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  1. Brouwer versus Hilbert: 1907–1928.J. Posy Carl - 1998 - Science in Context 11 (2):291-325.
    The ArgumentL. E. J. Brouwer and David Hubert, two titans of twentieth-century mathematics, clashed dramatically in the 1920s. Though they were both Kantian constructivists, their notoriousGrundlagenstreitcentered on sharp differences about the foundations of mathematics: Brouwer was prepared to revise the content and methods of mathematics (his “Intuitionism” did just that radically), while Hilbert's Program was designed to preserve and constructively secure all of classical mathematics.Hilbert's interests and polemics at the time led to at least three misconstruals of intuitionism, misconstruals which (...)
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  • Making sense of (in)determinate truth: the semantics of free variables.John Cantwell - 2018 - Philosophical Studies 175 (11):2715-2741.
    It is argued that truth value of a sentence containing free variables in a context of use, just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate truth value. (...)
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  • Structuralist Neologicism†.Francesca Boccuni & Jack Woods - 2020 - Philosophia Mathematica 28 (3):296-316.
    Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles, refer. Focusing on numerical terms, this allows us to treat abstraction principles as implicit definitions determining all properties of the numbers, achieving a key (...)
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  • Possible Worlds: A Neo-Fregean Alternative.Sandy Berkovski - 2011 - Axiomathes 21 (4):531-551.
    I outline a neo-Fregean strategy in the debate on the existence of possible worlds. The criterion of identity and the criterion of application are formulated. Special attention is paid to the fact that speakers do not possess proper names for worlds. A broadly Quinean solution is proposed in response to this difficulty.
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  • Grounding, Conceivability, and the Mind-Body Problem.David Elohim - 2018 - Synthese 195 (2):919-926.
    This paper challenges the soundness of the two-dimensional conceivability argument against the derivation of phenomenal truths from physical truths in light of a hyperintensional, ground-theoretic regimentation of the ontology of consciousness. The regimentation demonstrates how ontological dependencies between truths about consciousness and about physics cannot be witnessed by epistemic constraints, when the latter are recorded by the conceivability—i.e., the epistemic possibility—thereof. Generalizations and other aspects of the philosophical significance of the hyperintensional regimentation are further examined.
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  • Mathematical Generality, Letter-Labels, and All That.F. Acerbi - 2020 - Phronesis 65 (1):27-75.
    This article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully general, (...)
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  • Epistemic Modality and Hyperintensionality in Mathematics.Timothy Bowen - 2017 - Dissertation, Arché, University of St Andrews
    This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...)
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  • Generic Structures.Leon Horsten - 2019 - Philosophia Mathematica 27 (3):362-380.
    In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.
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  • Aristotle’s Hylomorphism: The Causal-Explanatory Model.Michail Peramatzis - 2018 - Metaphysics 1 (1):12-32.
    There are several innocuous or trivial ways in which to explicate Aristotle’s hylomorphism. For example: objects are characterisable in terms of matter and form; or analysable into matter and form; or understood on the basis of matter and form. Serious problems arise when we seek to specify the sorts of relation holding among the different contributors to the hylomorphic picture. Here are some central general questions: a. What types of relation are most suitable for each n-tuple of contributors? b. What (...)
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  • Forms of Luminosity.Hasen Khudairi - 2017
    This dissertation concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...)
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  • Constructive Versus Ontological Construals of Cantorian Ordinals.Wolfram Hinzen - 2003 - History and Philosophy of Logic 24 (1):45-63.
    In a recent paper, Kit Fine offers a reconstruction of Cantor's theory of ordinals. It avoids certain mentalistic overtones in it through both a non-standard ontology and a non-standard notion of abstraction. I argue that this reconstruction misses an essential constructive and computational content of Cantor's theory, which I in turn reconstruct using Martin-Löf's theory of types. Throughout, I emphasize Kantian themes in Cantor's epistemology, and I also argue, as against Michael Hallett's interpretation, for the need for a constructive understanding (...)
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  • Choice functions and the scopal semantics of indefinites.Yoad Winter - 1997 - Linguistics and Philosophy 20 (4):399-467.
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  • Modal Foundations for Predicate Logic.Johan van Benthem - 1997 - Logic Journal of the IGPL 5 (2):259-286.
    The complexity of any logical modeling reflects both the intrinsic structure of a topic described and the weight of the formal tools. Some of this weight seems inherent in even the most basic logical systems. Notably, standard predicate logic is undecidable. In this paper, we investigate ‘lighter’ versions of this general purpose tool, by modally ‘deconstructing’ the usual semantics, and locating implicit choice points in its set up. The first part sets out the interest of this program and the modal (...)
