Abstract Objects

Edited by Sam Cowling (Denison University)
About this topic
Summary

Abstract entities such as numbers, propositions, and universals are usually contrasted with concrete entities such as tables, tadpoles, and quasars. While concrete entities are typically held to exist contingently, stand in causal relations, and occupy space and time, abstract entities are usually (though controversially) held to be necessary existents that are causally inert and "outside" of space and time. According to platonists, there are at least some abstract entities, but, given the peculiar metaphysical status of abstract entities, concerns arise about how we might come to know or refer to them. Further controversies surround the nature of the abstract-concrete distinction, the essential features of abstract entities, and the plausibility of nominalism, according to which there are no abstract entities.

Key works The literature on abstract entities is vast and closely connected to debates in the philosophy of mathematics, philosophy of science, philosophy of language, and epistemology. Burgess & Rosen 1997 is the leading survey of nominalist views regarding mathematical entities and includes an excellent survey of the nominalist-platonist debate. Two papers by Paul Benacerraf—Benacerraf 1973 and Benacerraf 1965—are hugely influential. Notable recent work regarding nominalist options in the philosophy of mathematics and other domains include Field 1980, Azzouni 2004, Leng 2010, and Hofweber 2016.  Guides to the specialist literature regarding specific kinds of abstract entities can be found in other entries, but some useful starting points are as follows. On possible worlds, see Divers 2002. On types, see Wetzel 2009. On propositions, see King et al 2014. On fictional entities, see Thomasson 1998.
Introductions Rosen 2008 and Szabo 2003 are useful survey articles of the issues raised by abstract entities. There are also a host of good entries in the Stanford Encyclopedia of Philosophy on topics related to abstract entities. Balaguer 2008, Linnebo 2009, and Rodriguez-Pereyra 2008 are excellent places to start. Armstrong 1989 is a leading introduction to the metaphysics of properties, which are usually held to be abstract entities. MacBride 1999 and MacBride 2003 survey fictionalist and neo-Fregean approaches to abstract mathematical entities. General introductions to metaphysics with useful sections on abstract entities include Jubien 1997 and Loux & Crisp 1997. Cowling 2017 is a fairly comprehensive and accessible discussion of the metaphysics of abstract entities.
Related categories
Subcategories:
Properties* (3,338 | 152)
Ontology of Music* (552 | 327)
Ontology of Mathematics* (2,412 | 328)
Words* (562)
The Nature of Sets* (256 | 98)
Numbers* (364)
See also:History/traditions: Abstract Objects

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  1. The Ontological Diversity of Visual Artworks.Sherri Irvin - 2008 - In Kathleen Stock & Katherine Thomson-Jones (eds.), New Waves in Aesthetics. Palgrave Macmillan. pp. 1-19.
    Virtually everyone who has advanced an ontology of art has accepted a constraint to the effect that claims about ontology should cohere with the sort of appreciative claims made about artworks within a mature and reflective version of critical practice. I argue that such a constraint, which I agree is appropriate, rules out a one-size-fits-all ontology of contemporary visual art (and thus of visual art in general). Mature critical practice with respect to contemporary art accords artists a significant degree of (...)
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  2. Words, Species, and Kinds.J. T. M. Miller - 2021 - Metaphysics 4 (1):18–31.
    It has been widely argued that words are analogous to species such that words, like species, are natural kinds. In this paper, I consider the metaphysics of word-kinds. After arguing against an essentialist approach, I argue that word-kinds are homeostatic property clusters, in line with the dominant approach to other biological and psychological kinds.
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  3. Uploads, Faxes, and You: Can Personal Identity Be Transmitted?Jonah Goldwater - 2021 - American Philosophical Quarterly 58 (3):233–250.
    Abstract. Could a person or mind be uploaded—transmitted to a computer or network—and thereby survive bodily death? I argue ‘mind uploading’ is possible only if a mind is an abstract object rather than a concrete particular. Two implications are notable. One, if someone can be uploaded someone can be multiply-instantiated, such that there could be as many instances of a person as copies of a book. Second, mind uploading’s possibility is incompatible with the leading theories of personal identity, insofar as (...)
