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Principles of Mathematics

New York,: Routledge (1903)

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  1. Predication as Ascription.David Liebesman - 2015 - Mind 124 (494):517-569.
    I articulate and defend a necessary and sufficient condition for predication. The condition is that a term or term-occurrence stands in the relation of ascription to its designatum, ascription being a fundamental semantic relation that differs from reference. This view has dramatically different semantic consequences from its alternatives. After outlining the alternatives, I draw out these consequences and show how they favour the ascription view. I then develop the view and elicit a number of its virtues.
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  • Fregeanism, sententialism, and scope.Harvey Lederman - 2022 - Linguistics and Philosophy 45 (6):1235-1275.
    Among philosophers, Fregeanism and sententialism are widely considered two of the leading theories of the semantics of attitude reports. Among linguists, these approaches have received little recent sustained discussion. This paper aims to bridge this divide. I present a new formal implementation of Fregeanism and sententialism, with the goal of showing that these theories can be developed in sufficient detail and concreteness to be serious competitors to the theories which are more popular among semanticists. I develop a modern treatment of (...)
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  • Russell and Bradley: Rehabilitating the Creation Narrative of Analytic Philosophy.Samuel Lebens - 2017 - Journal for the History of Analytical Philosophy 5 (7).
    According to Stewart Candlish, Russell and Moore had misunderstood F. H. Bradley’s monism. According to Jonathan Schaffer, they had misunderstood monism more generally. A key thread of the creation narrative of analytic philosophy, according to which Russell and Moore successfully undermined monism to give rise to a new movement is, therefore, in doubt. In this paper, I defend the standard narrative against those who seek to revise it.
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  • Solving the Conjunction Problem of Russell's Principles of Mathematics.Gregory Landini - 2020 - Journal for the History of Analytical Philosophy 8 (8).
    The quantification theory of propositions in Russell’s Principles of Mathematics has been the subject of an intensive study and in reconstruction has been found to be complete with respect to analogs of the truths of modern quantification theory. A difficulty arises in the reconstruction, however, because it presents universally quantified exportations of five of Russell’s axioms. This paper investigates whether a formal system can be found that is more faithful to Russell’s original prose. Russell offers axioms that are universally quantified (...)
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  • Russell on Negative Judgement.Anssi Korhonen - 2020 - Topoi 39 (3):727-742.
    This paper concerns Bertrand Russell’s changing views on negative judgement. ‘Negative judgement’ is considered in the context of three theories of judgement that Russell put forth at different times: a dual relation theory ; a multiple relation theory ; a psychological theory of judgement. Four issues are singled out for a more detailed discussion: quality dualism versus quality monism, that is, the question whether judgement comes in two kinds, acceptance and rejection, or whether there is only one judgement-quality ; the (...)
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  • Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's response adequate?Kevin C. Klement - 2001 - History and Philosophy of Logic 22 (1):13-28.
    In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy (...)
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  • Propositional unity: what’s the problem, who has it and who solves it?Jeffrey C. King - 2013 - Philosophical Studies 165 (1):71-93.
    At least since Russell’s influential discussion in The Principles of Mathematics, many philosophers have held there is a problem that they call the problem of the unity of the proposition. In a recent paper, I argued that there is no single problem that alone deserves the epithet the problem of the unity of the proposition. I there distinguished three problems or questions, each of which had some right to be called a problem regarding the unity of the proposition; and I (...)
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  • Standard Formalization.Jeffrey Ketland - 2022 - Axiomathes 32 (3):711-748.
    A standard formalization of a scientific theory is a system of axioms for that theory in a first-order language (possibly many-sorted; possibly with the membership primitive $$\in$$ ). Suppes (in: Carvallo M (ed) Nature, cognition and system II. Kluwer, Dordrecht, 1992) expressed skepticism about whether there is a “simple or elegant method” for presenting mathematicized scientific theories in such a standard formalization, because they “assume a great deal of mathematics as part of their substructure”. The major difficulties amount to these. (...)
