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Parts of Classes

Mind 100 (3):394-397 (1991)

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  1. Logic and philosophy of mathematics in the early Husserl.Stefania Centrone - 2010 - New York: Springer.
    This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...
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  • Grounding and the Existence of God.Joshua R. Sijuwade - 2021 - Metaphysica (2):193-245.
    In this article, I seek to assess the extent to which Theism, the claim that there is a God, can provide a true fundamental explanation for the instantiation of the grounding relation that connects the various entities within the layered structure of reality. More precisely, I seek to utilise the explanatory framework of Richard Swinburne within a specific metaphysical context, a ground-theoretic context, which will enable me to develop a true fundamental explanation for the existence of grounding. And thus, given (...)
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  • Numbers and Everything.Gonçalo Santos - 2013 - Philosophia Mathematica 21 (3):297-308.
    I begin by drawing a parallel between the intuitionistic understanding of quantification over all natural numbers and the generality relativist understanding of quantification over absolutely everything. I then argue that adoption of an intuitionistic reading of relativism not only provides an immediate reply to the absolutist's charge of incoherence but it also throws a new light on the debates surrounding absolute generality.
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  • Surreal Time and Ultratasks.Haidar Al-Dhalimy & Charles J. Geyer - 2016 - Review of Symbolic Logic 9 (4):836-847.
    This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an ultratask (a sequence which (...)
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  • Intersectionality as emergence.Marta Jorba & Dan López de Sa - forthcoming - Philosophical Studies:1-21.
    Intersectionality is the notion that concerns the complexity of the experiences of individuals in virtue of their belonging to multiple socially significant categories. One of its main insights is that the way society is structured around categories such as gender, race, sexuality, class, etc., produces distinctive and specific forms of discrimination and privilege for groups in the intersections. In this paper, we suggest conceiving intersectionality as a general metaphysical framework wherein specific claims to the effect that the experiences of discrimination (...)
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  • Nominalism.Zoltan Szabo - 2003 - In Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford handbook of metaphysics. New York: Oxford University Press.
    …entities? 2. How to be a nominalist 2.1. “Speak with the vulgar …” 2.2. “…think with the learned” 3. Arguments for nominalism 3.1. Intelligibility, physicalism, and economy 3.2. Causal..
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  • A Theory of Granular Partitions.Thomas Bittner & Barry Smith - 2003 - In Matt Duckham, Michael F. Goodchild & Michael Worboys (eds.), Foundations of Geographic Information Science. London: Taylor & Francis. pp. 117-151.
    We have a variety of different ways of dividing up, classifying, mapping, sorting and listing the objects in reality. The theory of granular partitions presented here seeks to provide a general and unified basis for understanding such phenomena in formal terms that is more realistic than existing alternatives. Our theory has two orthogonal parts: the first is a theory of classification; it provides an account of partitions as cells and subcells; the second is a theory of reference or intentionality; it (...)
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  • Abstract Objects.David Liggins - 2024 - Cambridge: Cambridge University Press.
    Philosophers often debate the existence of such things as numbers and propositions, and say that if these objects exist, they are abstract. But what does it mean to call something 'abstract'? And do we have good reason to believe in the existence of abstract objects? This Element addresses those questions, putting newcomers to these debates in a position to understand what they concern and what are the most influential considerations at work in this area of metaphysics. It also provides advice (...)
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  • Parthood.Theodore Sider - 2007 - Philosophical Review 116 (1):51-91.
    There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..
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  • Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
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  • Naturalism in mathematics and the authority of philosophy.Alexander Paseau - 2005 - British Journal for the Philosophy of Science 56 (2):377-396.
    Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism is self-refuting. I then focus on reinterpretation naturalism, which comes in two forms, and examine the (...)
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  • Method in Analytic Metaphysics.Daniel Nolan - 2016 - In Herman Cappelen, Tamar Gendler & John P. Hawthorne (eds.), The Oxford Handbook of Philosophical Methodology. Oxford, United Kingdom: Oxford University Press.
