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Fiction and Metaphysics

New York: Cambridge University Press (1998)

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  1. Um quadro dialógico para ficções como objetos hipotéticos.Shahid Rahman & Juan Redmond - 2015 - Filosofia Unisinos 16 (1).
    Recent work on the development of a dialogical approach to the logic of fiction stresses the notion of existence as choice. Moreover, this approach to existence has been combined with the notion of ontolog-ical dependence as deployed by A. Thomasson’s artifactual theory of fiction. In order to implement such a combination within the dialogical frame several predicates of ontological dependence have been de-fined. However, the definition of such predicates seems to lean on a model-theoretic semantics for mod-al logic after all. (...)
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  • Mechanisms and explanatory realization relations.Thomas W. Polger - 2010 - Synthese 177 (2):193 - 212.
    My topic is the confluence of two recently active philosophical research programs. One research program concerns the metaphysics of realization. The other research program concerns scientific explanation in terms of mechanisms. In this paper I introduce a distinction between descriptive and explanatory approaches to realization. I then use this distinction to argue that a well-known account of realization, due to Carl Gillett, is incompatible with a well-known account of mechanistic explanation, due to Peter Machamer, Lindley Darden, and Carl Craver (MDC, (...)
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  • Vergil and dido.Jérôme Pelletier - 2003 - Dialectica 57 (2):191–203.
    According to many realist philosophers of fiction, one needs to posit an ontology of existing fictional characters in order to give a correct account of discourse about fiction. The realists' claim is opposed by pretense theorists for whom discourse about fiction involves, as discourse in fiction, pretense. On that basis, pretense theorists claim that one does not need to embrace an ontology of fictional characters to give an account of discourse about fiction. The ontolog-ical dispute between realists and pretense theorists (...)
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  • Structures as Relations.Michele Paolini Paoletti - 2021 - Synthese 198 (Suppl 11):S2671-S2690.
    I shall explore in this article the hypothesis that structures are relations between the components of complex entities. After having introduced hylomorphism, its major advantages and the major views of the nature of structures, I shall introduce the distinctions between external and internal relations and the one between symmetrical and non-symmetrical relations. I shall also describe the theory of non-symmetrical relations that I accept, i.e., the O-Roles theory, as most structures seem to be external and non-symmetrical relations. Later on, I (...)
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  • Vague fictional objects.Elisa Paganini - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (2):158-184.
    ABSTRACTI propose a different account of fictional objects from the ones already present in the literature. According to my account, fictional objects are culturally created abstract objects dependent for their existence on the pretence attitude adopted by a group of people towards a single fictional content. My work is divided into three parts: in the first one, I present how fictional objects come into existence according to my proposal; in the second part, I illustrate how the existence of fictional objects (...)
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  • Mental Files and the Theory of Fiction: A Reply to Zoltán Vecsey.Eleonora Orlando - 2021 - Espes. The Slovak Journal of Aesthetics 10 (1):79-88.
    In this work I reply to Zoltán Vecsey’s criticisms of the semantic account of fictional names I put forward in Orlando. The main tenet of that proposal is that fictional names refer to individual concepts, which I understand in terms of mental files. In Vecsey, the author presents three main objections: no referential shift can be ascribed to fictional names, fictional names are supposed to play two conflicting functions, and the mental file framework is incompatible with an antirealist view of (...)
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  • Files for Fiction.Eleonora Orlando - 2017 - Acta Analytica 32 (1):55-71.
    In this essay, I appeal to the mental file approach in order to give an anti-realist semantic analysis of statements containing fictional names. I claim that fictive and parafictive uses of them express conceptual, though not general, propositions constituted by mental files, anchored in the conceptual world of the corresponding fictional story. Moreover, by positing a referential shift determined by the presence of a simulative referential intention characteristic of those uses, it is possible to take them to be true with (...)
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  • Fiction, prepositional attitudes, and some truths about falsehood.Alex Orenstein - 2003 - Dialectica 57 (2):177–190.