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  • On the alleged equivalence between Newtonian and relativistic cosmology.Pierre Kerszberg - 1987 - British Journal for the Philosophy of Science 38 (3):347-380.
    Among the many controversial contributions of E. A. Milne to cosmology, the only one which is taken seriously today (to the extent that it has been absorbed as a premise in most scientific approaches to the problem of the universe as a totality) is his early suggestion that a formal equivalence may be made between Newtonian and Relativistic cosmology. My own paper suggests that, over and above any logical validity in the alleged equivalence, the actual way in which it has (...)
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  • ∈ : Formal concepts in a material world truthmaking and exemplification as types of determination.Philipp Keller - 2007 - Dissertation, University of Geneva
    In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations between properties. (...)
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  • 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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  • Primitive Directionality and Diachronic Grounding.Naoyuki Kajimoto, Kristie Miller & James Norton - 2019 - Acta Analytica 35 (2):195-211.
    Eternalists believe that there is no ontological difference between the past, present and future. Thus, a challenge arises: in virtue of what does time have a direction? Some eternalists, Oaklander and Tegtmeier ) argue that the direction of time is primitive. A natural response to positing primitive directionality is the suspicion that said posit is too mysterious to do any explanatory work. The aim of this paper is to relieve primitive directionality of some of its mystery by offering a novel (...)
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  • Scattered Exemplification and Many-Place Copulas.Ingvar Johansson - 2013 - Axiomathes 23 (2):235-246.
    Can there be relational universals? If so, how can they be exemplified? A monadic universal is by definition capable of having a scattered spatiotemporal localization of its different exemplifications, but the problem of relational universals is that one single exemplification seems to have to be scattered in the many places where the relata are. The paper argues that it is possible to bite this bullet, and to accept a hitherto un-discussed kind of exemplification relation called ‘scattered exemplification’. It has no (...)
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  • What is a Change?Guillermo Hurtado - 2004 - Canadian Journal of Philosophy 34 (sup1):81-96.
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  • Quasi-set theory: a formal approach to a quantum ontology of properties.Federico Holik, Juan Pablo Jorge, Décio Krause & Olimpia Lombardi - 2022 - Synthese 200 (5):1-26.
    In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate meta-language to speak of the proposed ontology of properties and its structure.
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  • Handedness, Idealism, and Freedom.Desmond Hogan - 2021 - Philosophical Review 130 (3):385-449.
    Incongruent counterparts are pairs of objects which cannot be enclosed in the same spatial limits despite an exact similarity in magnitude, proportion, and relative position of their parts. Kant discerns in such objects, whose most familiar example is left and right hands, a “paradox” demanding “demotion of space and time to mere forms of our sensory intuition.” This paper aims at an adequate understanding of Kant’s enigmatic idealist argument from handed objects, as well as an understanding of its relation to (...)
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  • Three varieties of mathematical structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.
    Three principal varieties of mathematical structuralism are compared: set-theoretic structuralism (‘STS’) using model theory, Shapiro's ante rem structuralism invoking sui generis universals (‘SGS’), and the author's modal-structuralism (‘MS’) invoking logical possibility. Several problems affecting STS are discussed concerning, e.g., multiplicity of universes. SGS overcomes these; but it faces further problems of its own, concerning, e.g., the very intelligibility of purely structural objects and relations. MS, in contrast, overcomes or avoids both sets of problems. Finally, it is argued that the modality (...)
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  • Critical studies/book review. [REVIEW]Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):231-237.
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  • Frege on Identity and Identity-Statements: A Reply to Thau and Caplan.Richard G. Heck - 2003 - Canadian Journal of Philosophy 33 (1):83-102.
    The paper argues, as against Thau and Caplan, that the traditional interpretation that Frege abandoned his earlier views about identity and identity--statements is correct.
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  • On Identity Statements: In Defense of a Sui Generis View.Tristan Haze - 2016 - Disputatio 8 (43):269-293.