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  4. Living in a Tokenized (Think: Cryptic) Reality.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory.
    Zero and one (modern) are yin and yang (ancient), circumference and diameter (literally and figuratively) of an always-conserved (omnipresent) circular-linear relationship. Explaining everything in Nature.
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  5. Pour comprendre le monde et revenir à la raison. La théorie du tout d'un généticien.Gilbert B. Côté - manuscript
    French translation by G. B. Côté and Roger Lapalme of "A Geneticist's Roadmap to Sanity" (G. B. Côté, 2019) with added bibliography. -/- À voir le monde d’aujourd’hui, on pourrait croire que nous avons perdu la raison. Je veux explorer ici les fondements mêmes de notre existence. Je discuterai brièvement du libre arbitre, de l’éthique, de la religion, de la souffrance, du dualisme cartésien et de l’état de conscience, avec un arrière-plan promulguant l’importance de la physique quantique d’aujourd’hui et de (...)
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  6. Abstract Objects and Semantics: An Essay on Prospects and Problems with Abstraction Principles as a Means of Justifying Reference to Abstract Objects.Gnatek Zuzanna - 2020 - Dissertation, Trinity College, Dublin
  7. Dwojaka natura ontologiczna znaków językowych i problem ich wzajemnych relacji.Urszula Wybraniec-Skardowska - 2021 - Ruch Filozoficzny 77 (1):7-24.
    The subject matter of this work covers the issues or problems listed below: * The problem of the ontological status of language signs and a more general philosophical problem connected with it: * What is language as a system of signs, which – on the one hand – serves to: 1) represent our knowledge about the reality which is being recognized, and, on the other one to: 2) a. explore and better cognize or discover it, b. describe it in an (...)
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  8. Abstraction: How to Understand It.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
  9. Ontology and Arbitrariness.David Builes - forthcoming - Australasian Journal of Philosophy.
    In many different ontological debates, anti-arbitrariness considerations push one towards two opposing extremes. For example, in debates about mereology, one may be pushed towards a maximal ontology (mereological universalism) or a minimal ontology (mereological nihilism), because any intermediate view seems objectionably arbitrary. However, it is usually thought that anti-arbitrariness considerations on their own cannot decide between these maximal or minimal views. I will argue that this is a mistake. Anti-arbitrariness arguments may be used to motivate a certain popular thesis in (...)
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  10. The Future of 'NFT'.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory.
    Hidden behind any 'one' is some 'other' 'one'... thus, the circle is conserved (circularity is the core dynamic in Nature) (producing a completely tokenized reality).
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  11. Euclid's Error: The Mathematics Behind Foucault, Deleuze, and Nietzsche.Ilexa Yardley - 2021 - Intelligent Design Center.
    We have to go all the way back to Euclid, and, actually, before, to figure out the basis for representation, and therefore, interpretation. Which is, pure and simple, the conservation of a circle. As articulated by Foucault, Deleuze, and Nietzsche. 'Pi' (in mathematics) is the background state for everything (a.k.a. 'mind').Providing the explanation for (and the current popularity, and, thus, the 'genius' behind) NFT (non fungible tokens). 'Reality' has, finally, caught up with the 'truth.'.
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  12. What Is Metascientific Ontology?François Maurice - 2021 - Mεtascience 2:online.
    Metascientific ontology differs from philosophical ontologies in its objectives, objects and methods. By an examination of the ontological theories of Mario Bunge, we will show their main objective is a unified representation of the world as known through the sciences, that their objects of study are scientific concepts, and that their methods do not differ from those that one expects to find in any rational activity. Metascientific ontology is therefore not transcendent because it does not seek to represent non-concrete objects (...)
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  13. Qu'est-ce que l'ontologie métascientifique?François Maurice - 2021 - Mεtascience 2:prépublication.