    This paper presents an anti‐realist account of fictional objects. Arguing for the involvement of non‐veridical prepositional attitude ascriptions in the understanding of fiction, I maintain that there is no need to invoke Meinongian objects, possibilia or abstract objects for this purpose. In addition I argue against object dependent views . I make a case for empty names playing a more significant role than that accorded on direct reference accounts of names. I close by noting points of similarity and of difference (...)
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  • Creationism and cardinality.Daniel Nolan & Alexander Sandgren - 2014 - Analysis 74 (4):615-622.
    Creationism about fictional entities requires a principle connecting what fictions say exist with which fictional entities really exist. The most natural way of spelling out such a principle yields inconsistent verdicts about how many fictional entities are generated by certain inconsistent fictions. Avoiding inconsistency without compromising the attractions of creationism will not be easy.
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  • Development and natural kinds: Some lessons from biology.Marco J. Nathan & Andrea Borghini - 2014 - Synthese 191 (3):539-556.
    While philosophers tend to consider a single type of causal history, biologists distinguish between two kinds of causal history: evolutionary history and developmental history. This essay studies the peculiarity of development as a criterion for the individuation of biological traits and its relation to form, function, and evolution. By focusing on examples involving serial homologies and genetic reprogramming, we argue that morphology (form) and function, even when supplemented with evolutionary history, are sometimes insufficient to individuate traits. Developmental mechanisms bring in (...)
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  • Fictional Surrogates.Ioan-Radu Motoarca - 2014 - Philosophia 42 (4):1033-1053.
    It is usually taken for granted, in discussions about fiction, that real things or events can occur as referents of fictional names . In this paper, I take issue with this view, and provide several arguments to the effect that it is better to take the names in fiction to refer to fictional surrogates of real objects. Doing so allows us to solve a series of problems that arise on the reference-continuity view. I also show that the arguments philosophers usually (...)
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  • Intentionality: Some Lessons from the History of the Problem from Brentano to the Present.Dermot Moran - 2013 - International Journal of Philosophical Studies 21 (3):317-358.
    Intentionality (‘directedness’, ‘aboutness’) is both a central topic in contemporary philosophy of mind, phenomenology and the cognitive sciences, and one of the themes with which both analytic and Continental philosophers have separately engaged starting from Brentano and Edmund Husserl’s ground-breaking Logical Investigations (1901) through Roderick M. Chisholm, Daniel C. Dennett’s The Intentional Stance, John Searle’s Intentionality, to the recent work of Tim Crane, Robert Brandom, Shaun Gallagher and Dan Zahavi, among many others. In this paper, I shall review recent discussions (...)
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  • Interpretive Context, Counterpart Theory and Fictional Realism without Contradictions.Raphael Morris - 2019 - Disputatio 11 (54):231-253.
    Models for truth in fiction must be able to account for differing versions and interpretations of a given fiction in such a way that prevents contradictions from arising. I propose an analysis of truth in fiction designed to accommodate this. I examine both the interpretation of claims about truth in fiction (the ‘Interpretation Problem’) and the metaphysical nature of fictional worlds and entities (the ‘Metaphysical Problem’). My reply to the Interpretation Problem is a semantic contextualism influenced by Cameron (2012), while (...)
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  • Truth Predicates, Truth Bearers, and their Variants.Friederike Moltmann - 2018 - Synthese (Suppl 2):1-28.
    This paper argues that truth predicates in natural language and their variants, predicates of correctness, satisfaction and validity, do not apply to propositions (not even with 'that'-clauses), but rather to a range of attitudinal and modal objects. As such natural language reflects a notion of truth that is primarily a normative notion of correctness constitutive of representational objects. The paper moreover argues that 'true' is part of a larger class of satisfaction predicates whose semantic differences are best accounted for in (...)
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  • The semantics of existence.Friederike Moltmann - 2013 - Linguistics and Philosophy 36 (1):31-63.
    The notion of existence is a very puzzling one philosophically. Often philosophers have appealed to linguistic properties of sentences stating existence. However, the appeal to linguistic intuitions has generally not been systematic and without serious regard of relevant issues in linguistic semantics. This paper has two aims. On the one hand, it will look at statements of existence from a systematic linguistic point of view, in order to try to clarify what the actual semantics of such statements in fact is. (...)