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  • The primacy of place: An investigation in Brentanian ontology.Barry Smith - 1989 - Topoi 8 (1):43-51.
    What follows is an investigation of the ontology of Franz Brentano with special reference to Brentano's later and superficially somewhat peculiar doctrine to the effect that the substances of the material world are three dimensional places. Taken as a whole, Brentano's philosophy is marked by three, not obviously compatible, trait. In the first place, his work is rooted in the metaphysics of Aristotle, above all in Aristotle's substance/accident ontology and in the Aristotelian theory of categories. In the second place, Brentano (...)
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  • Austrian Philosophy: The Legacy of Franz Brentano.Barry Smith - 1994 - Chicago: Open Court.
    This book is a survey of the most important developments in Austrian philosophy in its classical period from the 1870s to the Anschluss in 1938. Thus it is intended as a contribution to the history of philosophy. But I hope that it will be seen also as a contribution to philosophy in its own right as an attempt to philosophize in the spirit of those, above all Roderick Chisholm, Rudolf Haller, Kevin Mulligan and Peter Simons, who have done so much (...)
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  • Identity, indiscernibility, and Ante Rem structuralism: The tale of I and –I.Stewart Shapiro - 2008 - Philosophia Mathematica 16 (3):285-309.
    Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...)
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  • An “I” for an I: Singular terms, uniqueness, and reference.Stewart Shapiro - 2012 - Review of Symbolic Logic 5 (3):380-415.
    There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and (...)
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  • Arbitrary reference, numbers, and propositions.Michele Palmira - 2018 - European Journal of Philosophy 26 (3):1069-1085.
    Reductionist realist accounts of certain entities, such as the natural numbers and propositions, have been taken to be fatally undermined by what we may call the problem of arbitrary identification. The problem is that there are multiple and equally adequate reductions of the natural numbers to sets (see Benacerraf, 1965), as well as of propositions to unstructured or structured entities (see, e.g., Bealer, 1998; King, Soames, & Speaks, 2014; Melia, 1992). This paper sets out to solve the problem by canvassing (...)
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  • XI*—A Few More Remarks on Logical Form.Alex Oliver - 1999 - Proceedings of the Aristotelian Society 99 (1):247-272.
    Alex Oliver; XI*—A Few More Remarks on Logical Form, Proceedings of the Aristotelian Society, Volume 99, Issue 1, 1 June 1999, Pages 247–272, https://doi.org/10.
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  • Understanding induction.John Macnamara - 1991 - British Journal for the Philosophy of Science 42 (1):21-48.
    The paper offers a new understanding of induction in the empirical sciences, one which assimilates it to induction in geometry rather than to statistical inference. To make the point a system of notions, essential to logically sound induction, is defined. Notable among them are arbitrary object and particular property. A second aim of the paper is to bring to light a largely neglected set of assumptions shared by both induction and deduction in the empirical sciences. This is made possible by (...)
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  • Notes on Stratified Semantics.Shay Allen Logan - 2019 - Journal of Philosophical Logic 48 (4):749-786.
    In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature, 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71, 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are, 27–59, 1988; Mares, Studia Logica 51, 1–20, 1992), both of which (...)
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  • Dedekind and Hilbert on the foundations of the deductive sciences.Ansten Klev - 2011 - Review of Symbolic Logic 4 (4):645-681.
    We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed by elucidation, whereas (...)
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  • Free choiceness and non-individuation.Jacques Jayez & Lucia M. Tovena - 2005 - Linguistics and Philosophy 28 (1):1 - 71.
    . Fresh evidence from Free Choice Items (FCIs) in French question the current perception of the class. The role of some standard distinctions found in the literature is weakened or put in a new perspective. The distinction between universal and existential is no longer an intrinsic property of FCIs. Similarly, the opposition between variation-based vs intension-based analyses is relativized. We show that the regime of free choiceness can be characterized by an abstract constraint, that we call Non-Individuation (NI), and which (...)
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  • Unified Foundations for Essence and Ground.Kit Fine - 2015 - Journal of the American Philosophical Association 1 (2):296-311.
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  • Knowledge of Validity.Sinan Dogramaci - 2010 - Noûs 44 (3):403-432.
    What accounts for how we know that certain rules of reasoning, such as reasoning by Modus Ponens, are valid? If our knowledge of validity must be based on some reasoning, then we seem to be committed to the legitimacy of rule-circular arguments for validity. This paper raises a new difficulty for the rule-circular account of our knowledge of validity. The source of the problem is that, contrary to traditional wisdom, a universal generalization cannot be inferred just on the basis of (...)