    L’ontologie métascientifique se distingue des ontologies philosophiques par ses objectifs, ses objets et ses méthodes. Par un examen des théories ontologiques de Mario Bunge, nous montrerons que leur principal objectif est l’élaboration d’une représentation unifiée du monde tel que connu via les sciences, que leurs objets d’étude sont les concepts scientifiques, et que leurs méthodes ne diffèrent pas de celles qu’on s’attend à trouver dans toute activité rationnelle. L’ontologie métascientifique n’est donc pas transcendante parce qu’elle ne cherche pas à représenter (...)
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  14. The Billionaire.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
    Zero and one. Circumference and diameter. Intelligent anarchy. Explanation for abstraction (as a noun) (as a verb).
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  15. Meinongian Merits and Maladies.Samuel Hoadley-Brill - manuscript
    According to what has long been the dominant school of thought in analytic meta-ontology––defended not only by W. V. O. Quine, but also by Bertrand Russell, Alvin Plantinga, Peter van Inwagen, and many others––the meaning of ‘there is’ is identical to the meaning of ‘there exists.’ The most (in)famous aberration from this view is advanced by Alexius Meinong, whose ontological picture has endured extensive criticism (and borderline abuse) from several subscribers to the majority view. Meinong denies the identity of being (...)
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  16. Translation and Metaphysics: A Case for Fictional Characters.Italo Lins Lemos - 2020 - Cadernos de Tradução 40 (1):110-126.
    If different translations of the same literary work have different syntaxes and semantics, how are they supposed to be about one and the same fictional character? In order to answer this question it’s necessary to (a) know what fictional characters are and (b) present reference conditions for them. Relying on Amie Thomasson’s (1999, 2003, 2007) and Saul Kripke’s (1980, 2013) works I argue that fictional characters are abstract artifacts whose reference is fixed by the baptism performed by an author; and (...)
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  17. Erik Wielenberg’s Metaphysics of Morals.William Lane Craig - 2018 - Philosophia Christi 20 (2):333-338.
    Focusing on Erik Wielenberg’s metaphysic of morals, I argue that his moral Platonism is, given the presumption against the existence of abstract objects, unmotivated. Moreover, Godless Normative Realism is implausible in light of the mysterious causal relations said to obtain between concrete objects and moral abstracta. His appeals to theism in order to motivate such causal connections is nugatory. If Wielenberg walks back his moral Platonism, then his metaphysics of morals collapses and Godless Normative Realism becomes explanatorily vacuous.
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  18. On Infinite Size.Bruno Whittle - 2015 - Oxford Studies in Metaphysics 9:3-19.
    This chapter challenges Cantor’s notion of the ‘power’, or ‘cardinality’, of an infinite set. According to Cantor, two infinite sets have the same cardinality if and only if there is a one-to-one correspondence between them. Cantor showed that there are infinite sets that do not have the same cardinality in this sense. Further, he took this result to show that there are infinite sets of different sizes. This has become the standard understanding of the result. The chapter challenges this, arguing (...)
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  19. Should Physicalists Fear Abstracta?B. G. Montero - 2017 - Journal of Consciousness Studies 24 (9-10):40-49.
    Susan Schneider argues that physicalism must be false if abstracta are part of the physicalist's dependence base. In opposition to her view, here I set out some reasons to think that abstracta in general, including abstracta that are woven into the dependence base, are something physicalists can countenance with consistency.
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  20. Abstract Objects and the Core-Periphery Distinction in the Ontological and the Conceptual Domain of Natural Language.Friederike Moltmann - 2020 - In José Luis Falguera & María De La Martínez Vidal (eds.), Abstract Objects: For and Against. Springer. pp. 255-276.
    This paper elaborates distinctions between a core and a periphery in the ontological and the conceptual domain associated with natural language. The ontological core-periphery distinction is essential for natural language ontology and is the basis for the central thesis of my 2013 book Abstract Objects and the Semantics of Natural Language, namely that natural language permits reference to abstract objects in its periphery, but not its core.
