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* (3,556 | 167)
Ontology of Music* (564 | 330)
Ontology of Mathematics* (2,633 | 344)
Words* (551)
The Nature of Sets* (286 | 111)
Numbers* (370)
See also:History/traditions: Abstract Objects

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  1. The 'Two Universes' Theory.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory/.
    The human lives in two universes. One inside. The other outside. One completely abstract. The other concrete. Telling all of us something important about Nature and ‘reality.’.
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  2. Ontology and Arbitrariness.David Builes - 2022 - Australasian Journal of Philosophy 100 (3):485-495.
    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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  3. Stairway to Heaven.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
    The metaphor proves reality, and observation, all of it (the human mind) (and, therefore, a universal mind), is unified, made possible, and controlled, by the conservation of a circle. Metaphorically 'speaking'…pi in mathematics is the technical term for the word 'mind' (any context): the stairway to heaven (and-or hell)… (See, Also: Magical Thinking).
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  4. Immanence in Abundance.Chad Carmichael - forthcoming - Erkenntnis:1-19.
    In this paper, I develop a theory on which each of a thing’s abundant properties is immanent in that thing. On the version of the theory I will propose, universals are abundant, each instantiated universal is immanent, and each uninstantiated universal is such that it could have been instantiated, in which case it would have been immanent. After setting out the theory, I will defend it from David Lewis’s argument that such a combination of immanence and abundance is absurd. I (...)
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  5. The Singularity.Ilexa Yardley - 2022 - Intelligent Design Center.
    The 'singularity' in Nature is a concrete-abstraction (think: tokenization) of the circular-linear relationship between 'me' and 'you.' Also, known as, 'me' and 'me' ('you' and 'you'). (Any and every 'me.') (Any and every 'you'.) Explaining the ontology, and, thus, the epistemology, of technology and finance (physics and psychology) (biology and philosophy). The abstract 'object.' The notion of 'self.' Any NFT (non-fungible and-or fungible token). The 'genetics of information.' The 'tokenized' state.
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  6. Object-Oriented 'Reality'.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory.
  7. Negation.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory.
    Negation is a sophisticated form of duplication. Proving (and demonstrating) 'The Singularity.' Eliminating the need for proof.
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  8. Words on Kripke’s Puzzle.Maciej Tarnowski & Maciej Głowacki - 2022 - Synthese 200 (4):1-21.
    In this paper we present a solution to Saul Kripke’s Puzzle About Belief Meaning and use, Dordrecht, 1979) based on Kaplan’s metaphysical picture of words. Although it is widely accepted that providing such a solution was one of the main incentives for the development of Kaplan’s theory, it was never presented by Kaplan in a systematic manner and was regarded by many as unsatisfactory. We agree with these critiques, and develop an extension of Kaplan’s theory by introducing the notion of (...)
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  9. The Cryptic Universe.Ilexa Yardley - 2022 - Intelligent Design Center.
    Information, and, thus, technology (any and every system and-or discipline), depends upon the tokenization (and, thus, the conservation) of a circle (one zero and one one) (one circumference and one diameter). Explaining the human mind, the ‘abstract object,’ and the cryptic universe. Where any (and every) ‘universe’ (think: unit) is totally dependent on the circular-linear relationship between abstract and concrete reality (which is fully accessible (and, thus, only, understandable)) via the Circular Theory diagram (a cryptic, concrete, fully tokenized, abstraction) (for (...)
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  10. The Information Economy.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory.
    Everything in a human 'universe' (a human mind) depends upon finance. This is because finance is the tokenization, and, therefore, the conservation (the representation) of an uber-basic circle. One zero and (or) one one produces an unlimited number (variation) (combination) of zeroes and ones. Which is exactly what is happening in all disciplines (philosophy, physics, psychology, biology, technology, media).
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  11. Mereology and The 'Singularity'.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory/.
    There is a conserved circular-linear relationship between an individual and a group (a part and a whole) (half and whole) (whole and half). Explaining mereology and producing the 'singularity' (a universal theory of everything, all disciplines) (which may be impossible for humans to accept).