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  • Names.Sam Cumming - 2009 - Stanford Encyclopedia of Philosophy.
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  • Situated representations and ad hoc concepts.Jérome Dokic - 2007 - In María José Frápolli (ed.), Saying, Meaning and Referring: Essays on François Recanati's Philosophy of Language. Palgrave-Macmillan.
    Situation theorists such as Jon Barwise, John Etchemendy, and John Perry have advanced the hypothesis that linguistic and mental representations are ‘situated' in the sense that they are true or false only relative to partial situations. François Recanati has done an important task in reviving and in many respects deepening situation theory. In this chapter, I explore some aspects of Recanati's own account. I focus on situated mental representations, and stress the connection between them and ad hoc or temporary concepts.
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  • Logical Indefinites.Jack Woods - 2014 - Logique Et Analyse -- Special Issue Edited by Julien Murzi and Massimiliano Carrara 227: 277-307.
    I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.
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  • Conceivability and Haecceitism.Hasen Khudairi - manuscript
    This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I argue that the interaction between the multi-dimensional intensional framework and intensional plural quantification enables epistemic possibilities to target the haecceitistic properties of individuals. I outline the elements of plural logic, and I specify, then, a multi-dimensional intensional formula encoding the relation between the epistemic possibility of haecceity comprehension and its metaphysical possibility. I conclude by addressing objections from the indeterminacy (...)
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  • The Bishop and Priest: Toward a point-of-view based epistemology of true contradictions.Eric Dietrich - 2008 - Logos Architekton 2 (2):35-58..
    True contradictions are taken increasingly seriously by philosophers and logicians. Yet, the belief that contradictions are always false remains deeply intuitive. This paper confronts this belief head-on by explaining in detail how one specific contradiction is true. The contradiction in question derives from Priest's reworking of Berkeley's argument for idealism. However, technical aspects of the explanation offered here differ considerably from Priest's derivation. The explanation uses novel formal and epistemological tools to guide the reader through a valid argument with, not (...)
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  • Situated mental representations.Jérôme Dokic - unknown
    Situation theorists such as John Barwise, John Etchemendy, John Perry and François Recanati have put forward the hypothesis that linguistic representations are situated in the sense that they are true or false only relative to partial situations which are not explicitly represented as such. Following Recanati's lead, I explore this hypothesis with respect to mental representations. First, I introduce the notion of unarticulated constituent, due to John Perry. I suggest that the question of whether there really are such constituents should (...)
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  • Metafisica e ontologia.Kevin Mulligan - 2009 - Swiss Philosophical Preprints.
    Le parole “metafisica” e “ontologia” si dicono in molti modi diversi nella filosofia del XX secolo, tanto all’interno della filosofia analitica quanto altrove. Sono spesso usate per parlare della teoria o dell’analisi di ciò che c’è, delle specie principali di ciò che c’è e dei loro rapporti. Ma i positivisti viennesi, per esempio, chiamavano “metafisiche” le filosofie che non amavano (Carnap, 1985; Campbell, 1976, cap. 2); e se Quine parla dell’impegno ontologico o ontico di una teoria, non intende con ciò (...)
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  • Métaphysique et Ontologie.Kevin Mulligan - 2009 - Swiss Philosophical Preprints.
    Les mots « métaphysique » et « ontologie » se disent de façons multiples à l’intérieur de la philosophie analytique et ailleurs dans la philosophie du vingtième siècle. Ils sont souvent employés pour parler de la théorie ou l’analyse de ce qu’il y a, des espèces principales de ce qu’il y a et de leurs rapports. Mais les positivistes viennois, par exemple, appelaient « métaphysiques » les philosophies qu’ils n’aimaient pas (Carnap 1985, Campbell 1976 ch. 2)1. Et si Quine parle (...)
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  • Husserlian essentialism revisited : a study of essence, necessity and predication.Nicola Spinelli - 2016 - Dissertation, University of Warwick
    Husserlian Essentialism is the view, maintained byEdmundHusserl throughout his career, that necessary truths obtain because essentialist truths obtain. In this thesis I have two goals. First, to reconstruct and flesh out Husserlian Essentialism and its connections with surrounding areas of Husserl's philosophy in full detail – something which has not been done yet. Second, to assess the theoretical solidity of the view. As regards the second point, after having presented Husserlian Essentialism in the first two chapters, I raise a serious (...)
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