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  21. Sympathy for the Scientist: Re-Calibrating a Heideggerian Critique of Metaphysics.Jonathan Morgan - manuscript
    This paper attempts to develop an ethico-aesthetic framework for enriching one's life and ethical outlook. Drawing primarily from Nietzsche, Foucault, and Heidegger, an argument is made that Heidegger's understanding of this issue was mistaken. The ontological crisis of modernity is not the overt influence of mathematics as a worldview over poetics and more traditionally aesthetic approaches. It is the rampant mis-and over-application of abstraction within one's view of the world while denying the material realities of life as we live it. (...)
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  22. Putnam, Peano, and the Malin Génie: Could We Possibly Bewrong About Elementary Number-Theory?Christopher Norris - 2002 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 33 (2):289-321.
    This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following, Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a (...)
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  23. Towards an Account of Epistemic Luck for Necessary Truths.James Collin - 2018 - Acta Analytica 33 (4):483-504.
    Modal epistemologists parse modal conditions on knowledge in terms of metaphysical possibilities or ways the world might have been. This is problematic. Understanding modal conditions on knowledge this way has made modal epistemology, as currently worked out, unable to account for epistemic luck in the case of necessary truths, and unable to characterise widely discussed issues such as the problem of religious diversity and the perceived epistemological problem with knowledge of abstract objects. Moreover, there is reason to think that this (...)
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  24. Towards a Pluralist Theory of Singular Thought.Michele Palmira - 2018 - Synthese 195 (9):3947-3974.
    This paper investigates the question of how to correctly capture the scope of singular thinking. The first part of the paper identifies a scope problem for the dominant view of singular thought maintaining that, in order for a thinker to have a singular thought about an object o, the thinker has to bear a special epistemic relation to o. The scope problem has it is that this view cannot make sense of the singularity of our thoughts about objects to which (...)
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  25. Repeatable Artworks and the Relevant Similarity Relation.Sherri Irvin - 2018 - Journal of Aesthetic Education 52 (2):30.
    Repeatable artworks, such as novels and musical works, have often been construed as universals whose instances are particular printings or performances. In Art and Art-Attempts, Christy Mag Uidhir offers a nominalist account of repeatable artworks, eschewing talk of universals. Mag Uidhir argues that all artworks are concrete, and artworks that we regard as repeatable are simply unified by a relevant similarity relation: we use the name Beloved to refer to two concrete printed novels because they are relevantly similar to each (...)
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  26. Introduction to the Symposium on Christy Mag Uidhir's Art and Art-Attempts.Sherri Irvin - 2018 - Journal of Aesthetic Education 52 (2):1.
    Christy Mag Uidhir’s Art and Art-Attempts begins from two deceptively simple observations: artworks are the product of intentions, and intentions are the kinds of things that can fail to be realized successfully. Drawing on these observations, he argues that most contemporary theories of art must be rejected because they are not substantively intention-dependent: that is, they do not account for the fact that an attempt to make an artwork can fail. From his view that artworks must be the product of (...)
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  27. Causal Powers and Isomeric Chemical Kinds.Andrew McFarland - 2018 - Synthese 195 (4):1441-1457.
    Some philosophers have claimed that kinds can be construed as mereologically complex structural properties. This essay examines several strategies aimed at construing a certain class of natural kinds, namely isomeric chemical kinds, in accordance with this view. In particular, the essay examines views which posit structural proper parts in addition to micro-constitutive parts to individuate isomeric chemical kinds. It then goes on to argue that the phenomenon of chirality in stereochemistry gives the proponent of kinds-as-complex-properties evidence for positing the existence (...)
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  28. Towards a Unified Framework for Decomposability of Processes.Valtteri Lahtinen & Antti Stenvall - 2017 - Synthese 194 (11):4411-4427.
    The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on sequential and parallel decomposability of processes in the framework of monoidal categories: We will give a precise definition, what it means for processes to be decomposable. Moreover, through examples, we argue that viewing parallel processes as coupled in this framework can be seen as a category (...)
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  29. Chapter 6: Reifying Terms.Friederike Moltmann - 2013 - In Abstract Objects and the Semantics of Natural Language. Oxford: Oxford University Press.