    This paper is about the meaning and function of identity statements involving proper names. There are two prominent views on this topic, according to which identity statements ascribe a relation: the object-view, on which identity statements ascribe a relation borne by all objects to themselves, and the name-view, on which an identity statement 'a is b' says that the names 'a' and 'b' codesignate. The object- and name-views may seem to exhaust the field. I make a case for treating identity (...)
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  • The Inferential Significance of Frege’s Assertion Sign.Mitchell S. Green - 2002 - Facta Philosophica 4 (2):201-229.
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  • Epistemic Modality edited by Andy Egan and Brian Weatherson. [REVIEW]D. Gregory - 2013 - Analysis 73 (1):186-188.
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  • In defense of Aristotelian universals.Alessandro Giordani & Eric Tremolanti - 2022 - Synthese 200 (2):1-18.
    To be an Aristotelian about universals is to hold that universals depend for their existence on their exemplifiers. An argument against Aristotelianism about universals has recently been put forward by Costa to the effect that a contradiction follows from assuming a certain formulation of Aristotelianism together with some highly plausible principles governing the notions employed in that formulation. In this paper, we provide different ways of articulating the Aristotelian position which, while being related with some of the main contributions in (...)
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  • Fictionalism and Meinongianism.Nathaniel Gan - 2021 - Theoria : An International Journal for Theory, History and Fundations of Science 36 (1):49-62.
    Fictionalism about a kind of disputed object is often motivated by the fact that the view interprets discourse about those objects literally without an ontological commitment to them. This paper argues that this motivation is inadequate because some viable alternatives to fictionalism have similar attractions. Meinongianism—the view that there are true statements about non-existent objects—is one such view. Meinongianism bears significant similarity to fictionalism, so intuitive doubts about its viability are difficult to sustain for fictionalists. Moreover, Meinongianism avoids some of (...)
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  • Non-Boolean classical relevant logics I.Tore Fjetland Øgaard - 2019 - Synthese (8):1-32.
    Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic (...)
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  • On the Notion of Object. A Logical Genealogy.Fernando Ferreira - 2012 - Disputatio 4 (34):609-624.
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  • If structured propositions are logical procedures then how are procedures individuated?Marie Duží - 2019 - Synthese 196 (4):1249-1283.
    This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode. Moreover, procedures are not (...)
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  • Hilbertian Structuralism and the Frege-Hilbert Controversy†.Fiona T. Doherty - 2019 - Philosophia Mathematica 27 (3):335-361.
    ABSTRACT This paper reveals David Hilbert’s position in the philosophy of mathematics, circa 1900, to be a form of non-eliminative structuralism, predating his formalism. I argue that Hilbert withstands the pressing objections put to him by Frege in the course of the Frege-Hilbert controversy in virtue of this early structuralist approach. To demonstrate that this historical position deserves contemporary attention I show that Hilbertian structuralism avoids a recent wave of objections against non-eliminative structuralists to the effect that they cannot distinguish (...)
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  • Symmetric relations.Scott Dixon - 2023 - Philosophical Studies 180 (12):3615-3639.
    There are two ways to characterize symmetric relations. One is intensional: necessarily, _Rxy_ iff _Ryx_. In some discussions of relations, however, what is important is whether or not a relation gives rise to the same completion of a given type (fact, state of affairs, or proposition) for each of its possible applications to some fixed relata. Kit Fine calls relations that do ‘strictly symmetric’. Is there is a difference between the notions of necessary and strict symmetry that would prevent them (...)
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  • When Science Confronts Philosophy: Three Case Studies.Eric Dietrich - 2020 - Axiomathes 1:1-22.
    This paper examines three cases of the clash between science and philosophy: Zeno’s paradoxes, the Frame Problem, and a recent attempt to experimentally refute skepticism. In all three cases, the relevant science claims to have resolved the purported problem. The sciences, construing the term broadly, are mathematics, artificial intelligence, and psychology. The goal of this paper is to show that none of the three scientific solutions work. The three philosophical problems remain as vibrant as ever in the face of robust (...)
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  • The limits of logical empiricism: selected papers of Arthur Pap.Arthur Pap - 2006 - Dordrecht: Springer. Edited by Alfons Keupink & Sanford Shieh.
