About this topic
Summary A slogan form of the thesis of composition as identity says that a whole is the same as its parts. Beyond that, there is no agreement on what the thesis of composition as identity is. A strong version of it says that a whole is identical with its parts. More precisely, it says either that a whole is identical with each one of its parts distributively, but not with all of them collectively; or that a whole is identical with each one of its parts distributively and collectively; or that a whole is identical with all its parts collectively, but not distributively. Composition as identity is thus committed to, in some form or other, a revision or generalization of the traditional laws of identity. A weaker version of composition as identity says that composition is very much like, but not the same as, the identity relation.
Key works The classic readings are Baxter 1988, Baxter 1988, Lewis 1990 and Sider 2007
Introductions The only introductions to this topic are Wallace 2011, Wallace 2011 and Cotnoir 2014
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134 found
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  1. Mereological Atomism's Quantum Problems.Ryan Miller - manuscript
    The popular metaphysical view that concrete objects are grounded in their ultimate parts is often motivated by appeals to realist interpretations of contemporary physics. This paper argues that an examination of mainstream interpretations of quantum mechanics undercuts such atomist claims. First, mereological atomism is only plausible in conjunction with Bohmian mechanics. Second, on either an endurantist or perdurantist theory of time, atomism exacerbates Bohmianism’s existing tensions with serious Lorentz invariance in a way that undermines the realist appeal of both views. (...)
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  2. Rethinking Wholes and Parts: Reflections on Reductionism, Holism, and Mereology.Mark Sharlow - manuscript
    In this set of excerpts from an earlier book, I examine some philosophical issues surrounding the whole-part relationship. I present a series of thought experiments and other arguments designed to undermine the view that wholes are "nothing but" their parts.
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  3. On the Overlap Between Everything and Nothing.Massimiliano Carrara, Filippo Mancini & Jeroen Smid - forthcoming - Logic and Logical Philosophy.
    Graham Priest has recently proposed a solution to the problem of the One and the Many which involves inconsistent objects and a non-transitive identity relation. We show that his solution entails either that the object everything is identical with the object nothing or that they are mutual parts; depending on whether Priest goes for an extensional or a non-extensional mereology.
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  4. Dao as a Unified Composition or Plurality: A Nihilism Perspective.Rafal Banka - 2023 - Dao: A Journal of Comparative Philosophy 22 (3):1-15.
    This article departs from a mereological conceptualization of the Daoist metaphysi- cal system in the Daodejing 道德經. I discuss what parthood status applies to dao 道. Whereas it is quite intuitive that you 有—the region of concrete objects—has parthood relationships and compositions (entities made from parts), the other, undif- ferentiated region, dao, poses a considerable problem. This problem can be charac- terized in the following way: (a) dao cannot be characterized as a particular com- position, which entails that it does (...)
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  5. The essence of the mental.Ray Buchanan & Alex Grzankowski - 2023 - European Journal of Philosophy 31 (4):1061-1072.
    Your belief that Obama is a Democrat would not be the belief that it is if it did not represent Obama, nor would the pain in your ankle be the state that it is if, say, it felt like an itch. Accordingly, it is tempting to hold that phenomenal and representational properties are essential to the mental states that have them. But, as several theorists have forcefully argued (including Kripke (1980) and Burge (1979, 1982)) this attractive idea is seemingly in (...)
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  6. A (Cross‐Count) Compositional Christology.Joshua R. Sijuwade - 2023 - Heythrop Journal 64 (4):532-555.
    This article aims to provide a new philosophical explication of the doctrine of the Incarnation. A compositional model of the doctrine is formulated within the Dispositional Personhood account of Lynne Rudder Baker and the Composition as Identity framework of Donald L.M. Baxter. Formulating the doctrine of the Incarnation within this account and framework will enable it to be explicated in a clear and consistent manner, and the oft‐raised objections against this type of model can be answered.
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  7. Composite Objects are Mere Manys.Simon Thunder - 2023 - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics Volume 13. Oxford, GB: Oxford University Press. pp. 20-50.
