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Epistemic Modality and Hyperintensionality in Mathematics

Dissertation, Arché, University of St Andrews (2017)

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  1. The realm of the infinite.H. W. Woodin - 2011 - In Michał Heller & W. H. Woodin (eds.), Infinity: new research frontiers. New York: Cambridge University Press.
  • Kit Fine: First-Order Modal Theories I--Sets.First-Order Modal Theories.First-Order Modal Theories III--Facts.W. Kroon - 1988 - Journal of Symbolic Logic 53 (4):1262-1269.
  • Action.Elisabeth Pacherie - 2012 - In Keith Frankish & William Ramsey (eds.), The Cambridge Handbook of Cognitive Science. Cambridge: Cambridge University Press. pp. 92--111.
    In recent years, the integration of philosophical with scientific theorizing has started to yield new insights. This chapter surveys some recent philosophical and empirical work on the nature and structure of action, on conscious agency, and on our knowledge of actions.
     
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  • Frege's theorem.Richard G. Heck - 2011 - New York: Clarendon Press.
    The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.
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  • Computational complexity of the semantics of some natural language constructions.Marcin Mostowski & Dominika Wojtyniak - 2004 - Annals of Pure and Applied Logic 127 (1-3):219--227.
    We consider an example of a sentence which according to Hintikka's claim essentially requires for its logical form a Henkin quantifier. We show that if Hintikka is right then recognizing the truth value of the sentence in finite models is an NP-complete problem. We discuss also possible conclusions from this observation.
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  • Introduction to Metamathematics.H. Rasiowa - 1954 - Journal of Symbolic Logic 19 (3):215-216.
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  • Introduction to Metamathematics.Ann Singleterry Ferebee - 1968 - Journal of Symbolic Logic 33 (2):290-291.
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  • ‘Ought’ and Resolution Semantics.Fabrizio Cariani - 2011 - Noûs 47 (3):534-558.
    I motivate and characterize an intensional semantics for ‘ought’ on which it does not behave as a universal quantifier over possibilities. My motivational argument centers on taking at face value some standard challenges to the quantificational semantics, especially to the idea that ‘ought’-sentences satisfy the principle of Inheritance. I argue that standard pragmatic approaches to these puzzles are either not sufficiently detailed or unconvincing.
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  • Hale and Wright on the Metaontology of Neo-Fregeanism.Matti Eklund - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics. Oxford, England: Oxford University Press UK.
  • Possibility.[author unknown] - 1942 - Revue Philosophique de la France Et de l'Etranger 133 (7):92-93.
     
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  • Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
    This is identical with the first edition (see 21: 2716) except for the addition of a Supplement containing 5 previously published articles and the bringing of the bibliography (now 73 items) up to date. The 5 added articles present clarifications or modifications of views expressed in the first edition. (PsycINFO Database Record (c) 2009 APA, all rights reserved).
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  • The rules of thought.Jonathan Jenkins Ichikawa & Benjamin W. Jarvis - 2013 - Oxford: Oxford University Press. Edited by Benjamin W. Jarvis.
    Ichikawa and Jarvis offer a new rationalist theory of mental content and defend a traditional epistemology of philosophy. They argue that philosophical inquiry is continuous with non-philosophical inquiry, and can be genuinely a priori, and that intuitions do not play an important role in mental content or the a priori.
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  • Max Black's objection to mind-body identity.Ned Block - 2006 - Oxford Studies in Metaphysics 2:3-78.
    considered an objection that he says he thought was first put to him by Max Black. He says.
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  • Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
    Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
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  • Logical information and epistemic space.Mark Jago - 2009 - Synthese 167 (2):327 - 341.
    Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only those (...)
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  • Knowledge and Belief: An Introduction to the Logic of the Two Notions.Jaakko Hintikka - 1962 - Studia Logica 16:119-122.
     