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  12. Why Mathematics Can Never Explain Reality.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
    Why Mathematics Can Never ‘Explain’ Reality: Well, for one thing, as everybody knows, there is no ‘Reality.’ All symbolic systems require the conservation of a circle, which is the core, and, thus, the only, dynamic in Nature. It is not possible to have X without Y (X without one other X) because it is not possible to have a circumference (a zero) without a diameter (a one). So, this proves the token for 'tokenization' that is necessary for general relativity (more (...)
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  13. Memetics.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory/.
    Meme means ‘copy.’ Bio means ‘two.’ Biomemetics is (the study of) (the belief that) the tokenization of reality is a (continual) (and perpetual) copy of the number ‘two.’ Explaining, fundamentality, universals, abstraction, representation, tokenization, the 'self' in any discipline. Identity, Complementarity, Reality.
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  14. Circular Thinking.Ilexa Yardley - 2020 - Https://Medium.Com/the-Circular-Theory.
    Circular Thinking is essential (required) in order to understand ‘reality’ (Nature in general)… including the relationship between mind and matter (abstraction and representation).
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  15. Thinking About Thought.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory/.
    A thought is not possible without the conservation of a circle. Thus, the representation of a thought is, also, not possible without (the conservation of) a circle.
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  16. What the Metaverse has to do with Physics.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
  17. Man-Made Systems vs. Mind-Made Systems.Ilexa Yardley - 2022 - Https://Medium.Com/the-Circular-Theory.
    Mind does not operate using sequence (also known, to ‘man,’ as ‘time’). Think: philosophical, and physical, fusion.
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  18. Abstract Events in Semantics.Gilles Kassel - 2022 - Philosophia 50 (4):1913-1930.
    Here, we defend the thesis whereby the event plays a main role of sense in the meaning of certain sentences. This thesis is based on the one hand on recent work in the metaphysics of so-called “happening” entities, which has led to a distinction between concrete physical processes and abstract events, the latter being conceived as psychological constructs accounting for stabilities or changes in the world. Furthermore, we look back at the work on intentionality carried out in the Brentanian school (...)
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  19. How a Simple Circle Controls the Whole Universe.Ilexa Yardley - 2017 - Https://Medium.Com/the-Circular-Theory/.
    Complementarity is the basis for identity because duplicity is the basis for a unit. Proving we already have a ‘theory of everything’ at our disposal: Conservation of the Circle.
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  20. Neutrality and Force in Field's Epistemological Objection to Platonism.Ylwa Sjölin Wirling - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Field’s challenge to platonists is the challenge to explain the reliable match between mathematical truth and belief. The challenge grounds an objection claiming that platonists cannot provide such an explanation. This objection is often taken to be both neutral with respect to controversial epistemological assumptions, and a comparatively forceful objection against platonists. I argue that these two characteristics are in tension: no construal of the objection in the current literature realises both, and there are strong reasons to think that no (...)
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  21. Diane, I am Now Upside Down.Kristopher G. Phillips & Veronica McMullen - 2018 - In Richard Greene & Rachel Robison-Greene (eds.), Twin Peaks and Philosophy: That's Damn Fine Philosophy! Chicago, IL, USA: pp. 165-178.
    Using Twin Peaks' Agent Dale Cooper as an example, we explore the paradox of fiction. Employing resources from Aimee Thomasson's account of fictional characters in conjunction with some research on parasocial interaction, we make offer a potential solution for the paradox.
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  22. The Universal System Architecture of Nature.Ilexa Yardley - 2022 - Intelligent Design Center.
    The conservation of a circle produces the universal system architecture of Nature, and, therefore, the architecture for a quantum information system. There is a mandatory circle (a circular-linear relationship) between mind and matter (abstract and concrete 'reality') explaining (and exposing) both (you need both in order to have either) (complementarity is required (another word) for 'identity').
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  23. Contemporary Art: Ontology.Sherri Irvin - 2014 - In Michael Kelly (ed.), Encyclopedia of Aesthetics, 2nd ed., Vol. 2. Oxford University Press. pp. 170-172.