    A ubiquitous assumption about composite material objects is that—if they exist at all—they are single things. This chapter articulates and defends manyism, which rejects that assumption. According to manyism, each composite object is simply its many parts. Since manyism accepts the existence of composite objects, it is distinct from nihilism; since manyism denies that composite objects are each one in number in addition to being many in number, it is distinct from the view known as composition as identity (CAI). What’s (...)
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  8. Parts and Wholes.Meg Wallace - 2023 - Cambridge: Cambridge University Press (Cambridge Elements in Metaphysics).
    The Odd Universe Argument aims to show that from four intuitive assumptions about parts and wholes, we can conclude a priori that there is an odd number of things in the universe. This Element is an opinionated survey of philosophical issues involving parthood, composition, identity, and counting, guided by an investigation into where this argument has gone awry. We first walk through some general methodology, basic mereology, and plural logic. Next, we explore questions about the nature of composition and decomposition. (...)
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  9. Mortal Objects: Identity and Persistence Through Life and Death.Steven Luper - 2022 - New York, NY: Cambridge University Press.
    How might we change ourselves without ending our existence? What could we become, if we had access to an advanced form of bioengineering that allowed us dramatically to alter our genome? Could we remain in existence after ceasing to be alive? What is it to be human? Might we still exist after changing ourselves into something that is not human? What is the significance of human extinction? Steven Luper addresses these questions and more in this thought-provoking study. He defends an (...)
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  10. Identity.Harold Noonan & Benjamin L. Curtis - 2022 - Stanford Encyclopedia of Philosophy.
    Much of the debate about identity in recent decades has been about personal identity, and specifically about personal identity over time, but identity generally, and the identity of things of other kinds, have also attracted attention. Various interrelated problems have been at the centre of discussion, but it is fair to say that recent work has focussed particularly on the following areas: the notion of a criterion of identity; the correct analysis of identity over time, and, in particular, the disagreement (...)
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  11. Counting Composites.Jonathan D. Payton - 2022 - Australasian Journal of Philosophy 100 (4):695-710.
    I defend the thesis that Composition Entails Identity (CEI): that is, a whole is identical to all of its parts, taken together. CEI seems to be inconsistent, since it seems to require that the parts of a whole possess incompatible number properties (for instance, being one thing and being many things). I show that these number properties are, in fact, compatible.
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  12. Composition and plethological innocence.Jonathan D. Payton - 2022 - Analysis 82 (1):67-74.
    According to Composition as Identity, a whole is distinct from each of its parts individually, but identical to all of them taken together. It is sometimes claimed that, if you accept CAI, then your belief in a whole is ‘ontologically innocent’ with respect to your belief in its parts. This claim is false. But the defender of CAI can claim a different advantage for her view. Following Agustín Rayo, I distinguish ontology from plethology. I then show that CAI allows us (...)
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  13. Mereology and Identity.Massimiliano Carrara & Giorgio Lando - 2021 - Synthese:4205-4227.
  14. Composition as Identity and the Innocence of Mereology.Roberto Loss - 2021 - Philosophy and Phenomenological Research 105 (1):128-143.
    According to the thesis known as ‘Composition as Identity’ (‘CAI’), every entity is identical to the parts it fuses. Many authors in the literature acknowledge that, in spite of its controversial character, one attractive virtue of CAI is its apparent ability to give a straightforward account of the innocence of mereology. In this paper I will present a simple argument according to which CAI entails that no composite entity can be said to be ontologically innocent in the relevant sense. After (...)
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  15. Composition as identity, now with all the pluralities you could want.Jonathan D. Payton - 2021 - Synthese 199 (3-4):8047-8068.
    According to ‘composition as identity’, a composite object is identical to all its parts taken together. Thus, a plurality of composite objects is identical to the plurality of those objects’ parts. This has the consequence that, e.g., the bricks which compose a brick wall are identical to the atoms which compose those bricks, and hence that the plurality of bricks must include each of those atoms. This consequence of CAI is in direct conflict with the standard analysis of plural definite (...)
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  16. Collocation and Constitution.David-Hillel Ruben - 2021 - Metaphysica 22 (2):251-261.