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  • Aboutness.Stephen Yablo - 2014 - Oxford: Princeton University Press.
    Aboutness has been studied from any number of angles. Brentano made it the defining feature of the mental. Phenomenologists try to pin down the aboutness-features of particular mental states. Materialists sometimes claim to have grounded aboutness in natural regularities. Attempts have even been made, in library science and information theory, to operationalize the notion. But it has played no real role in philosophical semantics. This is surprising; sentences have aboutness-properties if anything does. Aboutness is the first book to examine through (...)
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  • Topics of Thought. The Logic of Knowledge, Belief, Imagination.Franz Berto, Peter Hawke & Aybüke Özgün - 2022 - Oxford: Oxford University Press.
    When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also by (...)
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  • Constructing the impossible.Kit Fine - 2021 - In Lee Walters & John Hawthorne (eds.), Conditionals, Paradox, and Probability: Themes from the Philosophy of Dorothy Edgington. Oxford, England: Oxford University press.
     
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  • Belief as Question‐Sensitive.Seth Yalcin - 2018 - Philosophy and Phenomenological Research 97 (1):23-47.
  • Inquiry.Robert C. Stalnaker - 1984 - Cambridge University Press.
    The abstract structure of inquiry - the process of acquiring and changing beliefs about the world - is the focus of this book which takes the position that the "pragmatic" rather than the "linguistic" approach better solves the philosophical problems about the nature of mental representation, and better accounts for the phenomena of thought and speech. It discusses propositions and propositional attitudes (the cluster of activities that constitute inquiry) in general and takes up the way beliefs change in response to (...)
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  • On the Plurality of Worlds.David K. Lewis - 1986 - Malden, Mass.: Wiley-Blackwell.
    This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.
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  • Knowledge and its limits.Timothy Williamson - 2000 - New York: Oxford University Press.
    Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...)
  • Index.Stephen Yablo - 2014 - In Aboutness. Oxford: Princeton University Press. pp. 219-222.
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  • The Cognitive Penetrability of Perception: New Philosophical Perspectives.A. Raftopoulos & J. Zeimbekis (eds.) - 2015 - Oxford: Oxford University Press.
    Examines the nature of cognitive penetrability hypothesis, which holds that our beliefs, desires, and possibly our emotions literally affect how we see the world. Assesses both cognitive penetrability and impenetrability and explores their philosophical consequences.
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  • De interpretatione =. Aristoteles & Hermann Weidemann - 2014 - Boston: De Gruyter. Edited by Hermann Weidemann.
    This new edition of Aristotle s De interpretatione provides an improved text compared to the 1949 Oxford edition, based upon an evaluation of the seven earliest surviving medieval manuscripts as well as many translations and commentaries from late antiquity. A text-critical apparatus provides information about the different readings.".
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  • Epiphenomenal qualia.Frank Jackson - 1982 - Philosophical Quarterly 32 (April):127-136.
  • The Conscious Brain: How Attention Engenders Experience.Jesse Prinz - 2012 - , US: Oup Usa.
    The Conscious Brain brings neuroscientific evidence to bear on enduring philosophical questions. Major philosophical and scientific theories of consciousness are surveyed, challenged, and extended.
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  • Contributions to the founding of the theory of transfinite numbers.Georg Cantor - 1955 - Dover Publications.
    Introduction, Contributions to the founding of the theory of transfinite numbers, Article I, Article II.
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  • A Counterfactual Approach to Explanation in Mathematics.Sam Baron, Mark Colyvan & David Ripley - 2020 - Philosophia Mathematica 28 (1):1-34.
    ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.
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  • Truth and probability.Frank Ramsey - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. New York: Routledge. pp. 52-94.
     
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  • A subjectivist’s guide to objective chance.David K. Lewis - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. New York: Routledge. pp. 263-293.
  • The Reliability Challenge and the Epistemology of Logic.Joshua Schechter - 2010 - Philosophical Perspectives 24 (1):437-464.
    We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...)
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  • What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
  • How Not to Change the Subject.Sally Haslanger - 2020 - In Teresa Marques & Åsa Wikforss (eds.), Shifting Concepts: The Philosophy and Psychology of Conceptual Variability. Oxford: Oxford University Press.
     