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  • Propositions, attitudinal objects, and the distinction between actions and products.Friederike Moltmann - 2013 - Canadian Journal of Philosophy, Supplementary Volume on Propositions, Edited by G. Rattan and D. Hunter 43 (5-6):679-701.
    This paper argues that attitudinal objects, entities of the sort of John's judgment, John's thought, and John's claim, should play the role of propositions, as the cognitive products of cognitive acts, not the acts themselves.
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  • An object‐based truthmaker semantics for modals.Friederike Moltmann - 2018 - Philosophical Issues 28 (1):255-288.
    Possible worlds semantics faces a range of difficulties for at least certain types of modals, especially deontic modals with their distinction between heavy and light permissions and obligations. This paper outlines a new semantics of modals that aims to overcome some of those difficulties. The semantics is based on an a novel ontology of modal objects, entities like obligations, permissions, needs, as well as epistemic states, abilities, and essences. Moreover, it is based on truthmaking, in the sense of Fine’s recent (...)
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  • Me and My Imaginary Friend: Critical Study of Virtual Subjects, Fugitive Selves.Kris McDaniel - 2022 - Analysis 82 (3):526-536.
    Jonardon Ganeri’s recent book – henceforth, ‘Virtual Subjects’ – is an intriguing introduction to some aspects of the philosophical thought of Fernando Pessoa.
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  • Ontology for information systems: artefacts as a case study.Massimiliano Carrara & Marzia Soavi - 2008 - Mind and Society 7 (2):143-156.
    The goal of the paper is to analyse some specific features of a very central concept for top-level ontologies for information systems: i.e. the concept of artefact. Specifically, we analyse the relation to be a copy of that is strongly linked to the notion of artefact and—as we will demonstrate—could be useful to distinguish artefacts from objects of other kinds. Firstly, we outline some intuitive and commonsensical reasons for the need of a clarification of the notion of artefact in ontologies (...)
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  • Five New Arguments for The Dynamic Theory of Time.Ned Markosian - 2022 - Philosophical Perspectives 36 (1):158-181.
    According to The Static Theory of Time, time is like space in various ways, and there is no such thing as the passage of time. According to The Dynamic Theory of Time, on the other hand, time is very different from space, and the passage of time is an all-too-real phenomenon. This paper first offers some suggestions about how we should understand these two theories, and then introduces five new arguments for The Dynamic Theory of Time.
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  • Category mistakes and figurative language.Ofra Magidor - 2015 - Philosophical Studies (1):1-14.
    Category mistakes are sentences such as ”The number two is blue’ or ”Green ideas sleep furiously’. Such sentences are highly infelicitous and thus a prominent view claims that they are meaningless. Category mistakes are also highly prevalent in figurative language. That is to say, it is very common for sentences which are used figuratively to be such that, if taken literally, they would constitute category mistakes. In this paper I argue that the view that category mistakes are meaningless is inconsistent (...)
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  • Necessarily, Sherlock Holmes Is Not a Person.David Liebesman - 2014 - Analytic Philosophy 55 (3):306-318.
    In the appendix to Naming and Necessity, Kripke espouses the view that necessarily, Sherlock Holmes is not a person. To date, no compelling argument has been extracted from Kripke’s remarks. I give an argument for Kripke’s conclusion that is not only interpretively plausible but also philosophically compelling. I then defend the argument against salient objections.
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  • Models, Fictions, and Realism: Two Packages.Arnon Levy - 2012 - Philosophy of Science 79 (5):738-748.
    Some philosophers of science – the present author included – appeal to fiction as an interpretation of the practice of modeling. This raises the specter of an incompatibility with realism, since fiction-making is essentially non-truth-regulated. I argue that the prima facie conflict can be resolved in two ways, each involving a distinct notion of fiction and a corresponding formulation of realism. The main goal of the paper is to describe these two packages. Toward the end I comment on how to (...)
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  • Authorial Intention, Readers’ Creation, and Reference Shift.Jeonggyu Lee - 2022 - Philosophical Quarterly 72 (2):381-401.