    Many philosophers accept the view that, when one object constitutes a second, the two objects can be entirely in the same place at the same time. But what of two objects such that neither constitutes the other? Can they be collocated? If there can be such a pair of objects, they would have to share the same material constituents. To show that there are two collocated objects and not just one object at a specific time and place, one has to (...)
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  17. Organisms, activity, and being: on the substance of process ontology.Christopher J. Austin - 2020 - European Journal for Philosophy of Science 10 (2):1-21.
    According to contemporary ‘process ontology’, organisms are best conceptualised as spatio-temporally extended entities whose mereological composition is fundamentally contingent and whose essence consists in changeability. In contrast to the Aristotelian precepts of classical ‘substance ontology’, from the four-dimensional perspective of this framework, the identity of an organism is grounded not in certain collections of privileged properties, or features which it could not fail to possess, but in the succession of diachronic relations by which it persists, or ‘perdures’ as one entity (...)
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  18. Debunking Arguments and Metaphysical Laws.Jonathan Barker - 2020 - Philosophical Studies 177 (7):1829-1855.
    I argue that one’s views about which “metaphysical laws” obtain—including laws about what is identical with what, about what is reducible to what, and about what grounds what—can be used to deflect or neutralize the threat posed by a debunking explanation. I use a well-known debunking argument in the metaphysics of material objects as a case study. Then, after defending the proposed strategy from the charge of question-begging, I close by showing how the proposed strategy can be used by certain (...)
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  19. Is it identity all the way down? From supersubstantivalism to composition as identity and back again.Michael J. Duncan & Kristie Miller - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 1.
    We argue that, insofar as one accepts either supersubstantivalism or strong composition as identity for the usual reasons, one has (defeasible) reasons to accept the other as well. Thus, all else being equal, one ought to find the package that combines both views—the Identity Package—more attractive than any rival package that includes one, but not the other, of either supersubstantivalism or composition as identity.
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  20. The limits of classical mereology: Mixed fusions and the failures of mereological hybridism.Joshua Kelleher - 2020 - Dissertation, The University of Queensland
    In this thesis I argue against unrestricted mereological hybridism, the view that there are absolutely no constraints on wholes having parts from many different logical or ontological categories, an exemplar of which I take to be ‘mixed fusions’. These are composite entities which have parts from at least two different categories – the membered (as in classes) and the non-membered (as in individuals). As a result, mixed fusions can also be understood to represent a variety of cross-category summation such as (...)
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  21. Composition, identity and plural ontology.Roberto Loss - 2020 - Synthese 198 (10):9193-9210.
    According to ‘Strong Composition as Identity’, if an entity is composed of a plurality of entities, it is identical to them. As it has been argued in the literature, SCAI appears to give rise to some serious problems which seem to suggest that SCAI-theorists should take their plural quantifier to be governed by some ‘weak’ plural comprehension principle and, thus, ‘exclude’ some kinds of pluralities from their plural ontology. The aim of this paper is to argue that, contrary to what (...)
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  22. Correction to: On atomic composition as identity.Roberto Loss - 2020 - Synthese 198 (Suppl 18):4543-4543.
    and in Sect. 5 should be reformulated as follows.
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  23. Pluralities, Collectives, and Composites.Claudio Masolo, Laure Vieu, Stefano Borgo, Roberta Ferrario & Daniele Porello - 2020 - In Boyan Brodaric & Fabian Neuhaus (eds.), Formal Ontology in Information Systems - Proceedings of the 11th International Conference, {FOIS} 2020, Cancelled / Bozen-Bolzano, Italy, September 14-17, 2020. Frontiers in Artificial Intelligence and Applications 330. pp. 186-200.
    Forests, cars and orchestras are very different ontological entities, and yet very similar in some aspects. The relationships they have with the elements they are composed of is often assumed to be reducible to standard ontological relations, like parthood and constitution, but how this could be done is still debated. This paper sheds light on the issue starting from a linguistic and philosophical analysis aimed at understanding notions like plurality, collective and composite, and propos- ing a formal approach to characterise (...)
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  24. Aristotle's Ontology of Change.Mark Sentesy - 2020 - Chicago, IL, USA: Northwestern University Press.