    Arthur Pap’s work played an important role in the development of the analytic tradition. This role goes beyond the merely historical fact that Pap’s views of dispositional and modal concepts were influential. As a sympathetic critic of logical empiricism, Pap, like Quine, saw a deep tension in logical empiricism at its very best in the work of Carnap. But Pap’s critique of Carnap is quite different from Quine’s, and represents the discovery of limits beyond which empiricism cannot go, where there (...)
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  • Bertrand Russell and Ludwig Wittgenstein, personal and academic relationship (3rd edition).Natalia Tomashpolskaia - 2023 - Analítica 3:10-38.
    In this article, the author analyses the relationship between two prominent philosophers of the 20th century in Europe and Great Britain—Ludwig Wittgenstein and Bertrand Russell. According to a lot of correspondence available nowadays we can reconstruct not only the environment of thought in Cambridge in the beginning and the first half of the 20th century but to find out some very personal, subjective grounds for the changes of relationship between thinkers, misunderstandings between them. Such a kind of biographical-historical reconstruction does (...)
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  • Is Intentionality a Relation? A Dialogue.David Bourget & Angela Mendelovici - forthcoming - Argumenta.
    This dialogue explores the question of whether intentionality—the “ofness”, “aboutness”, or “directedness” of mental states—is a relation. We explore three views: the Naive View, on which intentionality is a relation to ordinary, everyday objects, facts, and other such items; the Abstract Contents View, on which intentionality is a relation to mind-independent abstract entities that are our contents; and the Aspect View, on which intentionality is a matter of having intentional states with particular (non-relational) aspects that are our contents. We consider (...)
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  • Arguments, Suppositions, and Conditionals.Pavese Carlotta - forthcoming - Semantics and Linguistic Theory.
    Arguments and conditionals are powerful means language provides us to reason about possibilities and to reach conclusions from premises. These two kinds of constructions exhibit several affinities—e.g., they both come in different varieties depending on the mood; they share some of the same connectives (i.e., ‘then’); they allow for similar patterns of modal subordination. In the light of these affinities, it is not surprising that prominent theories of conditionals—old and new suppositionalisms as well as dynamic theories of conditionals—as well as (...)
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  • Metasemantics, moderate inflationism, and correspondence truth.Graham Seth Moore - 2023 - Dissertation, University of British Columbia
    An object-based correspondence theory of truth holds that a truth-bearer is true whenever its truth conditions are met by objects and their properties. In order to develop such a view, the principal task is to explain how truth-bearers become endowed with their truth conditions. Modern versions of the correspondence theory see this project as the synthesis of two theoretical endeavours: basic metasemantics and compositional semantics. Basic metasemantics is the theory of how simple, meaningful items (e.g. names and concepts) are endowed (...)
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  • Dimensional Analysis: Essays on the Metaphysics and Epistemology of Quantities.Mahmoud Jalloh - 2023 - Dissertation, University of Southern California
    This dissertation draws upon historical studies of scientific practice and contemporary issues in the metaphysics and epistemology of science to account for the nature of physical quantities. My dissertation applies this integrated HPS approach to dimensional analysis—a logic for quantitative physical equations which respects the distinct dimensions of quantities (e.g. mass, length, charge). Dimensional analysis and its historical development serve both as subjects of study and as a sources for solutions to contemporary problems. The dissertation consists primarily of three related (...)
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  • Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
    An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.
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  • Measurement in Science.Eran Tal - 2015 - Stanford Encyclopedia of Philosophy.
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  • The Metaphysics of Mass Expressions.Mark Steen - 2012 - Stanford Encyclopedia of Philosophy.
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  • Josiah Royce.Kelly A. Parker - 2008 - Stanford Encyclopedia of Philosophy.
    Josiah Royce (1855-1916) was the leading American proponent of absolute idealism, the metaphysical view (also maintained by G. W. F. Hegel and F. H. Bradley) that all aspects of reality, including those we experience as disconnected or contradictory, are ultimately unified in the thought of a single all-encompassing consciousness. Royce also made original contributions in ethics, philosophy of community, philosophy of religion and logic. His major works include The Religious Aspect of Philosophy (1885), The World and the Individual (1899-1901), The (...)