    This paper deals with the identity problems of fictional objects, focusing on Anthony Everett's and Stuart Brock's leading criticisms against fictional creationism, the view that fictional objects are abstract objects created by our acts involving literary practices. My primary aim is to argue that creationism based on referentialism has enough resources to individuate fictional objects and hence can address the alleged identity problems: every alleged problematic case regarding the identity of fictional objects is well explained in terms of the notions (...)
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  • Would this paper exist if I hadn’t written it?Samuel Lebens - 2015 - Philosophical Studies 172 (11):3059-3080.
    This paper wants to know whether it would exist, or could exist, in worlds in which I didn't write it. Before we can answer this question, we first of all have to inquire as to what, exactly, this paper is. After exploring two forms of Platonism, and a theory that defines literary works in terms of events, I shall argue that the term ‘this paper’ is actually infected with ambiguity. Does this paper need me? It depends upon what you mean (...)
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  • A Uniform, Concretist Metaphysics for Linguistic Types.Giorgio Lando - 2019 - Metaphysica 20 (2):195-221.
    I argue that it is not acceptable to restrict the claim that linguistic types are concrete entities (type-concretism) to some categories of linguistic types (such as words or proper names), while at the same time conceding that other categories of linguistic types (such as sentence types) are abstract entities. Moreover, I suggest a way in which type-concretism can be extended to every linguistic type, thereby responding to the so-called productivity objection to type-concretism, according to which, whenever tokens of a type (...)
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  • Quantified negative existentials.Frederick Kroon - 2003 - Dialectica 57 (2):149–164.
    This paper suggests that quantified negative existentials about fiction—statements of the form “There are some / many / etc. Fs in work W who don't exist”—offer a serious challenge to the theorist of fiction: more serious, in a number of ways, that singular negative existentials. I argue that the temptation to think that only a realist semantics of such statements is plausible should be resisted. There are numerous quantified negative existentials found in other areas that seem equally “true” but where (...)
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  • Much ado about nothing: Priest and the reinvention of noneism. [REVIEW]Frederick Kroon - 2008 - Philosophy and Phenomenological Research 76 (1):199–207.
  • Fictionalism in Metaphysics.Frederick Kroon - 2011 - Philosophy Compass 6 (11):786-803.
    This is a survey of contemporary work on ‘fictionalism in metaphysics’, a term that is taken to signify both the place of fictionalism as a distinctive anti‐realist metaphysics in which usefulness rather than truth is the norm of acceptance, and the fact that philosophers have given fictionalist treatments of a range of specifically metaphysical notions.
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  • What is Wrong with Self-Grounding?David Mark Kovacs - 2018 - Erkenntnis 83 (6):1157-1180.
    Many philosophers embrace grounding, supposedly a central notion of metaphysics. Grounding is widely assumed to be irreflexive, but recently a number of authors have questioned this assumption: according to them, it is at least possible that some facts ground themselves. The primary purpose of this paper is to problematize the notion of self-grounding through the theoretical roles usually assigned to grounding. The literature typically characterizes grounding as at least playing two central theoretical roles: a structuring role and an explanatory role. (...)
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  • The Deflationary Theory of Ontological Dependence.David Mark Kovacs - 2018 - Philosophical Quarterly 68 (272):481-502.
    When an entity ontologically depends on another entity, the former ‘presupposes’ or ‘requires’ the latter in some metaphysical sense. This paper defends a novel view, Dependence Deflationism, according to which ontological dependence is what I call an aggregative cluster concept: a concept which can be understood, but not fully analysed, as a ‘weighted total’ of constructive and modal relations. The view has several benefits: it accounts for clear cases of ontological dependence as well as the source of disagreement in controversial (...)
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  • Deflationary Nominalism and Puzzle Avoidance.David Mark Kovacs - 2019 - Philosophia Mathematica 27 (1):88-104.
    In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...)
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  • The Vagueness Argument Against Abstract Artifacts.Daniel Z. Korman - 2014 - Philosophical Studies 167 (1):57-71.
    Words, languages, symphonies, fictional characters, games, and recipes are plausibly abstract artifacts— entities that have no spatial location and that are deliberately brought into existence as a result of creative acts. Many accept that composition is unrestricted: for every plurality of material objects, there is a material object that is the sum of those objects. These two views may seem entirely unrelated. I will argue that the most influential argument against restricted composition—the vagueness argument—doubles as an argument that there can (...)
