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George Boolos [76]George S. Boolos [16]G. Boolos [2]Georges Boolos [1]
  1. George Boolos, John Burgess, Richard P. & C. Jeffrey (2007). Computability and Logic. Cambridge University Press.
    Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Turing’s theory of computability to Ramsey’s theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a (...)
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  2. George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
    This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...
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  3. George Boolos (1984). To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables). Journal of Philosophy 81 (8):430-449.
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  4.  64
    George Boolos (1993). The Logic of Provability. Cambridge University Press.
    This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (CUP, 1979). Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self referential' (...)
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  5. George Boolos (1985). Nominalist Platonism. Philosophical Review 94 (3):327-344.
  6.  31
    George Boolos (1979). The Unprovability of Consistency: An Essay in Modal Logic. Cambridge University Press.
    The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted (...)
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  7. George Boolos & Richard G. Heck (1998). Die Grundlagen der Arithmetik, 82-3. In Matthias Schirn (ed.), Bulletin of Symbolic Logic. Clarendon Press 407-28.
    This paper contains a close analysis of Frege's proofs of the axioms of arithmetic §§70-83 of Die Grundlagen, with special attention to the proof of the existence of successors in §§82-83. Reluctantly and hesitantly, we come to the conclusion that Frege was at least somewhat confused in those two sections and that he cannot be said to have outlined, or even to have intended, any correct proof there. The proof he sketches is in many ways similar to that given in (...)
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  8. George Boolos (1971). The Iterative Conception of Set. Journal of Philosophy 68 (8):215-231.
  9.  70
    Hilary Putnam & George Boolos (eds.) (1990). Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge University Press.
    In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, (...)
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  10. George S. Boolos (1975). On Second-Order Logic. Journal of Philosophy 72 (16):509-527.
  11.  2
    George Boolos (1981). Review of Robert M. Solovay's Provability Interpretations of Modal Logic. Journal of Symbolic Logic 46 (3):661-662.
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  12.  72
    George Boolos (1989). Iteration Again. Philosophical Topics 17 (2):5-21.
  13. George Boolos (1994). Gödel's Second Incompleteness Theorem Explained in Words of One Syllable. Mind 103 (409):1-3.
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  14. George S. Boolos (2010). The Logic of Provability. Cambridge University Press.
    This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency. Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does (...)
     
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  15.  99
    George Boolos (1985). Reading the Begriffsschrift. Mind 94 (375):331-344.
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  16. George Boolos & Hilary Putnam (1968). Degrees of Unsolvability of Constructible Sets of Integers. Journal of Symbolic Logic 33 (4):497-513.
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  17. George Boolos (1984). Don't Eliminate Cut. Journal of Philosophical Logic 13 (4):373 - 378.
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  18. George Boolos (1990). The Standard of Equality of Numbers. In Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge University Press 261--77.
     