    This article focuses on the main methods used in analytic metaphysics. It first considers five important sources of constraints on metaphysical theorizing: linguistic and conceptual analysis, consulting intuitions, employing the findings of science, respecting folk opinion, and applying theoretical virtues in metaphysical theory choice such as preferring simpler theories, or preferring more explanatory theories. It then examines the role of formal methods in metaphysics as well as the role of metaphysical communities, traditions, and the place of the history of metaphysics (...)
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  • Of Numbers and Electrons.Cian Dorr - 2010 - Proceedings of the Aristotelian Society 110 (2pt2):133-181.
    According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world (...)
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  • Deferentialism.Chris Daly & David Liggins - 2011 - Philosophical Studies 156 (3):321-337.
    There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...)
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  • Metaphysically Reductive Causation.Ned Hall & L. A. Paul - 2013 - Erkenntnis 78 (1):9-41.
    There are, by now, many rival, sophisticated philosophical accounts of causation that qualify as ‘metaphysically reductive’. This is a good thing: these collective efforts have vastly improved our understanding of causation over the last 30 years or so. They also put us in an excellent position to reflect on some central methodological questions: What exactly is the point of offering a metaphysical reduction of causation? What philosophical scruples ought to guide the pursuit of such a reduction? Finally, how should answers (...)
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  • Aristotle on Predication.Phil Corkum - 2015 - European Journal of Philosophy 23 (3):793-813.
    A predicate logic typically has a heterogeneous semantic theory. Subjects and predicates have distinct semantic roles: subjects refer; predicates characterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. In this paper, I will examine evidence for ascribing to Aristotle the (...)
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  • Semantic values in higher-order semantics.Stephan Krämer - 2014 - Philosophical Studies 168 (3):709-724.
    Recently, some philosophers have argued that we should take quantification of any (finite) order to be a legitimate and irreducible, sui generis kind of quantification. In particular, they hold that a semantic theory for higher-order quantification must itself be couched in higher-order terms. Øystein Linnebo has criticized such views on the grounds that they are committed to general claims about the semantic values of expressions that are by their own lights inexpressible. I show that Linnebo’s objection rests on the assumption (...)
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  • Existence and Number.Kris McDaniel - 2013 - Analytic Philosophy 54 (2):209-228.
    The Frege-Russell view is that existence is a second-order property rather than a property of individuals. One of the most compelling arguments for this view is based on the premise that there is an especially close connection between existence and number. The most promising version of this argument is by C.J.F Williams (1981, 1992). In what follows, I argue that this argument fails. I then defend an account according to which both predications of number and existence attribute properties to individuals.
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  • Logical parts.Laurie A. Paul - 2002 - Noûs 36 (4):578–596.
    I argue for a property mereology and for mereological bundle theory. I then apply this theory to the one over many problem (universals) and puzzles concerning persistence and material constitution.
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  • 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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  • How the Lewisian can Account for Kit Fine's Essentialist Beliefs.Cristina Nencha - forthcoming - Erkenntnis:1-17.
    The Lewisean counterpart theorist– despite not defending a genuinely essentialist view of what is possible, de re, of individuals – generally has a way to make essentialist claims come out as true, in those contexts in which they are endorsed by a committed essentialist. In this paper, I am going to show that the normal system that the Lewisean adopts when she wants to make the essentialist a truth-teller does not work with Kit Fine: his essentialist beliefs, which support his (...)
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  • Fundamental Quantification and the Language of the Ontology Room.Daniel Z. Korman - 2013 - Noûs 49 (2):298-321.
    Nihilism is the thesis that no composite objects exist. Some ontologists have advocated abandoning nihilism in favor of deep nihilism, the thesis that composites do not existO, where to existO is to be in the domain of the most fundamental quantifier. By shifting from an existential to an existentialO thesis, the deep nihilist seems to secure all the benefits of a composite-free ontology without running afoul of ordinary belief in the existence of composites. I argue that, while there are well-known (...)
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  • An Argument for Micropsychism: If There is a Conscious Whole, There Must be Conscious Parts.Arjen Rookmaaker - 2024 - Kriterion – Journal of Philosophy 38.