    This chapter develops a semantics for 'reifying terms' of the sort 'the proposition that S', 'the fact that S', 'the property of being P', 'the number eight', 'the concept horse', 'the truth value true', 'the kind humane being'. This semantics is developed within the broader perspective of the ontology of natural language involving abstract objects only at its periphery, not its core.
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  30. Nominalization, Specification, and Investigation.Richard Lawrence - 2017 - Dissertation, University of California, Berkeley
    Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...)
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  31. VI—Nominalistic Adequacy.Jeffrey Ketland - 2011 - Proceedings of the Aristotelian Society 111 (2pt2):201-217.
    Instrumentalist nominalism responds to the indispensability arguments by rejecting the demand that successful mathematicized scientific theories be nominalized, and instead claiming merely that such theories are nominalistically adequate: the concreta behave ‘as if’ the theory is true. This article examines some definitions of the concept of nominalistic adequacy and concludes with some considerations against instrumentalist nominalism.
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  32. The Adequacy of Resemblance Nominalism About Perfect Naturalness.Ralf Busse - 2018 - Philosophy and Phenomenological Research (2):443-469.
    Resemblance Nominalism About Perfect Naturalness is the view that perfect naturalness of classes is best defined by a conceptual primitive of resemblance between particulars. The adequacy of RNPN is defended by outlining nominalism as the strictly anti-constitutive view that the particulars’ being the fundamental ways they are is not constituted by anything further, supplying a doubly plural contrastive and graded resemblance predicate that allows for a definition of perfect naturalness on an actualist basis, and proving a representation and a uniqueness (...)
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  33. Indiscernible Universals.Gonzalo Rodriguez-Pereyra - 2017 - Inquiry: An Interdisciplinary Journal of Philosophy 60 (6):604-624.
    Universals have traditionally thought to obey the identity of indiscernibles, that is, it has traditionally been thought that there can be no perfectly similar universals. But at least in the conception of universals as immanent, there is nothing that rules out there being indiscernible universals. In this paper, I shall argue that there is useful work indiscernible universals can do, and so there might be reason to postulate indiscernible universals. In particular, I shall argue that postulating indiscernible universals can allow (...)
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  34. Can Emotions Have Abstract Objects? The Example of Awe.Fredericks Rachel - 2018 - Philosophia 46 (3):733-746.
    Can we feel emotions about abstract objects, assuming that abstract objects exist? I argue that at least some emotions can have abstract objects as their intentional objects and discuss why this conclusion is not just trivially true. Through critical engagement with the work of Dacher Keltner and Jonathan Haidt, I devote special attention to awe, an emotion that is particularly well suited to show that some emotions can be about either concrete or abstract objects. In responding to a possible objection, (...)
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  35. Jakub Mácha, Wittgenstein on Internal and External Relations: Tracing All the Connections . 262 Pages. Hardcover ISBN 9781474242141. [REVIEW]Aloisia Moser - 2017 - Philosophical Investigations 40 (2):196-200.
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  36. Categoricity, Open-Ended Schemas and Peano Arithmetic.Adrian Ludușan - 2015 - Logos and Episteme 6 (3):313-332.
    One of the philosophical uses of Dedekind’s categoricity theorem for Peano Arithmetic is to provide support for semantic realism. To this end, the logical framework in which the proof of the theorem is conducted becomes highly significant. I examine different proposals regarding these logical frameworks and focus on the philosophical benefits of adopting open-ended schemas in contrast to second order logic as the logical medium of the proof. I investigate Pederson and Rossberg’s critique of the ontological advantages of open-ended arithmetic (...)
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  37. Frege's Conception of Numbers as Objects. [REVIEW]Michael D. Resnik - 1984 - Journal of Philosophy 81 (12):778-783.
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  38. Abstract Objects, by Bob Hale. [REVIEW]Harold W. Noonan - 1989 - Philosophical Quarterly 39 (156):354-357.
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  39. Some Descriptive Properties of Relations. I.Henry Lanz - 1931 - Philosophical Review 40:341.
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  40. WRIGHT, C. "Frege's Conception of Numbers as Objects". [REVIEW]D. Gillies - 1984 - Mind 93:613.