    This book investigates what change is, according to Aristotle, and how it affects his conception of being. Mark Sentesy argues that change leads Aristotle to develop first-order metaphysical concepts such as matter, potency, actuality, sources of being, and the teleology of emerging things. He shows that Aristotle’s distinctive ontological claim—that being is inescapably diverse in kind—is anchored in his argument for the existence of change. -/- Aristotle may be the only thinker to have given a noncircular definition of change. When (...)
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  25. Composition as analysis: the meta-ontological origins (and future) of composition as identity.Martina Botti - 2019 - Synthese 198 (Suppl 18):4545-4570.
    In this paper, I argue that the debate on Composition as Identity—the thesis that any composite object is identical to its parts—is deadlocked because both the defenders and the detractors of the claim have so far failed to take its philosophical core at face value and have, as a result, defended and criticized respectively something that is not Composition as Identity. After establishing how Composition as Identity should properly be understood and proposing for it a new interpretation centered around the (...)
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  26. Composition as identity, Leibniz’s Law, and slice-sensitive emergent properties.Phillip Bricker - 2019 - Synthese:4389-4409.
    Moderate composition as identity holds that there is a generalized identity relation, “being the same portion of reality,” of which composition and numerical identity are distinct species. Composition is a genuine kind of identity; but unlike numerical identity, it fails to satisfy Leibniz’s Law. A composite whole and its parts differ with respect to their numerical properties: the whole is one; the parts (collectively) are many. Moderate composition as identity faces the challenge: how, in the absence of Leibniz’s Law, can (...)
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  27. Baxter and Cotnoir on Composition as Identity.Joongol Kim - 2019 - 철학사상 [CHUL HAK SA SANG: Journal of Philosophical Ideas] 73:105-125.
    This paper provides a critical examination of three related attempts to defend Composition as Identity (CI), namely the thesis that if some things compose something, then they are it. First, it will be argued against Donald Baxter’s view of composition as ‘loose identity’ that by construing composition as strictly a many-many relation, the view trivializes CI, and cannot be an option for the advocate of CI who takes composition as a genuine many-one relation. Second, it is argued against Baxter’s modified (...)
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  28. No universalism without gunk? Composition as identity and the universality of identity.Manuel Lechthaler - 2019 - Synthese 198 (Suppl 18):4441-4452.
    Philosophers disagree whether composition as identity entails mereological universalism. Bricker :264–294, 2016) has recently considered an argument which concludes that composition as identity supports universalism. The key step in this argument is the thesis that any objects are identical to some object, which Bricker justifies with the principle of the universality of identity. I will spell out this principle in more detail and argue that it has an unexpected consequence. If the universality of identity holds, then composition as identity not (...)
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  29. On atomic composition as identity.Roberto Loss - 2019 - Synthese 198 (Suppl 18):4519-4542.
    In this paper I address two important objections to the theory called ‘ Composition as Identity’ : the ‘wall-bricks-and-atoms problem’, and the claim that CAI entails mereological nihilism. I aim to argue that the best version of CAI capable of addressing both problems is the theory I will call ‘Atomic Composition as Identity’ which consists in taking the plural quantifier to range only over proper pluralities of mereological atoms and every non-atomic entity to be identical to the plurality of atoms (...)
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  30. The Mereology of Emergence.Ryan Miller - 2019 - Dissertation, The University of St Andrews
    The debate about the ontological innocence of mereology has generally been framed as a debate about the plausibility of Universal Fusion. Ontologically loaded fusions must be more than the sum of their parts, and this seems to violate parsimony if fusion is universal. Less attention has been paid to the question of what sort of emergence mereological fusions must exhibit if they are irreducible to their parts. The philosophy of science literature provides several models of such strong emergence. Examining those (...)
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  31. Bivalent Selection and Graded Darwinian Individuality.Daniel J. Molter - 2019 - British Journal for the Philosophy of Science (1):axz026.