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  • Meaning and necessity.Rudolf Carnap - 1947 - Chicago,: University of Chicago Press.
    "This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.... The chief virtue of the book is its systematic character. From Frege to Quine most philosophical logicians have restricted themselves by piecemeal and local assaults on the problems involved. The book is marked by a genial tolerance. Carnap sees himself as proposing conventions rather than asserting truths. However he provides plenty of matter (...)
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  • What is Cantor’s continuum problem?Kurt Gödel - 1964 - In Paul Benacerraf & Hilary Putnam (eds.), Philosophy of Mathematics: Selected Readings. Englewood Cliffs, NJ, USA: Cambridge University Press. pp. 470–485.
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  • What is Cantor’s continuum problem?Kurt Gödel - 1964 - In Paul Benacerraf & Hilary Putnam (eds.), Philosophy of Mathematics: Selected Readings. Englewood Cliffs, NJ, USA: Cambridge University Press. pp. 470–485.
     
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  • Mind and World.John McDowell - 1994 - Cambridge: Harvard University Press.
    Much as we would like to conceive empirical thought as rationally grounded in experience, pitfalls await anyone who tries to articulate this position, and ...
  • Computing machinery and intelligence.Alan M. Turing - 1950 - Mind 59 (October):433-60.
    I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to (...)
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  • Intention.G. E. M. Anscombe - 1957 - Cambridge, Mass.: Harvard University Press.
    This is a welcome reprint of a book that continues to grow in importance.
  • Statements partly about observation.David Lewis - 1988 - Philosophical Papers 17 (1):1-31.
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  • Knowledge as a Mental State.Jennifer Nagel - 2013 - Oxford Studies in Epistemology 4:275-310.
    In the philosophical literature on mental states, the paradigmatic examples of mental states are beliefs, desires, intentions, and phenomenal states such as being in pain. The corresponding list in the psychological literature on mental state attribution includes one further member: the state of knowledge. This article examines the reasons why developmental, comparative and social psychologists have classified knowledge as a mental state, while most recent philosophers--with the notable exception of Timothy Williamson-- have not. The disagreement is traced back to a (...)
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  • A Logical Foundation for Potentialist Set Theory.Sharon Berry - 2022 - Cambridge University Press.
    In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends (...)
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  • The Perils of Dogmatism.Crispin Wright - 2007 - In Susana Nuccetelli & Gary Seay (eds.), Themes From G. E. Moore: New Essays in Epistemology and Ethics. Oxford University Press.
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  • Warrant for nothing (and foundations for free)?Crispin Wright - 2004 - Aristotelian Society Supplementary Volume 78 (1):167–212.
  • The Contents of Visual Experience.Susanna Siegel - 2010 - , US: Oxford University Press USA.
    What do we see? We are visually conscious of colors and shapes, but are we also visually conscious of complex properties such as being John Malkovich? In this book, Susanna Siegel develops a framework for understanding the contents of visual experience, and argues that these contents involve all sorts of complex properties. Siegel starts by analyzing the notion of the contents of experience, and by arguing that theorists of all stripes should accept that experiences have contents. She then introduces a (...)
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  • Intuition.Elijah Chudnoff - 2013 - New York, NY: Oxford University Press.
    Elijah Chudnoff elaborates and defends a view of intuition according to which intuition purports to, and reveals, how matters stand in abstract reality by making us aware of that reality through the intellect. He explores the experience of having an intuition; justification for beliefs that derives from intuition; and contact with abstract reality.
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  • The Intellectual Given.John Bengson - 2015 - Mind 124 (495):707-760.
    Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...)
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  • Methodological solipsism considered as a research strategy in cognitive psychology.Jerry A. Fodor - 1979 - Behavioral and Brain Sciences 3 (1):63-73.
    The paper explores the distinction between two doctrines, both of which inform theory construction in much of modern cognitive psychology: the representational theory of mind and the computational theory of mind. According to the former, propositional attitudes are to be construed as relations that organisms bear to mental representations. According to the latter, mental processes have access only to formal (nonsemantic) properties of the mental representations over which they are defined.The following claims are defended: (1) That the traditional dispute between (...)
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