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  • Imagination extended and embedded: artifactual versus fictional accounts of models.Tarja Knuuttila - 2017 - Synthese 198 (Suppl 21):5077-5097.
    This paper presents an artifactual approach to models that also addresses their fictional features. It discusses first the imaginary accounts of models and fiction that set model descriptions apart from imagined-objects, concentrating on the latter :251–268, 2010; Frigg and Nguyen in The Monist 99:225–242, 2016; Godfrey-Smith in Biol Philos 21:725–740, 2006; Philos Stud 143:101–116, 2009). While the imaginary approaches accommodate surrogative reasoning as an important characteristic of scientific modeling, they simultaneously raise difficult questions concerning how the imagined entities are related (...)
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  • The idols of inner-sense.Chad Kidd - 2015 - Philosophical Studies 172 (7):1759-1782.
    Many philosophers hold one of two extreme views about our capacity to have phenomenally conscious experience : either that inner-sense enables us to know our experience and its properties infallibly or the contrary conviction that inner-sense is utterly fallible and the evidence it provides completely defeasible. Both of these are in error. This paper presents an alternative conception of inner-sense, modeled on disjunctive conceptions of perceptual awareness, that avoids both erroneous extremes, but that builds on the commonsense intuitions that motivate (...)
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  • Phenomenal consciousness with infallible self-representation.Chad Kidd - 2011 - Philosophical Studies 152 (3):361-383.
    In this paper, I argue against the claim recently defended by Josh Weisberg that a certain version of the self-representational approach to phenomenal consciousness cannot avoid a set of problems that have plagued higher-order approaches. These problems arise specifically for theories that allow for higher-order misrepresentation or—in the domain of self-representational theories—self-misrepresentation. In response to Weisberg, I articulate a self-representational theory of phenomenal consciousness according to which it is contingently impossible for self-representations tokened in the context of a conscious mental (...)
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  • Fiction cannot be true.László Kajtár - 2017 - Philosophical Studies 174 (9):2167-2186.
    According to the dominant theory of intentionalism, fiction and non-fiction are in a “mix-and-match” relationship with truth and falsity: both fiction and nonfiction can be either true or false. Intentionalists hold that fiction is a property of a narrative that is intended to elicit not belief but imagination or make-belief in virtue of the audience’s recognizing that such is the intention of the fiction-maker. They claim that in unlikely circumstances these fictions can turn out to be accidentally true. On the (...)
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  • Artifacts and mind-dependence.Tim Juvshik - 2021 - Synthese 199 (3-4):9313-9336.
    I defend the intention-dependence of artifacts, which says that something is an artifact of kind K only if it is the successful product of an intention to make an artifact of kind K. I consider objections from two directions. First, that artifacts are often mind- and intention-dependent, but that this isn’t necessary, as shown by swamp cases. I offer various error theories for why someone would have artifact intuitions in such cases. Second, that while artifacts are necessarily mind-dependent, they aren’t (...)
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  • Abstract Objects, Causal Efficacy, and Causal Exclusion.Tim Juvshik - 2018 - Erkenntnis 83 (4):805-827.
    objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...)
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  • Artifactualization without Physical Modification.Tim Juvshik - 2021 - Res Philosophica 98 (4):545-572.
    Much recent discussion has focused on the nature of artifacts, particularly on whether they have essences. While it is often held that artifacts are intention-dependent and necessarily have functions, it is equally commonly held, though far less discussed, that artifacts are the result of physical modification of some material objects. This paper argues that the physical modification condition on artifacts is false. First, it formulates the physical modification condition perspicuously for the first time. Second, it offers counterexamples to this condition, (...)
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  • Relativity and the Causal Efficacy of Abstract Objects.Tim Juvshik - 2020 - American Philosophical Quarterly 57 (3):269-282.
    Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, that (...)
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  • Pure and impure stipulata.Cory Juhl - 2009 - Philosophy and Phenomenological Research 79 (3):637-652.