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  19.  36
    George Boolos (1996). The Hardest Logic Puzzle Ever. The Harvard Review of Philosophy 6 (1):62-65.
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  20.  30
    George Boolos (1986). Saving Frege From Contradiction. Proceedings of the Aristotelian Society 87:137--151.
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  21. George Boolos (1977). On Deciding the Provability of Certain Fixed Point Statements. Journal of Symbolic Logic 42 (2):191-193.
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  22.  27
    George Boolos (1990). On “Seeing” the Truth of the Gödel Sentence. Behavioral and Brain Sciences 13 (4):655-656.
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  23. George Boolos (1987). The Consistency of Frege's Foundations of Arithmetic. In J. Thomson (ed.), On Being and Saying: Essays in Honor of Richard Cartwright. MIT Press 3--20.
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  24.  72
    George Boolos (1995). Frege's Theorem and the Peano Postulates. Bulletin of Symbolic Logic 1 (3):317-326.
  25.  47
    George Boolos & Giovanni Sambin (1991). Provability: The Emergence of a Mathematical Modality. Studia Logica 50 (1):1 - 23.
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  26. George Boolos (1998). Reply to Charles Parsons' ``Sets and Classes''. In Richard Jeffrey (ed.), Logic, Logic, and Logic. Harvard University Press 30-36.
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  27.  55
    George Boolos (1987). A Curious Inference. Journal of Philosophical Logic 16 (1):1 - 12.
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  28. George Boolos (1998). Must We Believe in Set Theory? In Richard Jeffrey (ed.), Logic, Logic, and Logic. Harvard University Press 120-132.
  29.  61
    George Boolos & Giovanni Sambin (1985). An Incomplete System of Modal Logic. Journal of Philosophical Logic 14 (4):351 - 358.
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  30.  26
    George Boolos (1980). On Systems of Modal Logic with Provability Interpretations. Theoria 46 (1):7-18.
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  31. George Boolos (1993). Whence the Contradiction? Aristotelian Society Supplementary Volume 67:211--233.
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  32.  36
    George Boolos (1997). Constructing Cantorian Counterexamples. Journal of Philosophical Logic 26 (3):237-239.
    Cantor's diagonal argument provides an indirect proof that there is no one-one function from the power set of a set A into A. This paper provides a somewhat more constructive proof of Cantor's theorem, showing how, given a function f from the power set of A into A, one can explicitly define a counterexample to the thesis that f is one-one.
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  33.  45
    George Boolos (1980). Provability, Truth, and Modal Logic. Journal of Philosophical Logic 9 (1):1 - 7.
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  34.  58
    George Boolos (1991). Zooming Down the Slippery Slope. Noûs 25 (5):695-706.
  35.  19
    George Boolos & Vann McGee (1987). The Degree of the Set of Sentences of Predicate Provability Logic That Are True Under Every Interpretation. Journal of Symbolic Logic 52 (1):165-171.
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  36.  2
    George Boolos (1987). IX—Saving Frege From Contradiction. Proceedings of the Aristotelian Society 87 (1):137-152.
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  37. George Boolos (1996). On the Proof of Frege's Theorem. In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell 143--59.
     
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  38.  26
    George Boolos (1980). Omega-Consistency and the Diamond. Studia Logica 39 (2-3):237 - 243.
    G is the result of adjoining the schema (qAA)qA to K; the axioms of G* are the theorems of G and the instances of the schema qAA and the sole rule of G* is modus ponens. A sentence is -provable if it is provable in P(eano) A(rithmetic) by one application of the -rule; equivalently, if its negation is -inconsistent in PA. Let -Bew(x) be the natural formalization of the notion of -provability. For any modal sentence A and function mapping sentence (...)
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  39.  10
    George Boolos (1976). On Deciding the Truth of Certain Statements Involving the Notion of Consistency. Journal of Symbolic Logic 41 (4):779-781.
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  40.  2
    George Boolos (1984). On ‘Syllogistic Inference’. Cognition 17 (2):181-182.
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  41. George Boolos (1995). Quotational Ambiguity. In Paolo Leonardi & Marco Santambrogio (eds.), On Quine: New Essays. Cambridge University Press 283--296.
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  42.  10
    George Boolos (1984). Trees and Finite Satisfiability: Proof of a Conjecture of Burgess. Notre Dame Journal of Formal Logic 25 (3):193-197.
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  43.  42
    George Boolos (1984). The Justification of Mathematical Induction. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:469 - 475.
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  44.  2
    George Boolos (1970). On the Semantics of the Constructible Levels. Mathematical Logic Quarterly 16 (2):139-148.
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  45.  23
    George Boolos (1982). Extremely Undecidable Sentences. Journal of Symbolic Logic 47 (1):191-196.
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  46.  1
    George Boolos & Raymond M. Smullyan (1979). What is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles. Philosophical Review 88 (3):496.
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  47.  6
    George S. Boolos (1974). Arithmetical Functions and Minimalization. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (23‐24):353-354.
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  48.  16
    George Boolos & Peter Clark (1993). Basic Law (V). Aristotelian Society Supplementary Volume 67 (1):213 - 249.
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  49.  6
    George Boolos (1993). The Analytical Completeness of Dzhaparidze's Polymodal Logics. Annals of Pure and Applied Logic 61 (1-2):95-111.
    The bimodal provability logics of analysis for ordinary provability and provability by the ω-rule are shown to be fragments of certain ‘polymodal’ logics introduced by G.K. Dzhaparidze. In addition to modal axiom schemes expressing Löb's theorem for the two kinds of provability, the logics treated here contain a scheme expressing that if a statement is consistent, then the statement that it is consistent is provable by the ω-rule.
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  50.  24
    George S. Boolos (1970). A Proof of the Löwenheim-Skolem Theorem. Notre Dame Journal of Formal Logic 11 (1):76-78.
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