    Many philosophers today accept that phenomenal truths cannot be explained in terms of ordinary physical truths. Two possible routes to accounting for consciousness have received much attention: the emergentist route is to accept that ordinary experience is inexplicable in physical terms but that microscopic entities as described in physics nonetheless bring about conscious experience. The second route is to argue that microscopic entities have features not described in physics which can fully explain conscious experience. The view associated with panprotopsychism is (...)
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  • The Stuff That Matters.N. G. Laskowski - 2024 - In Russ Shafer-Landau (ed.), Oxford Studies of Metaethics 19. Oxford University Press USA.
    On one way of talking about a traditional metaethical topic, realists accept that some items appear on the list of what exists in the moral or more broadly normative domain of inquiry. They then divide over whether those items are like what science and experience suggest that all other items on the list of what exists across all domains are like – naturalistic and secular. Reductive naturalists answer this further question affirmatively. Why don’t nonnaturalists? I explore the answer that it’s (...)
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  • Fundamentality and Ontological Minimality.Tuomas E. Tahko - 2018 - In Ricki Bliss & Graham Priest (eds.), Reality and its Structure: Essays in Fundamentality. Oxford, UK: Oxford University Press. pp. 237-253.
    In this chapter, a generic definition of fundamentality as an ontological minimality thesis is sought and its applicability examined. Most discussions of fundamentality are focused on a mereological understanding of the hierarchical structure of reality, which may be combined with an atomistic, object-oriented metaphysics. But recent work in structuralism, for instance, calls for an alternative understanding and it is not immediately clear that the conception of fundamentality at work in structuralism is commensurable with the mereological conception. However, it is proposed (...)
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  • Propositions and Parthood: The Universe and Anti-Symmetry.Chris Tillman & Gregory Fowler - 2012 - Australasian Journal of Philosophy 90 (3):525 - 539.
    It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of denying (...)
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  • Against Fantology.Barry Smith - 2005 - In Johann C. Marek & Maria E. Reicher (eds.), Experience and Analysis. Vienna: HPT&ÖBV. pp. 153-170.
    The analytical philosophy of the last hundred years has been heavily influenced by a doctrine to the effect that the key to the correct understanding of reality is captured syntactically in the ‘Fa’ (or, in more sophisticated versions, in the ‘Rab’) of standard first order predicate logic. Here ‘F’ stands for what is general in reality and ‘a’ for what is individual. Hence “f(a)ntology”. Because predicate logic has exactly two syntactically different kinds of referring expressions—‘F’, ‘G’, ‘R’, etc., and ‘a’, (...)
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  • Truthmaking.Kelly Trogdon - 2020 - In Michael J. Raven (ed.), Routledge Handbook of Metaphysical Grounding. Routledge. pp. 396-407.
    Discussion of grounding-theoretic accounts of truthmaking in terms of the theoretical role of “catching cheaters”.
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  • The Taming of the Grounds.Noël Blas Saenz - 2022 - Canadian Journal of Philosophy 52 (8):789-809.
    As it is presently employed, grounding permits grounding many things from one ground. In this paper, I show why this is a mistake by pushing for a uniqueness principle on grounding. After arguing in favor of this principle, I say something about it and kinds of grounding, discuss a similar principle, and consider its import on a formal feature of grounding, ontology, and ontological simplicity.
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  • Early Russell on Types and Plurals.Kevin Klement - 2014 - Journal for the History of Analytical Philosophy 2 (6):1-21.
    In 1903, in _The Principles of Mathematics_ (_PoM_), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before _PoM_ even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...)
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  • On the Plurality of Parts of Classes.Daniel Nolan - forthcoming - Dialectica.
    The ontological pictures underpinning David Lewis's Parts of Classes and On the Plurality of Worlds are in some tension. One tension concerns whether the sets and classes of Parts of Classes can be found in Lewis's modal space, since they cannot in general be parts of any possible world. The second is that the atoms that are the mathematical ontology of Parts of Classes seem to meet the criteria for being possible worlds themselves, and so fail to be the material (...)
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  • Applied Mathematics without Numbers.Jack Himelright - 2023 - Philosophia Mathematica 31 (2):147-175.
