Switch to: Citations

Add references

You must login to add references.
  1. Goodman's Extensional Isomorphism and Syntactical Interpretations.Marek Polański - 2009 - Theoria 24 (2):203-211.
    The aim of the present paper is to provide a model-theoretic explication of Goodman's concept of extensional isomorphism. After some conceptual clarifications Goodman's concept of isomorphy turns out to be closely related to some variant of set-theoretic definability and some variants of syntactical interpretability.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Abstract Objects.Bob Hale - 1987 - Revue Philosophique de la France Et de l'Etranger 179 (1):109-109.
    Download  
     
    Export citation  
     
    Bookmark   135 citations  
  • A Mathematical Introduction to Logic.Herbert Enderton - 2001 - Bulletin of Symbolic Logic 9 (3):406-407.
    Download  
     
    Export citation  
     
    Bookmark   187 citations  
  • (1 other version)Metamathematics of First-Order Arithmetic.Petr Hajék & Pavel Pudlák - 1994 - Studia Logica 53 (3):465-466.
    Download  
     
    Export citation  
     
    Bookmark   144 citations  
  • (1 other version)Metamathematics of First-Order Arithmetic.P. Hájek & P. Pudlák - 2000 - Studia Logica 64 (3):429-430.
    Download  
     
    Export citation  
     
    Bookmark   83 citations  
  • Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
    Download  
     
    Export citation  
     
    Bookmark   235 citations  
  • (2 other versions)The Foundations of Arithmetic. A Logico-Mathematical Enquiry into the Concept of Number.Max Black - 1951 - Journal of Symbolic Logic 16 (1):67-67.
    Download  
     
    Export citation  
     
    Bookmark   38 citations  
  • (1 other version)Frege's Philosophy of Mathematics. [REVIEW]Bob Hale - 1999 - Philosophical Quarterly 49 (194):92-104.
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • (1 other version)Conceptual Truth.Timothy Williamson - 2006 - Aristotelian Society Supplementary Volume 80 (1):1-41.
    The paper criticizes epistemological conceptions of analytic or conceptual truth, on which assent to such truths is a necessary condition of understanding them. The critique involves no Quinean scepticism about meaning. Rather, even granted that a paradigmatic candidate for analyticity is synonymy with a logical truth, both the former and the latter can be intelligibly doubted by linguistically competent deviant logicians, who, although mistaken, still constitute counterexamples to the claim that assent is necessary for understanding. There are no analytic or (...)
    Download  
     
    Export citation  
     
    Bookmark   44 citations  
  • Mathematical Knowledge.Mark Steiner - 1977 - Mind 86 (343):467-469.
    Download  
     
    Export citation  
     
    Bookmark   45 citations  
  • (1 other version)Frege’s Theorem: An Introduction.Richard G. Heck - 1999 - The Harvard Review of Philosophy 7 (1):56-73.
    A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence.
    Download  
     
    Export citation  
     
    Bookmark   46 citations  
  • (1 other version)The Foundations of Arithmetic. A Logico-Mathematical Enquiry into the Concept of Number. [REVIEW]E. N. - 1951 - Journal of Philosophy 48 (10):342.
    Download  
     
    Export citation  
     
    Bookmark   33 citations  
  • Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.
    Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition (...)
    Download  
     
    Export citation  
     
    Bookmark   95 citations  
  • The Philosophy of Philosophy.Timothy Williamson - 2007 - Malden, MA: Wiley-Blackwell.
    The second volume in the _Blackwell Brown Lectures in Philosophy_, this volume offers an original and provocative take on the nature and methodology of philosophy. Based on public lectures at Brown University, given by the pre-eminent philosopher, Timothy Williamson Rejects the ideology of the 'linguistic turn', the most distinctive trend of 20th century philosophy Explains the method of philosophy as a development from non-philosophical ways of thinking Suggests new ways of understanding what contemporary and past philosophers are doing.
    Download  
     
    Export citation  
     
    Bookmark   736 citations  
  • On definitional equivalence and related topics.J. Corcoran - 1980 - History and Philosophy of Logic 1:231.
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  • Kleine Schriften.Gottlob Frege & Ignacio Angelelli - 1967 - G. Olms.
    Download  
     
    Export citation  
     
    Bookmark   70 citations  
  • (1 other version)Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of science today. New York: Oxford University Press.
    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.
    Download  
     
    Export citation  
     
    Bookmark   126 citations  
  • On the harmless impredicativity of N=('Hume's Principle').Crispin Wright - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 339--68.
    Download  
     
    Export citation  
     
    Bookmark   26 citations  
  • On formal and informal provability.Hannes Leitgeb - 2009 - In Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan. pp. 263--299.
    Download  
     
