophical explanations, e.g. of what it is for one thing to be a duplicate of another. (shrink)
The Substitution Anomaly is the failure of intuitively coreferential expressions of the corresponding forms “that S” and “the proposition that S” to be intersubstitutable salva veritate under certain ‘selective’ attitudinal verbs that grammatically accept both sorts of terms as complements. The Substitution Anomaly poses a direct threat to the basic assumptions of Millianism, which predict the interchangeability of “that S” and “the proposition that S”. Jeffrey King has argued persuasively that the most plausible Millian solution is to treat the selective (...) attitudinal verbs as lexically ambiguous , having distinct meanings associated with the different sorts of complement terms. In opposition this approach, I argue that there are independent reasons for maintaining the univocality of these verbs and that this can be done while accommodating the Substitution Anomaly and without sacrificing the transparency of the relevant attitude ascriptions. In particular, I show how, by employing an extended version of Edward Zalta’s system of intensional logic for abstractobjects, one can construct for a regimented fragment ℜ of English containing the relevant vocabulary a semantical theory ℑ which (a) treats ℜ’s selective attitudinal verbs as univocal, (b) regards genuine terms as occurring transparently under such verbs in sentences of ℜ, and yet (c) predicts the occurrence of the Substitution Anomaly in ℜ. (shrink)
I consider the field of aesthetics to be at its most productive and engaging when adopting a broadly philosophically informative approach to its core issues (e.g., shaping and testing putative art theoretic commitments against the relevant standard models employed in philosophy of language, metaphysics, and philosophy of mind) and to be at its most impotent and bewildering when cultivating a philosophically insular character (e.g., selecting interpretative, ontological, or conceptual models solely for fit with pre-fixed art theoretic commitments). For example, when (...) philosophical aesthetics tends toward insularity, we shouldn’t be surprised to find standard art-ontological categories incongruous with those standardly employed in contemporary metaphysics. Of course, when contemporary metaphysics tends to ignore aesthetic and art theoretic concerns, perhaps we likewise shouldn’t be surprised to find the climate of contemporary metaphysics inhospitable for a theory of art. While this may seem to suggest at least a prima facie tension between our basic art theoretic commitments considered from within philosophical aesthetics and our standard ontological commitments considered from without, I think any perceived tension or antagonism largely due to metaphysicians and aestheticians (at least implicitly) assuming there to be but two available methodological positions with respect to the relationship between contemporary metaphysics and philosophical aesthetics (in the relevant overlap areas). I call these two opposing views the Deference View and the Independence View. I argue that either view looks to lead to what I call the Paradox of Standards. (shrink)
This is a dialogue in which five characters are involved. Various issues in the philosophy of mathematics are discussed. Among those issues are these: numbers as abstractobjects, our knowledge of numbers as abstractobjects, a proof as showing a mathematical statement to be true as opposed to the statement being true in virtue of having a proof.
In this paper, I explore a seldom-recognized connection between the ontology of abstractobjects and a current issue in the philosophy of chemistry. Specifically, I argue that realism with regard to universals implies a view of chemical elements similar to F.A. Paneth’s thesis about the dual nature of the concept of element.