  • Proof of the Existence of Universals—and Roman Ingarden’s Ontology.Ingvar Johansson - 2009 - Metaphysica 10 (1):65-87.
    The paper ends with an argument that says: necessarily, if there are finitely spatially extended particulars, then there are monadic universals. Before that, in order to characterize the distinction between particulars and universals, Roman Ingarden’s notions of existential moments and modes (ways) of being are presented, and a new pair of such existential moments is introduced: multiplicity–monadicity. Also, it is argued that there are not only real universals, but instances of universals (tropes) and fictional universals too.
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  • Ingarden’s Aesthetic Argument against Husserl’s Transcendental Idealism Turn.Hicham Jakha - 2023 - Analiza I Egzystencja 63 (3):89-108.
    Husserl’s allegiance to realism came under attack following his Ideas. Ingarden was a fierce critic of his teacher’s turn to transcendental idealism and provided compelling arguments both for his idealist reading of Husserl and for his rejection of idealism. One of the main arguments Ingarden devised against Husserl’s turn was based on his aesthetics. Against Husserl, Ingarden established literary works and fictional objects as purely intentional objects that are (1) doubly structured, vis-à-vis their formal ontology, and (2) endowed with spots (...)
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  • Exploratory modeling and indeterminacy in the search for life.Franklin R. Jacoby - 2022 - European Journal for Philosophy of Science 12 (2):1-20.
    The aim of this article is to use a model from the origin of life studies to provide some depth and detail to our understanding of exploratory models by suggesting that some of these models should be understood as indeterminate. Models that are indeterminate are a type of exploratory model and therefore have extensive potential and can prompt new lines of research. They are distinctive in that, given the current state of scientific understanding, we cannot specify how and where the (...)
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  • Experiences as complex events.Michael Jacovides - 2010 - Southern Journal of Philosophy 48 (2):141-159.
    It is argued that experiences are complex events that befall their subjects. Each experience has a single subject and depends on the state or the event that it is of. The constituents of an experience are its subject, its grounding event or state, and everything that the subject is aware of during that time that's relevant to the telling of the story of how it was to participate in that event or be put in that state. The experience occurs where (...)
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  • An Ontology of Words.Nurbay Irmak - 2019 - Erkenntnis 84 (5):1139-1158.
    Words are indispensable linguistic tools for beings like us. However, there is not much philosophical work done about what words really are. In this paper, I develop a new ontology for words. I argue that words are abstract artifacts that are created to fulfill various kinds of purposes, and words are abstract in the sense that they are not located in space but they have a beginning and may have an end in time given that certain conditions are met. What (...)
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  • The problem of creation and abstract artifacts.Nurbay Irmak - 2020 - Synthese 198 (10):9695-9708.
    Abstract artifacts such as musical works and fictional entities are human creations; they are intentional products of our actions and activities. One line of argument against abstract artifacts is that abstract objects are not the kind of objects that can be created. This is so, it is argued, because abstract objects are causally inert. Since creation requires being caused to exist, abstract objects cannot be created. One common way to refute this argument is to reject the causal inefficacy of abstracta. (...)
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  • Pretense and fiction-directed thought.Michael R. Hicks - 2015 - Philosophical Studies 172 (6):1549-1573.
    Thought about fictional characters is special, and needs to be distinguished from ordinary world-directed thought. On my interpretation, Kendall Walton and Gareth Evans have tried to show how this serious fiction-directed thought can arise from engagement with a kind of pretending. Many criticisms of their account have focused on the methodological presupposition, that fiction-directed thought is the appropriate explanandum. In the first part of this paper, I defend the methodological claim, and thus the existence of the problem to which pretense (...)
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  • Fictions within fictions.Reina Hayaki - 2008 - Philosophical Studies 146 (3):379 - 398.
    This paper examines the logic of fictions within fictions. I argue that consistently nested consistent fictions must have certain formal characteristics. The most important is that they form a tree structure. Depending on one’s theory of fictional objects, additional constraints may apply regarding the appearance of a fictional object in two or more fictional universes. The background motivation for the paper is to use iterated fiction operators as a tool for making sense of iterated modal operators; I conclude by noting (...)
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