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Profile: Sean Walsh (University of Minnesota, Duluth)
Profile: Sean Walsh (University of California, Irvine)
Profile: Sean Walsh (University of California, Irvine)
  1. Sean Walsh (2014). Logicism, Interpretability, and Knowledge of Arithmetic. Review of Symbolic Logic 7 (1):84-119.
    A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of representation (...)
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  2. Sean Walsh (2012). Comparing Peano Arithmetic, Basic Law V, and Hume's Principle. Annals of Pure and Applied Logic 163 (11):1679-1709.
    This paper presents new constructions of models of Hume's Principle and Basic Law V with restricted amounts of comprehension. The techniques used in these constructions are drawn from hyperarithmetic theory and the model theory of fields, and formalizing these techniques within various subsystems of second-order Peano arithmetic allows one to put upper and lower bounds on the interpretability strength of these theories and hence to compare these theories to the canonical subsystems of second-order arithmetic. The main results of this paper (...)
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  3. Sean Walsh (2016). Fragments of Frege’s Grundgesetze and Gödel’s Constructible Universe. Journal of Symbolic Logic 81 (2):605-628.
    Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem shows that there is a model of a fragment of the Grundgesetze which defines a (...)
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  4.  89
    Sean Walsh (forthcoming). Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic. Journal of Philosophical Logic:1-50.
    This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church's intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...)
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  5.  74
    Salvatore Florio, Øystein Linnebo, Sean Walsh & Philip Welch (2015). Introduction. Notre Dame Journal of Formal Logic 56 (1):1-2.
    Introduction to a special issue based on a summer school on set theory and high-order logic.
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  6.  27
    Tim Button & Sean Walsh (forthcoming). Structure and Categoricity: Determinacy of Reference and Truth-Value in the Philosophy of Mathematics. Philosophia Mathematica:nkw007.
    This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent `internal' renditions of the famous categoricity arguments for arithmetic and set theory.
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  7.  48
    Sean Walsh & Sean Ebels-Duggan (2015). Relative Categoricity and Abstraction Principles. Review of Symbolic Logic 8 (3):572-606.
    Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory. Another great enterprise in contemporary philosophy of mathematics has been Wright's and Hale's project of founding mathematics on abstraction principles. In earlier work, it was noted that one traditional abstraction principle, namely Hume's Principle, had a certain relative categoricity property, which here we term natural relative categoricity. In this paper, we show (...)
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  8.  8
    Sean Walsh (2016). Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic. Journal of Philosophical Logic 45 (3):277-326.
    This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...)
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  9.  15
    Benjamin G. Rin & Sean Walsh (forthcoming). Realizability Semantics for Quantified Modal Logic: Generalizing Flagg's 1985 Construction. Review of Symbolic Logic.
    A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church's Thesis and a variant of a modal set theory (...)
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  10.  17
    Sean Walsh (2016). The Strength of Abstraction with Predicative Comprehension. Bulletin of Symbolic Logic 22 (1):105–120.
    Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law V from Frege's Grundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence (...)
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  11.  85
    Sean Walsh (2014). Empiricism, Probability, and Knowledge of Arithmetic. Journal of Applied Logic 12 (3):319–348.
    The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy (...)
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  12.  55
    Sean Walsh, Eleanor Knox & Adam Caulton (2014). Critical Review of Mathematics and Scientific Representation. [REVIEW] Philosophy of Science 81 (3):460-469.
  13.  80
    Sean Walsh (2012). Modal Mereology and Modal Supervenience. Philosophical Studies 159 (1):1-20.
    David Lewis insists that restrictivist composition must be motivated by and occur due to some intuitive desiderata for a relation R among parts that compose wholes, and insists that a restrictivist’s relation R must be vague. Peter van Inwagen agrees. In this paper, I argue that restrictivists need not use such examples of relation R as a criterion for composition, and any restrictivist should reject a number of related mereological theses. This paper critiques Lewis and van Inwagen (and others) on (...)
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  14.  18
    Sean Drysdale Walsh (2011). Maximality, Duplication, and Intrinsic Value. Ratio 24 (3):311-325.
    In this paper, I develop an argument for the thesis that ‘maximality is extrinsic’, on which a whole physical object is not a whole of its kind in virtue of its intrinsic properties. Theodore Sider has a number of arguments that depend on his own simple argument that maximality is extrinsic. However, Peter van Inwagen has an argument in defence of his Duplication Principle that, I will argue, can be extended to show that Sider's simple argument fails. However, van Inwagen's (...)