    The ontology of visual artworks might be thought comparable to the ontology of other sorts of artifacts: a work of painting seems to be materially constituted by a particular canvas with paint on it, just as a spoon is constituted by a particular piece of metal. But recent developments have complicated the situation, requiring a new account of the ontology of contemporary art. These developments also shed light on the ontology of works from earlier historical eras. This article discusses Artworks (...)
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  24. 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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  25. 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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  26. Norm and Object: A Normative Hylomorphic Theory of Social Objects.Asya Passinsky - 2021 - Philosophers' Imprint 21 (25):1-21.
    This paper is an investigation into the metaphysics of social objects such as political borders, states, and organizations. I articulate a metaphysical puzzle concerning such objects and then propose a novel account of social objects that provides a solution to the puzzle. The basic idea behind the puzzle is that under appropriate circumstances, seemingly concrete social objects can apparently be created by acts of agreement, decree, declaration, or the like. Yet there is reason to believe that no concrete object can (...)
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  27. Quantum Reality.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory.
    Reality at any scale (a singularity of singularities) involves the conservation of a circle. This is because zero and one (modern) (yin and yang) (ancient) are, technically, and, thus 'realistically' (literally), circumference and diameter. This means we are, always, tokenizing space, explaining 'the matrix,' 'information,' 'information systems,' and algorithms (mathematics and technology). This is because, what humans label, 'mind' and 'matter,' like any X and X (X and Y) (X and X') articulate, and, thus, conserve an always-present (totally prescient) circular-linear (...)
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  28. 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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  29. 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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  30. 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
  31. 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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  32. Why Crypto-Everything is Here to Stay.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
  33. Technology and the Realization of ‘Self’.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory.
    Everything in Nature is, technically, a non-fungible token for 'self.' Explaining the meaning of the word 'self' across all disciplines. Introduces and explains Biomemetics (neologism for the technological realization of 'self').
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  34. Abstraction: How to Understand It.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
  35. 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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  36. Duality.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory/.
  37. What Is Metascientific Ontology?François Maurice - 2022 - Mεtascience: Scientific General Discourse 2:22-44.
    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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  38. The Most Advanced Thinking on the Planet (In the Universe).Ilexa Yardley - 2020 - Https://Medium.Com/the-Circular-Theory/.
  39. The Proportionality Argument and the Problem of Widespread Causal Overdetermination.Alexey Aliyev - 2020 - Disputatio 12 (59):331-355.
    The consensus is that repeatable artworks cannot be identified with particular material individuals. A perennial temptation is to identify them with types, broadly construed. Such identification, however, faces the so-called “Creation Problem.” This problem stems from the fact that, on the one hand, it seems reasonable to accept the claims that repeatable artworks are types, types cannot be created, and repeatable artworks are created, but, on the other hand, these claims are mutually inconsistent. A possible solution to the Creation Problem (...)
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  40. Qu'est-ce que l'ontologie métascientifique?François Maurice - 2022 - Mεtascience: Discours Général Scientifique 2:19-43.
    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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  41. Configuration Symmetry.Ilexa Yardley - 2018 - Https://Medium.Com/the-Circular-Theory/.
  42. 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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  43. Philosophy: Origination and Destination.Ilexa Yardley - 2021 - Https://Medium.Com/the-Circular-Theory.
    An uber-simple circle is the basis for (and explains) everything in philosophy.
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  44. 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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  45. 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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  46. 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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  47. 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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  48. The Qubit: The Universal System Architecture of Nature (Relative Identity) (Self-Reference) (Quantum Entanglement).Ilexa Yardley - 2019 - Medium.Com/the-Circular-Theory.
    Relative identity produces, because it is produced by, an uber-simple, always-conserved, circle. Zero, and one, is circumference, and diameter, literally, and figuratively. Explaining the metaphor. And, Nature. Also, Self-referential reality. Quantum Entanglement. Philosophical, Psychological, Physical Fusion. (0(1)0).
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  49. 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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  50. 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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