Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Roy Cook

    Roy Cook

    In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence can be... more
    In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence can be explicated in terms of the meanings (so understood) of the logical connectives involved. He proposes a counterexample to such a view, his notorious binary connective tonk (which I will symbolize as⊗), whose meaning is given by the following introduction and elimination rules:
    In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in... more
    In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that such a formalization shows that Yablo's Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006 / 2011) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume.
    This paper is too short to have a separate abstract :-)
    There are (at least) two reasons for investigating abstraction principles for set theory. The first concerns the technical feasibility of a neo-logicist foundation for all of mathematics. The second concerns the connection between the... more
    There are (at least) two reasons for investigating abstraction principles for set theory. The first concerns the technical feasibility of a neo-logicist foundation for all of mathematics. The second concerns the connection between the theory of Fregean extensions (as codified in various restrictions of Basic Law V) and the mathematical notion of set (as codified in various axiomatic set theories, such as ZFC).
    Thus, there are important connections between the Liar paradox and the Curry paradox, and between the Liar paradox and the Yablo paradox. It would be ideal, then, if we could complete the 'triangle', and find direct connections between... more
    Thus, there are important connections between the Liar paradox and the Curry paradox, and between the Liar paradox and the Yablo paradox. It would be ideal, then, if we could complete the 'triangle', and find direct connections between the Curry paradox and the Yablo paradox.
    Both abstraction principles, however, are silent with regard to this identity – a special instance of the Caesar Problem. In what follows, we outline two distinct strategies to resolve the CR problem. The first strategy decides such... more
    Both abstraction principles, however, are silent with regard to this identity – a special instance of the Caesar Problem. In what follows, we outline two distinct strategies to resolve the CR problem. The first strategy decides such cross-abstraction identities in terms of whether or not the equivalence relations appearing on the right hand side of the abstraction principles are identical, while the second strategy settles such identities by appeal to the relevant equivalence classes.
    In The Foundations of Mathematics in the Theory of Sets, John Mayberry attacks the 2000-year-old problem of accounting for the foundations of mathematics. His account comes in three interrelated parts: determining exactly what one should... more
    In The Foundations of Mathematics in the Theory of Sets, John Mayberry attacks the 2000-year-old problem of accounting for the foundations of mathematics. His account comes in three interrelated parts: determining exactly what one should (and should not) expect from a foundation; arguing that set theory can in fact provide such a foundation, and presenting a novel version of set theory (or at least a novel exposition of traditional set theory) which can fulfil this foundational role.
    We shall assume throughout this essay that platonism1 regarding the subject matter of mathematics is correct. This is not to say that arguments for platonism–that is, arguments for the existence of abstract objects such as numbers, sets,... more
    We shall assume throughout this essay that platonism1 regarding the subject matter of mathematics is correct. This is not to say that arguments for platonism–that is, arguments for the existence of abstract objects such as numbers, sets, Hilbert spaces, and so on that comprise the subject matter of mathematics–are either uninteresting or unneeded. Nevertheless, I am not personally interested in such arguments.
    Logical pluralism is the view that there is more than one 'correct','best', or 'legitimate'logic. Some of the most interesting variants of this thesis argue for more than one 'legitimate'formal logic, yet retain the intuition that there... more
    Logical pluralism is the view that there is more than one 'correct','best', or 'legitimate'logic. Some of the most interesting variants of this thesis argue for more than one 'legitimate'formal logic, yet retain the intuition that there is a single natural language consequence relation (eg,[1] and [2]).
    An abstraction principle is any principle of the form: AE:(∀ α)(∀ β)[@ E (α)=@ E (β)↔ E (α, β)] where α and β are variables (or sequences of variables) ranging over entities of same 'type'(or sequences whose elements are, pairwise, of the... more
    An abstraction principle is any principle of the form: AE:(∀ α)(∀ β)[@ E (α)=@ E (β)↔ E (α, β)] where α and β are variables (or sequences of variables) ranging over entities of same 'type'(or sequences whose elements are, pairwise, of the same type), E is an equivalence relation on entities of that type (or, if α and β are sequences, then E is an equivalence relation on sequences of the relevant sort), and@ E a term-forming operator–an abstraction operator–mapping entities of the relevant type (or sequences of entities) onto objects.
    Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic is, the authors write in the preface, intended" to give philosophy students a basic grounding in philosophical logic, in a way that connects with the motivations... more
    Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic is, the authors write in the preface, intended" to give philosophy students a basic grounding in philosophical logic, in a way that connects with the motivations they derive elsewhere from philosophy"(p. ix). In providing a uniform framework within which one can study the behaviour of, and interactions between, modal, many-valued, intuitionistic, and paraconsistent logic, the text provides a useful contribution along these lines.
    THE STATE OF THE ECONOMY: NEO-LOGICISM AND INFLATION 1, 2 Roy T. Cook 1. Introduction In recent years there has been a resurgence of interest in logicism as a viable philosophy of mathematics, stemming in great part from Crispin Wright's... more
    THE STATE OF THE ECONOMY: NEO-LOGICISM AND INFLATION 1, 2 Roy T. Cook 1. Introduction In recent years there has been a resurgence of interest in logicism as a viable philosophy of mathematics, stemming in great part from Crispin Wright's Frege's Conception of Numbers as Objects [1984] and the formal and philosophical work of George Boolos. Before this work it was generally accepted that Frege's project of reducing mathematics to pure logic was devastated by Russell's detection of a paradox produced by Frege's notorious Basic Law V.
    ¹ And as Saul Kripke has forcefully argued. See Kripke (1975), p. 56. ² Actually, this way of formulating things obscures some important complications. For example, if it is propositions, and not sentences, that are the primary bearers of... more
    ¹ And as Saul Kripke has forcefully argued. See Kripke (1975), p. 56. ² Actually, this way of formulating things obscures some important complications. For example, if it is propositions, and not sentences, that are the primary bearers of truth, falsity, and the rest, then the sentence 'This sentence is false'would constitute, not a paradox, but a category mistake (thanks to an anonymous referee for pointing out the importance of this). Nevertheless, for the sake of simplicity I will continue to talk of sentences having truth values.
    Abstract In this paper I examine the prospects for a successful neo–logicist reconstruction of the real numbers, focusing on Bob Hale's use of a cut-abstraction principle. There is a serious problem plaguing Hale's project. Natural... more
    Abstract In this paper I examine the prospects for a successful neo–logicist reconstruction of the real numbers, focusing on Bob Hale's use of a cut-abstraction principle. There is a serious problem plaguing Hale's project. Natural generalizations of this principle imply that there are far more objects than one would expect from a position that stresses its epistemological conservativeness. In other words, the sort of abstraction needed to obtain a theory of the reals is rampantly inflationary.
    Abstract It is shown that the logical truth of instances of the T-schema is incompatible with the formal nature of logical truth. In particular, since the formality of logical truth entails that the set of logical truths is closed under... more
    Abstract It is shown that the logical truth of instances of the T-schema is incompatible with the formal nature of logical truth. In particular, since the formality of logical truth entails that the set of logical truths is closed under substitution, the logical truth of T-schema instances entails that all sentences are logical truths.
    As the title suggests, The Force of Argument: Essays in Honor of Timothy Smiley is a collection of essays on topics that Smiley worked on, written by friends, colleagues and former students. The volume does not seem to be connected to any... more
    As the title suggests, The Force of Argument: Essays in Honor of Timothy Smiley is a collection of essays on topics that Smiley worked on, written by friends, colleagues and former students. The volume does not seem to be connected to any particular event or milestone (such as is common with Festschrift-style volumes), but is instead a self-standing volume honouring Smiley, his influence and his work.
    Neo-logicism is the view that various branches of mathematics can be reformulated in terms of abstraction principles that we can stipulate, and thus come to know the truth of, a priori. The main success story of neo-logicism so far is the... more
    Neo-logicism is the view that various branches of mathematics can be reformulated in terms of abstraction principles that we can stipulate, and thus come to know the truth of, a priori. The main success story of neo-logicism so far is the derivation of arithmetic from Hume's Principle:
    Subscriptions: A subscription to Analysis comprises 4 issues. Prices include postage by surface mail; or for subscribers in the USA and Canada, by airfreight; or in India, Japan, Australia and New Zealand, by Air Speeded Post. Airmail... more
    Subscriptions: A subscription to Analysis comprises 4 issues. Prices include postage by surface mail; or for subscribers in the USA and Canada, by airfreight; or in India, Japan, Australia and New Zealand, by Air Speeded Post. Airmail rates are available on request. Analysis Advance Access contains papers that have recently been accepted but have not yet been included within an issue. Advance Access is updated daily. Annual Subscription Rates (Volume 72, 4 issues, 2012): Institutional