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  15.  17
    Sean Drysdale Walsh (2012). Kant's Theory of Right as Aristotelian Phronesis. International Philosophical Quarterly 52 (2):227-246.
    Many philosophers believe that a moral theory, given all the relevant facts, should be able to determine what is morally right and wrong. It is commonly argued that Aristotle’s ethical theory suffers from a fatal flaw: it places responsibility for determining right and wrong with the virtuous agent who has phronesis rather than with the theory itself. It is also commonly argued that Immanuel Kant’s ethical theory does provide a concept of right that is capable of determining right and wrong (...)
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  16.  17
    Sean Walsh (2012). Mencius' Jun-Zi, Aristotle's Megalopsuchos, & Moral Demands to Help the Global Poor. Comparative Philosophy 4 (1):103-129.
    Normal 0 false false false EN-US X-NONE X-NONE Normal 0 false false false EN-US ZH-TW X-NONE It is commonly believed that impartial utilitarian moral theories have significant demands that we help the global poor, and that the partial virtue ethics of Mencius and Aristotle do not. This ethical partiality found in these virtue ethicists has been criticized, and some have suggested that the partialistic virtue ethics of Mencius and Aristotle are parochial (i.e., overly narrow in their scope of concern). I (...)
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  17.  3
    Sean Walsh, Eleanor Knox & Adam Caulton (2014). Critical Review ofMathematics and Scientific RepresentationChristopher Pincock,Mathematics and Scientific Representation. Oxford: Oxford University Press , Xiv+330 Pp., $65.00. [REVIEW] Philosophy of Science 81 (3):460-469.
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  18.  6
    Sean Drysdale Walsh (2015). Contemplation and the Moral Life in Confucius and Aristotle. Dao: A Journal of Comparative Philosophy 14 (1):13-31.
    Aristotle’s best human life is attained through theoretical contemplation, and Confucius’ is attained through practical cultivation of the social self. However, I argue that in the best human life for both Confucius and Aristotle, a form of theoretical contemplation must occur and can only occur with an ethical commitment to community life. Confucius, like Aristotle, sees that the best contemplation comes after later-life, greater-learning and is central to ethical and community life. Aristotle, like Confucius, sees the best contemplation as presupposing (...)
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  19.  30
    Sean Walsh (2007). Incongruent Counterparts and Causality. Kant-Studien 98 (4):418-430.
    Two puzzles with regard to the Kritik der reinen Vernunft (KrV) are incongruent counterparts and causality. In De mundi sensibilis atque intelligibilis forma et principiis (MSI), Kant indicates that the experience of things like left and right hands, so-called incongruent counterparts, involve certain pure intuitions, and hence constitute one line of evidence for the claim that the concept of space itself is a pure intuition. In KrV, Kant again argues that the concept of space itself is a pure intuition, but (...)
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  20.  20
    Sean P. Walsh (2008). Review of Jens Timmermann, Kant's Groundwork of the Metaphysics of Morals: A Commentary. [REVIEW] Notre Dame Philosophical Reviews 2008 (4).
  21. Irene De-Torres, Guadalupe Dávila, Marcelo L. Berthier, Seán Froudist Walsh, Ignacio Moreno-Torres & Rafael Ruiz-Cruces (2013). Repeating with the Right Hemisphere: Reduced Interactions Between Phonological and Lexical-Semantic Systems in Crossed Aphasia? Frontiers in Human Neuroscience 7.
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  22. Sean Noah Walsh (2013). Counterrevolution and Repression in the Politics of Education: At the Midnight of Dissent. Lexington Books.
    In this book, Sean Noah Walsh applies Herbert Marcuse’s observations on counterrevolution to recent developments in education politics. Seemingly disparate issues such as the exercise of state power to reorganize curricula, the derision of intellectuals, the permeation of consumerism into the collegiate experience, and the expansion of online teaching belong to the same strategy in which the faculties of dissent are neutralized before they can develop and dissent is established as the paramount political obscenity.
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  23. Sean Walsh (2012). Empty Esotericisms: Doctrines Of Secret Writing And The Politics Of A Platonic Code. Polis 29:62-82.
     
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  24.  5
    Sean Noah Walsh (2012). Perversion and the Art of Persecution: Esotericism and Fear in the Political Philosophy of Leo Strauss. Lexington Books.
    This book critically examines Leo Strauss s claim that the philosophers of antiquity, especially Plato, wrote esoterically, hiding the highest truths exclusively between the lines.
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