    Philosophers are approaching a consensus that biological individuality, including evolutionary individuality, comes in degrees. Graded evolutionary individuality presents a puzzle when juxtaposed with another widely embraced view: that evolutionary individuality follows from being a selectable member of a Darwinian population. Population membership is, on the orthodox view, a bivalent condition, so how can members of Darwinian populations vary in their degree of individuality? This article offers a solution to the puzzle, by locating difference in degree of evolutionary individuality at the (...)
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  32. How to identify wholes with their parts.Jonathan D. Payton - 2019 - Synthese 198 (Suppl 18):4571-4593.
    I claim that a whole is identical to its parts. Many find this claim incredible: it seems that a whole and its parts must be distinct, for the whole is one thing while its parts are many things. Byeong-uk Yi has developed a version of this argument which exploits the resources of plural logic. Yi provides logical analyses of the predicates ‘one’ and ‘many’ which seem to show that nothing can satisfy them both. But there are two senses of the (...)
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  33. Why the social sciences are irreducible.Tobias Hansson Wahlberg - 2019 - Synthese 196 (12):4961-4987.
    It is often claimed that the social sciences cannot be reduced to a lower-level individualistic science. The standard argument for this position is the Fodorian multiple realizability argument. Its defenders endorse token–token identities between “higher-level” social objects and pluralities/sums of “lower-level” individuals, but they maintain that the properties expressed by social science predicates are often multiply realizable, entailing that type–type identities between social and individualistic properties are ruled out. In this paper I argue that the multiple realizability argument for explanatory (...)
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  34. Many, but one.Evan T. Woods - 2019 - Synthese 198 (Suppl 18):4609-4626.
    The problem of the many threatens to show that, in general, there are far more ordinary objects than you might have thought. I present and motivate a solution to this problem using many-one identity. According to this solution, the many things that seem to have what it takes to be, say, a cat, are collectively identical to that single cat.
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  35. Oneness, Aspects, and the Neo-Confucians.Donald L. M. Baxter - 2018 - In Philip J. Ivanhoe, Owen Flanagan, Victoria S. Harrison, Hagop Sarkissian & Eric Schwitzgebel (eds.), The Oneness Hypothesis: Beyond the Boundary of Self. New York, NY, USA: Columbia University Press.
    Confucius gave counsel that is notoriously hard to follow: "What you do not wish for yourself, do not impose on others" (Huang 1997: 15.24). People tend to be concerned with themselves and to be indifferent to most others. We are distinct from others so our self-concern does not include them, or so it seems. Were we to realize this distinctness is merely apparent--that our true self includes others--Confucius's counsel would be easier to follow. Concern for our true self would extend (...)
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  36. Failure of Boredom: The Pendulum of Composition as Identity.Claudio Calosi - 2018 - American Philosophical Quarterly 55 (3):281-292.
    This paper provides new arguments for the following claim: either strong composition as identity cannot retain the full strength of both the logical principles of one-one identity and its semantical principles or it only delivers cases of boring composition in that it entails mereological nihilism.
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  37. Contingent composition as identity.Giorgio Lando & Massimiliano Carrara - 2018 - Synthese.
    When the necessity of identity (NI) is combined with composition as identity (CAI), the contingency of composition (CC) is at risk. In the extant literature, either NI is seen as the basis for a refutation of CAI or CAI is associated with a theory of modality, such that: either NI is renounced (if counterpart theory is adopted); or CC is renounced (if the theory of modal parts is adopted). In this paper, we investigate the prospects of a new variety of (...)
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  38. Mereological Composition and Plural Quantifier Semantics.Manuel Lechthaler & Ceth Lightfield - 2018 - Philosophia 46 (4):943-958.
    Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings clarity (...)
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  39. A Sudden Collapse to Nihilism.Roberto Loss - 2018 - Philosophical Quarterly 68 (271):370-375.
    According to Composition is Identity, a whole is literally identical to the plurality of its parts. According to Mereological Nihilism, nothing has proper parts. In this note, it is argued that Composition is Identity can be shown to entail Mereological Nihilism in a much more simple and direct way than the one recently proposed by Claudio Calosi.
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  40. Saving the Ship.John Biro - 2017 - European Journal of Analytic Philosophy 13 (2):43-54.