    In this paper, I develop a "safety result" for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are "correct": roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some advantages (...)
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  • Introducción a la Ontología.Axel Barceló - manuscript
    Intuitivamente, la realidad está formada por entidades y hechos existentes y concretos. Sin embargo, nuestro lenguaje y pensamiento versa también sobre hechos meramente posibles, sobre cosas inexistentes y entidades abstractas. ¿Cómo es esto posible? ¿Significa ello que cuando hablamos y pensamos de estas otras cosas no hablamos de nada real? ¿o mas bien la realidad está mas poblada de lo que pensábamos y hay diferentes maneras de formar parte de la realidad además de la de existir de manera positiva y (...)
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  • The Lump Sum: A Theory of Modal Parts.Meg Wallace - 2019 - Philosophical Papers 48 (3):403-435.
    A lump theorist claims that ordinary objects are spread out across possible worlds, much like many of us think that tables are spread out across space. We are not wholly located in any one particular world, the lump theorist claims, just as we are not wholly spatially located where one’s hand is. We are modally spread out, a trans-world mereological sum of world-bound parts. We are lump sums of modal parts. And so are all other ordinary objects. In this paper, (...)
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  • Counterparts and Compositional Nihilism: A Reply to A. J. Cotnoir.Meg Wallace - 2013 - Thought: A Journal of Philosophy 2 (2):242-247.
    One of the primary burdens of the mereological nihilist is accounting for our ordinary intuitions about material objects. It certainly *seems* as if I am typing on a keyboard, which has particular keys and buttons as parts. But such intuitions are mistaken if mereological nihilism is right, leading to widespread error. So nihilists often propose paraphrases of our everyday utterances as compensation. Cotnoir aims to deliver a new paraphrase strategy on behalf of the nihilist: one that interprets parthood and composition (...)
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  • Mathematical anti-realism and explanatory structure.Bruno Whittle - 2021 - Synthese 199 (3-4):6203-6217.
    Plausibly, mathematical claims are true, but the fundamental furniture of the world does not include mathematical objects. This can be made sense of by providing mathematical claims with paraphrases, which make clear how the truth of such claims does not require the fundamental existence of mathematical objects. This paper explores the consequences of this type of position for explanatory structure. There is an apparently straightforward relationship between this sort of structure, and the logical sort: i.e. logically complex claims are explained (...)
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  • Granular knowledge and rational approximation in general rough sets – I.A. Mani - 2024 - Journal of Applied Non-Classical Logics 34 (2-3):294-329.
    Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown that (...)
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  • Counterpossibles in Science: The Case of Relative Computability.Matthias Jenny - 2018 - Noûs 52 (3):530-560.
    I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...)
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  • Full and partial grounding.Kelly Trogdon & D. Gene Witmer - 2021 - Journal of the American Philosophical Association 7 (2):252-271.
    Discussion of partial grounds that aren't parts of full grounds; definition of full grounding in terms of partial grounding.
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  • Homunculi Are People Too! Lewis's Definition of Personhood Debugged.Cody Gilmore - 2017 - Thought: A Journal of Philosophy 6 (1):54-60.
    David Lewis defends the following "non-circular definition of personhood": "something is a continuant person if and only if it is a maximal R-interrelated aggregate of person-stages. That is: if and only if it is an aggregate of person-stages, each of which is R-related to all the rest (and to itself), and it is a proper part of no other such aggregate." I give a counterexample, involving a person who is a part of another, much larger person, with a separate mental (...)
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  • Which Systems Are Conscious?Mark F. Sharlow - manuscript
    This document consists primarily of an excerpt (chapter 14) from the author’s book From Brain to Cosmos. In that excerpt, the author uses the concept of subjective fact developed earlier in the book to address a question about consciousness: which physical systems (organisms or machines) are conscious? (This document depends heavily upon the concept of subjective fact developed in From Brain to Cosmos. Readers unfamiliar with that concept are strongly advised to read chapters 2 and 3 of From Brain to (...)