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  41. The 'Direction' of Non-Symmetrical Relations.P. F. Strawson - 1972 - Critica 6 (16/17):3-13.
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  42. Receptivity and Our Knowledge of Intrinsic Properties.James Van Cleve - 2002 - Philosophy and Phenomenological Research 65 (1):218-237.
    This is a marvelous book. Langton offers a fresh interpretation of Kant, the main tenets of which she states in a few bold propositions and then goes on to elaborate with great clarity and care. She supports her interpretation with a wealth of citations accompanied by insightful commentary. The “Humility” of her title is the thesis that we can have no knowledge of the intrinsic properties of things, which is Langton’s gloss on the Kantian slogan that we can have no (...)
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  43. La Structure Métaphysique. [REVIEW]O. D. - 1976 - Review of Metaphysics 30 (2):360-361.
    This book is published as part of a series catering mainly to the undergraduate and is written on a fairly general, vulgarizing level. However, Schlanger—author of a monograph on the Medieval Jewish Neoplatonist Ibn Gabirol —takes the occasion to provide some reflections on the essence of philosophy and on the interpretation of its history. Of the two sections of the book, the first analyzes what is essential, non-contingent, in any philosophical system, and the second describes the essential aspect of a (...)
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  44. Gottlob Ernst Schulze: Positivist van Het Duitse Idealisme. [REVIEW]C. R. L. - 1979 - Review of Metaphysics 32 (3):535-535.
    Gottlob Schulze has been almost totally neglected by English-speaking philosophers and historians of philosophy. His German commentators have been almost unanimous in their claim that his "positivism" arises out of a misunderstanding of Kant’s transcendental method and an ability to connect the various subdivisions of his own philosophical system. The present study will probably do little to set aside that verdict. Schulze’s "positivism" is more Comtean than Kantian, though the general architectonic of his "system," however ill-fitted its parts, owes much (...)
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  45. Some Properties of Thin Πmath Image Sets.Yutaka Yasuda - 1987 - Mathematical Logic Quarterly 33 (3):199-200.
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  46. Problém abstraktních pojmů: Odpověď Davidu Peroutkovi.Lukáš Novák - 2007 - Studia Neoaristotelica 4 (1):90-95.
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  47. Problém abstraktních pojmů: Odpověď bosým karmelitánům.Lukáš Novák - 2007 - Studia Neoaristotelica 4 (2):185-192.
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  48. The Scotist Theory of Univocity: A Journal of Analytic Scholasticism.Lukáš Novák - 2006 - Studia Neoaristotelica 3 (1):17-27.
    The article explains the notion of univocity in line with the mature Scotistic doctrine, which plays so crucial a role in the Scotistic rejection of analogy as a middle ground between univocity and pure equivocity. Since univocity of a concept is found to consist in its perfect unity, and the perfect unity of a concept is achieved by means of perfect abstraction, the notion of this so-called abstraction by precision is made clear and contrasted with the so-called abstraction by confusion, (...)
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  49. Platonism Versus Nominalism: Carnap and Goodman.Susan Haack - 1978 - The Monist 61 (3):483-494.
    According to Goodman one important advantage of his Structure of Appearance over Carnap’s Aufbau is that his is a nominalist, whereas Carnap’s is a platonist, construction. Superficially, it is clear enough why Goodman should say this: Carnap employs set-theory, whereas Goodman allows himself only mereology. One object of this paper is to show that this superficial impression is rather misleading—that closer comparison of the two books reveals that each has a claim to be regarded as the more nominalist. Another aim (...)
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  50. The Nominalist Argument of the New Essays.Martha Brandt Bolton - 1996 - The Leibniz Review 6:1-24.
    There is in the New Essays a prominent line of argument that Leibniz took to have remarkable scope. If it works, it sweeps away most of the mainstays of Locke’s metaphysics: atoms, vacuum, real space and time, absolute rest, inactive faculties, and the tabula rasa. It alone does not suffice to undermine the possibility of thinking matter, but it contributes support to that most important of Leibniz’s claims against Locke. Because it is so central to the project of New Essays, (...)
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