    Export citation  
     
    Bookmark   46 citations  
  • On the proof of Frege's theorem.George Boolos - 1996 - In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. pp. 143--59.
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Frege’s Conception of Logic.Patricia Blanchette - 2012 - Oxford, England: Oup Usa.
    In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic.
    Download  
     
    Export citation  
     
    Bookmark   38 citations  
  • Subsystems of Second Order Arithmetic.Stephen George Simpson - 1998 - Springer Verlag.
    Stephen George Simpson. with definition 1.2.3 and the discussion following it. For example, taking 90(n) to be the formula n §E Y, we have an instance of comprehension, VYEIXVn(n€X<—>n¢Y), asserting that for any given set Y there exists a ...
    Download  
     
    Export citation  
     
    Bookmark   131 citations  
  • Cardinality, Counting, and Equinumerosity.Richard G. Heck - 2000 - Notre Dame Journal of Formal Logic 41 (3):187-209.
    Frege, famously, held that there is a close connection between our concept of cardinal number and the notion of one-one correspondence, a connection enshrined in Hume's Principle. Husserl, and later Parsons, objected that there is no such close connection, that our most primitive conception of cardinality arises from our grasp of the practice of counting. Some empirical work on children's development of a concept of number has sometimes been thought to point in the same direction. I argue, however, that Frege (...)
    Download  
     
    Export citation  
     
    Bookmark   45 citations  
  • Frege meets dedekind: A neologicist treatment of real analysis.Stewart Shapiro - 2000 - Notre Dame Journal of Formal Logic 41 (4):335--364.
    This paper uses neo-Fregean-style abstraction principles to develop the integers from the natural numbers (assuming Hume’s principle), the rational numbers from the integers, and the real numbers from the rationals. The first two are first-order abstractions that treat pairs of numbers: (DIF) INT(a,b)=INT(c,d) ≡ (a+d)=(b+c). (QUOT) Q(m,n)=Q(p,q) ≡ (n=0 & q=0) ∨ (n≠0 & q≠0 & m⋅q=n⋅p). The development of the real numbers is an adaption of the Dedekind program involving “cuts” of rational numbers. Let P be a property (of (...)
    Download  
     
    Export citation  
     
    Bookmark   58 citations  
  • The Structure of Appearance.Nelson Goodman - 1951 - Cambridge, MA, USA: Harvard University Press.
    With this third edition of Nelson Goodman's The Structure of Appear ance, we are pleased to make available once more one of the most in fluential and important works in the philosophy of our times. Professor Geoffrey Hellman's introduction gives a sustained analysis and appreciation of the major themes and the thrust of the book, as well as an account of the ways in which many of Goodman's problems and projects have been picked up and developed by others. Hellman also (...)
    Download  
     
    Export citation  
     
    Bookmark   270 citations  
  • A mathematical introduction to logic.Herbert Bruce Enderton - 1972 - New York,: Academic Press.
    A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional (...)
    Download  
     
    Export citation  
     
    Bookmark   121 citations  
  • Mathematical logic.J. Donald Monk - 1976 - New York: Springer Verlag.
    " There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.
    Download  
     
    Export citation  
     
    Bookmark   53 citations  
  • The foundations of arithmetic: a logico-mathematical enquiry into the concept of number.Gottlob Frege - 1968 - Evanston, Ill.: Northwestern University Press. Edited by J. L. Austin.
    § i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...
    Download  
     
    Export citation  
     
    Bookmark   142 citations  
  • Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
    This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics (...)
    Download  
     
    Export citation  
     
    Bookmark   244 citations  
  • Abstract objects.Bob Hale - 1987 - New York, NY, USA: Blackwell.
    Download  
     
    Export citation  
     
    Bookmark   151 citations  
  • Mathematics in philosophy: selected essays.Charles Parsons - 1983 - Ithaca, N.Y.: Cornell University Press.
    This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.
    Download  
     
    Export citation  
     
    Bookmark   52 citations  
  • On the untenability of Nelson's predicativism.St Iwan - 2000 - Erkenntnis 53 (1-2):147-154.
    By combining some technical results from metamathematicalinvestigations of systems of Bounded Arithmetic, I will givean argument for the untenability of Nelson 's finitistic program,encapsulated in his book Predicative Arithmetic.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • (1 other version)Where do the natural numbers come from?Harold T. Hodes - 1990 - Synthese 84 (3):347-407.
    Download  
     
    Export citation  
     
    Bookmark   29 citations  
  • (1 other version)Conceptual truth.Timothy Williamson - 2006 - Aristotelian Society Supplementary Volume 80 (1):1–41.
    The paper criticizes epistemological conceptions of analytic or conceptual truth, on which assent to such truths is a necessary condition of understanding them. The critique involves no Quinean scepticism about meaning. Rather, even granted that a paradigmatic candidate for analyticity is synonymy with a logical truth, both the former and the latter can be intelligibly doubted by linguistically competent deviant logicians, who, although mistaken, still constitute counterexamples to the claim that assent is necessary for understanding. There are no analytic or (...)
    Download  
     