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  • Time and Subjective Facts: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of excerpts (chapters 5 and 7-9) from the author’s book From Brain to Cosmos. These excerpts address some traditional philosophical problems about temporal flux and identity through time, using the concept of subjective fact that the author developed earlier in the book. (Readers unfamiliar with that concept are strongly advised to read chapters 2 and 3 of From Brain to Cosmos first. See the last page of this document for details on how to obtain those chapters.).
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  • Subjective Facts and Other Minds: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of an excerpt (chapter 6) from the author’s book From Brain to Cosmos. That excerpt presents an analysis of the problem of knowledge of other minds, using the concept of subjective fact that the author developed earlier in the book. (Readers unfamiliar with that concept are strongly advised to read chapters 2 and 3 of From Brain to Cosmos first. See the last page of this document for details on how to obtain those chapters.).
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  • Personal Identity and Subjective Time: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of an excerpt (chapter 5) from the author’s book From Brain to Cosmos. That excerpt presents an analysis of personal identity through time, using the concept of subjective fact that the author developed earlier in the book. (Readers unfamiliar with that concept are strongly advised to read chapters 2 and 3 of From Brain to Cosmos first. See the last page of this document for details on how to obtain those chapters.).
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  • Knowledge of How Things Seem to You: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of an excerpt (chapter 4) from the author’s book From Brain to Cosmos. That excerpt presents a study of a specific problem about knowledge: the logical justification of one’s knowledge of the immediate past. (This document depends heavily upon the concept of subjective fact that the author developed in chapters 2 and 3 of From Brain to Cosmos. Readers unfamiliar with that concept are strongly advised to read those chapters first. See the last page of this (...)
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  • Conscious Subjects in Detail: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of excerpts (chapters 5 and 10-12) from the author’s book From Brain to Cosmos. These excerpts address several traditional problems about the histories of conscious subjects, using the concept of subjective fact that the author developed earlier in the book. Topics include the persistence of conscious subjects through time, the unity or disunity of the self, and the possibility of splitting conscious subjects. (These excerpts depend heavily upon the author’s concept of subjective fact as developed in (...)
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  • Identity, Discernibility, and Composition.Donald L. M. Baxter - 2014 - In A. J. Cotnoir & Donald L. M. Baxter (eds.), Composition as Identity. Oxford University Press. pp. 244-253.
    There is more than one way to say that composition is identity. Yi has distinguished the Weak Composition thesis from the Strong Composition thesis and attributed the former to David Lewis while noting that Lewis associates something like the latter with me. Weak Composition is the thesis that the relation between the parts collectively and their whole is closely analogous to identity. Strong Composition is the thesis that the relation between the parts collectively and their whole is identity. Yi is (...)
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  • An Introduction to Subjective Facts: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This collection serves as an introduction to the concept of subjective fact, which plays a central role in some of the author's philosophical writings. The collection contains two book chapters and a paper. The first chapter (Chapter 2 of From Brain to Cosmos) begins with an informal characterization of the concept of subjective fact. Then it fleshes out this concept with examples, gives a more precise characterization, and addresses some potential weaknesses of the concept. This chapter shows how subjective fact (...)
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  • Beyond Physicalism and Idealism: Readings in From Brain to Cosmos.Mark F. Sharlow - manuscript
    This document consists primarily of an excerpt (chapter 13) from the author’s book From Brain to Cosmos. In that excerpt, the author presents a study of the notion of truth using the concept of subjective fact developed earlier in the book. The author argues that mind-body materialism is compatible with certain forms of metaphysical idealism. The chapter closes with some remarks on relativism with regard to truth. (This document depends heavily upon the concept of subjective fact developed in From Brain (...)
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  • From nature to grounding.Mark Jago - 2011 - In . pp. 199-216.
    Grounding is a powerful metaphysical concept; yet there is widespread scepticism about the intelligibility of the notion. In this paper, I propose an account of an entity’s nature or essence, which I then use to provide grounding conditions for that entity. I claim that an understanding of an entity’s nature, together with an account of how logically complex entities are grounded, provides all we need to understand how that entity is grounded. This approach not only allows us to say what (...)
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