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  • Propositional attitude reports.Thomas McKay - 2008 - Stanford Encyclopedia of Philosophy.
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  • Relations.Fraser MacBride - 2016 - Stanford Encyclopedia of Philosophy.
    In this paper I provide a state of the art survey and assessment of the contemporary debate about relations. After (1) distinguishing different varieties of relations, symmetric from non-symmetric, internal from external relations etc. and relations from their set-theoretic models or sequences, I proceed (2) to consider Bradley’s regress and whether relations can be eliminated altogether. Next I turn (3) to the question whether relations can be reduced, bringing to bear considerations from the philosophy of physics as well as metaphysics. (...)
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  • Logical Truth.Mario Gomez-Torrente - 2014 - Stanford Encyclopedia of Philosophy.
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  • The correspondence theory of truth.Marian David - 2008 - Stanford Encyclopedia of Philosophy.
    Narrowly speaking, the correspondence theory of truth is the view that truth is correspondence to a fact -- a view that was advocated by Russell and Moore early in the 20 th century. But the label is usually applied much more broadly to any view explicitly embracing the idea that truth consists in a relation to reality, i.e., that truth is a relational property involving a characteristic relation (to be specified) to some portion of reality (to be specified). During the (...)
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  • Type theory.Thierry Coquand - 2008 - Stanford Encyclopedia of Philosophy.
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  • Paradoxes and contemporary logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.
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  • Samethinking.Romain Bourdoncle - 2022 - Dissertation, École Normale Supérieure
    This thesis investigates the nature of the relation between mental representations in successful verbal communication, thought attribution, agreement, and disagreement — a relation which I call “samethinking”. The nature of samethinking raises several foundational questions about the nature of (non-natural) meaning, and the cognitive underpinnings of the emergence of culture. It bears on long-lasting puzzles in the philosophy of mind and language (such as Frege’s puzzle and Kripke’s puzzle about belief). Samethinking does not amount to sharing a reference (with “sharing" (...)
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  • Seppo Albert Kivinen universaalien identiteetti- ja eksistenssiehdoista.Markku Keinänen - 2022 - Ajatus 79: 53-71.
    This article (in Finnish) discusses Seppo Albert Kivinen's (1933-2021) views on identity and existence conditions of universals. Moreover, the article puts the views to larger context.
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  • نقدی بر واقع سلبی و برخی نظریه‌های ثبوت: مشکل تسلسل.مهدی اسدی - 2015 - حکمت معاصر 5 (4):25-36.
    در این مقاله نخست به گزارش و تحلیل مختصر ادعا و ادلة ثبوت معتزلی، دیدگاه سابق راسل دربارة شیء اعم از وجود در مبادی ریاضیات، و دیدگاه بعدی راسل دربارة واقعیت سلبی خواهم پرداخت، سپس به این مسئله اشاره خواهیم کرد که به‌ علت پویایی و احیای چنین دیدگاه‌هایی، حتی در سال‌های اخیر، بایسته است از نو به تحلیل و نقد جدی دیدگاه‌هایی چون واقع سلبی و نظریه‌های ثبوت پرداخته ‌شود و در رد آن‌ها صرفاً به حس شهودی خلاف آن‌ها (...)
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  • Seyn, ἕν, 道: Brevis tractatus meta-ontologicus de elephantis et testudinibus.Florian Marion - 2022 - Revue Philosophique De Louvain 119 (1):1-51.
    The question of ontological foundation has undergone a noteworthy revival in recent years: metaphysicians today quarrel about how exactly to understand the asymmetrical and hyperintensional relationship of grounding. One of the reasons for this revival is that the old quantificationalist meta-ontology inherited from Quine has been effectively criticised by leading philosophers favourable to a meta-ontology, the aim of which is to come to know “which facts/items ground (constitute the base of) which other facts/items”, thus to examine the relation of ontological (...)
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