    Export citation  
     
    Bookmark   65 citations  
  • Mathematics as a science of patterns: Ontology and reference.Michael Resnik - 1981 - Noûs 15 (4):529-550.
    Download  
     
    Export citation  
     
    Bookmark   107 citations  
  • (1 other version)Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
    On the neo-Fregean approach to the foundations of mathematics, elementary arithmetic is analytic in the sense that the addition of a principle wliich may be held to IMJ explanatory of the concept of cardinal number to a suitable second-order logical basis suffices for the derivation of its basic laws. This principle, now commonly called Hume's principle, is an example of a Fregean abstraction principle. In this paper, I assume the correctness of the neo-Fregean position on elementary aritlunetic and seek to (...)
    Download  
     
    Export citation  
     
    Bookmark   61 citations  
  • Frege and the rigorization of analysis.William Demopoulos - 1994 - Journal of Philosophical Logic 23 (3):225 - 245.
    This paper has three goals: (i) to show that the foundational program begun in the Begriffsschroft, and carried forward in the Grundlagen, represented Frege's attempt to establish the autonomy of arithmetic from geometry and kinematics; the cogency and coherence of 'intuitive' reasoning were not in question. (ii) To place Frege's logicism in the context of the nineteenth century tradition in mathematical analysis, and, in particular, to show how the modern concept of a function made it possible for Frege to pursue (...)
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • (1 other version)Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
    Download  
     
    Export citation  
     
    Bookmark   255 citations  
  • Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.
    Download  
     
    Export citation  
     
    Bookmark   341 citations  
  • Hume’s principle, beginnings.Albert Visser - 2011 - Review of Symbolic Logic 4 (1):114-129.
    In this note we derive Robinson???s Arithmetic from Hume???s Principle in the context of very weak theories of classes and relations.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Response to Dummett.Crispin Wright - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 389--405.
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • The Logicism of Frege, Dedekind, and Russell.William Demopoulos & Peter Clark - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press. pp. 129--165.
    The common thread running through the logicism of Frege, Dedekind, and Russell is their opposition to the Kantian thesis that our knowledge of arithmetic rests on spatio-temporal intuition. Our critical exposition of the view proceeds by tracing its answers to three fundamental questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified?
    Download  
     
    Export citation  
     
    Bookmark   20 citations  
  • The Tarskian Turn: Deflationism and Axiomatic Truth.Leon Horsten - 2011 - MIT Press.
    The work of mathematician and logician Alfred Tarski (1901--1983) marks the transition from substantial to deflationary views about truth.
    Download  
     
    Export citation  
     
    Bookmark   76 citations  
  • Frege: The Last Logicist.Paul Benacerraf - 1981 - Midwest Studies in Philosophy 6 (1):17-36.
    Download  
     
    Export citation  
     
    Bookmark   41 citations  
  • (1 other version)Mathematical knowledge.Mark Steiner - 1975 - Ithaca: Cornell University Press.
    Download  
     
    Export citation  
     
    Bookmark   43 citations  
  • Foundations without foundationalism: a case for second-order logic.Stewart Shapiro - 1991 - New York: Oxford University Press.
    The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...)
    Download  
     
    Export citation  
     
    Bookmark   231 citations  
  • (1 other version)Three Grades of Modal Involvement.W. V. Quine - 1976 - In Willard Van Orman Quine (ed.), The ways of paradox, and other essays. Cambridge: Harvard University Press. pp. 158-176.
    Download  
     
    Export citation  
     
    Bookmark   51 citations  
  • (1 other version)Logic, Logic, and Logic.George S. Boolos & Richard C. Jeffrey - 1998 - Cambridge, MA, USA: Harvard University Press. Edited by Richard C. Jeffrey.
    George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and (...)
    Download  
     
    Export citation  
     
    Bookmark   52 citations  
  • (1 other version)Kleine Schriften. [REVIEW]Michael Resnik - 1968 - Philosophy of Science 35 (4):424-425.
    Download  
     
    Export citation  
     
    Bookmark   39 citations  
  • (1 other version)Is Hume's principle analytic?Crispin Wright - 1999 - Notre Dame Journal of Formal Logic 40 (1):307-333.
    This paper is a reply to George Boolos's three papers (Boolos (1987a, 1987b, 1990a)) concerned with the status of Hume's Principle. Five independent worries of Boolos concerning the status of Hume's Principle as an analytic truth are identified and discussed. Firstly, the ontogical concern about the commitments of Hume's Principle. Secondly, whether Hume's Principle is in fact consistent and whether the commitment to the universal number by adopting Hume's Principle might be problematic. Also the so-called `surplus content' worry is discussed, (...)
    Download  
     
    Export citation  
     
    Bookmark   51 citations