    In defending the startling claim that that there are no artifacts, indeed, no inanimate material objects of the familiar sort, Peter van Inwagen has argued that truths about such putative objects can be paraphrased as truths that do not make essential reference to them and that we should endorse only the ontological commitments of the paraphrase. In this note I argue that the paraphrases van Inwagen recommends cannot meet his condition. Read one way, they lose us some truths. Read another, (...)
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  41. Composition as Identity. [REVIEW]A. R. J. Fisher - 2017 - Philosophical Quarterly 67 (267):409-412.
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  42. Composition and Identities.Manuel Lechthaler - 2017 - Dissertation, University of Otago
    Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...)
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  43. Composition as Abstraction.Jeffrey Sanford Russell - 2017 - Journal of Philosophy 114 (9):453-470.
    The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.
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  44. ‘Identity’ as a mereological term.Jeroen Smid - 2017 - Synthese 194 (7):2367-2385.
    The mereological predicate ‘is part of’ can be used to define the predicate ‘is identical with’. I argue that this entails that mereological theories can be ideologically simpler than nihilistic theories that do not use the notion of parthood—contrary to what has been argued by Ted Sider. Moreover, if one accepts an extensional mereology, there are good philosophical reasons apart from ideological simplicity to give a mereological definition of identity.
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  45. Counting on Strong Composition as Identity to Settle the Special Composition Question.Joshua Spencer - 2017 - Erkenntnis 82 (4):857-872.
    Strong Composition as Identity is the thesis that necessarily, for any xs and any y, those xs compose y iff those xs are non-distributively identical to y. Some have argued against this view as follows: if some many things are non-distributively identical to one thing, then what’s true of the many must be true of the one. But since the many are many in number whereas the one is not, the many cannot be identical to the one. Hence is mistaken. (...)
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  46. Baker’s Theory of Constitution and the Relations between Things.Mahdi Zakeri - 2017 - Metaphysics (University of Isfahan) 9 (23):51-68.
    Many ordinary things are made up of material things. For example, the statue of Ferdousi in the University of Tehran is made up of a particular piece of bronze. Calling the relation between the statue of Ferdousi and that piece of bronze material constitution, many philosophers have claimed that this relation between a material thing and the thing that it constitutes is identity. Baker, in contrast, believes that these things have genuine unity without necessary identity. In this article, I first (...)
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  47. Composition as Identity and Plural Cantor's Theorem.Einar Duenger Bohn - 2016 - Logic and Logical Philosophy 25 (3).
    I argue that Composition as Identity blocks the plural version of Cantor's Theorem, and that therefore the plural version of Cantor's Theorem can no longer be uncritically appealed to. As an example, I show how this result blocks a recent argument by Hawthorne and Uzquiano.
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  48. Mereological monism and Humean supervenience.Andrea Borghini & Giorgio Lando - 2016 - Synthese 197 (11):4745-4765.
    According to Lewis, mereology is the general and exhaustive theory of ontological composition, and every contingent feature of the world supervenes upon some fundamental properties instantiated by minimal entities. A profound analogy can be drawn between these two basic contentions of his metaphysics, namely that both can be intended as a denial of emergentism. In this essay, we study the relationships between Humean supervenience and two philosophical spin-offs of mereological monism: the possibility of gunk and the thesis of composition as (...)
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  49. Composition as a Kind of Identity.Phillip Bricker - 2016 - Inquiry: An Interdisciplinary Journal of Philosophy 59 (3):264-294.
    Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea that composition is merely analogous (...)
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  50. Composition, identity, and emergence.Claudio Calosi - 2016 - Logic and Logical Philosophy 25 (3):429-443.
    Composition as Identity is the thesis that a whole is, strictly and literally, identical to its parts, considered collectively. McDaniel [2008] argues against CAI in that it prohibits emergent properties. Recently Sider [2014] exploited the resources of plural logic and extensional mereology to undermine McDaniel’s argument. He shows that CAI identifies extensionally equivalent pluralities – he calls it the Collapse Principle – and then shows how this identification rescues CAI from the emergentist argument. In this paper I first give a (...)
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