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• catalog abstract ""The Conceptual Roots of Mathematics is a comprehensive study of the philosophy of mathematics, which is - as the book shows - central to epistemology and metaphysics."--Jacket.".
• catalog contributor b11194992.
• catalog created "2000.".
• catalog date "2000".
• catalog date "2000.".
• catalog dateCopyrighted "2000.".
• catalog description ""The Conceptual Roots of Mathematics is a comprehensive study of the philosophy of mathematics, which is - as the book shows - central to epistemology and metaphysics."--Jacket.".
• catalog description "Includes bibliographical references and index.".
• catalog description "Lattices and set theory -- Trees and mereology -- Prototopology. Togetherness -- Axiomatic approaches -- Whitehead's programme -- Failure -- Pointed and linear hopes -- Alternatives -- Mooreology -- More mereology -- Magnitude and measure. Quantum? and quot? -- Point of measuring -- Equivalence structures -- Additional rules -- Limits and zero -- Zeno -- Measures and numbers -- Down with set theory. Theory of magnitudes -- Russell's paradox -- Responses to paradox -- Formal approaches -- Skolem paradox -- Axiom of choice -- Continuum hypotheses -- Axioms and existence -- Axiom of extensionality -- Chastened logicism? Logicism -- Whiat is logic? -- Boolean plus -- Iterated modalities -- Completeness -- Paradox -- Second-order logic -- Analytic and A prioi truth -- Mathematical knowledge. Synthetic A priori? -- Not seeing but doing -- Pattern recognition -- Lakatos -- Cogency and dialogue -- On behalf of the fool -- Hilbert -- Bed theory of truth -- Mathematical knowledge -- ".
• catalog description "Monomorphsm and non-standard models -- Immigration control -- Fifth postulate -- Sorites arithmetic -- Dialogues -- Recursive reasoning -- Natural numbers -- Infinite. In defence of doubt -- Cardinality --Mostest -- Characterization of intuitionism -- Proofs and dialogues -- Verificationist arguments for intuitionism -- Selective skepticism -- Ultrafinitism -- Lax finitism -- Actualising potentiality -- All -- Implications of Godel's theorem. Pons asinorum -- Flavour of the Godelian argument -- Godel numbering -- Translation -- Diagonalization -- Conditions -- Corollaries and consequences -- Church's theorem and Turing's theorem -- Godel's second theorem -- Mechanism -- Godel's theorem and provability -- Transitive relations. Logic -- Equivalence relations -- Functions -- Identity in difference -- Ordering relations -- Macrostructure and microstructure -- Continuum -- Marriage of equivalence with order -- Converse transitivity -- Paradigm partial orderings -- ".
• catalog description "Plato's philosophies of mathematics. Meno -- A priori -- Relevance -- What are we talking about? -- How do we know? -- Modality -- Cogency -- Deduction -- Whence the premises? -- Geometry. Euclid -- Fifth postulate -- Non-Euclidean geometries -- Formal and physical geometry -- Conceptual constraints -- Which geometry? -- The theory of groups -- Pythagorean geometry has a better metric -- Desargues -- Formalism. More geometrico -- Formalising -- Maximum cogency -- Theory of formal systems -- Meaning and interpretation -- Epistemological formalism -- Logicist programme -- Numbers : the cardinal approach. Etymology -- Uses of numbers -- How many? -- Nought -- Quotifers and quotities -- Flege's extensions and sets -- Paradigm sets -- Numbers : the ordinal approach. Superlative approach -- Dedekind's successors -- And so on -- Grounding the ordinals -- How to count -- Ordinals and cardinals -- Numbers : the abstract approach. Third approach -- Peano -- ".
• catalog description "Realism revisited. Existence and reality -- Self-subsistent objects -- Meaning and impredicativity -- Bivalence and determinacy -- Competing truths -- Contingency and structure -- Coherence and depth -- Laws of the laws of nature -- Chastened isms.".
• catalog extent "xvii, 452 p. :".
• catalog identifier "041520738X (hardcover)".
• catalog isPartOf "International library of philosophy.".
• catalog issued "2000".
• catalog issued "2000.".
• catalog language "eng".
• catalog publisher "London ; New York : Routledge,".
• catalog subject "510.1 21".
• catalog subject "510/.1 21".
• catalog subject "Mathematics Philosophy.".
• catalog subject "QA8.4 .L833 2000".
• catalog tableOfContents "Lattices and set theory -- Trees and mereology -- Prototopology. Togetherness -- Axiomatic approaches -- Whitehead's programme -- Failure -- Pointed and linear hopes -- Alternatives -- Mooreology -- More mereology -- Magnitude and measure. Quantum? and quot? -- Point of measuring -- Equivalence structures -- Additional rules -- Limits and zero -- Zeno -- Measures and numbers -- Down with set theory. Theory of magnitudes -- Russell's paradox -- Responses to paradox -- Formal approaches -- Skolem paradox -- Axiom of choice -- Continuum hypotheses -- Axioms and existence -- Axiom of extensionality -- Chastened logicism? Logicism -- Whiat is logic? -- Boolean plus -- Iterated modalities -- Completeness -- Paradox -- Second-order logic -- Analytic and A prioi truth -- Mathematical knowledge. Synthetic A priori? -- Not seeing but doing -- Pattern recognition -- Lakatos -- Cogency and dialogue -- On behalf of the fool -- Hilbert -- Bed theory of truth -- Mathematical knowledge -- ".
• catalog tableOfContents "Monomorphsm and non-standard models -- Immigration control -- Fifth postulate -- Sorites arithmetic -- Dialogues -- Recursive reasoning -- Natural numbers -- Infinite. In defence of doubt -- Cardinality --Mostest -- Characterization of intuitionism -- Proofs and dialogues -- Verificationist arguments for intuitionism -- Selective skepticism -- Ultrafinitism -- Lax finitism -- Actualising potentiality -- All -- Implications of Godel's theorem. Pons asinorum -- Flavour of the Godelian argument -- Godel numbering -- Translation -- Diagonalization -- Conditions -- Corollaries and consequences -- Church's theorem and Turing's theorem -- Godel's second theorem -- Mechanism -- Godel's theorem and provability -- Transitive relations. Logic -- Equivalence relations -- Functions -- Identity in difference -- Ordering relations -- Macrostructure and microstructure -- Continuum -- Marriage of equivalence with order -- Converse transitivity -- Paradigm partial orderings -- ".
• catalog tableOfContents "Plato's philosophies of mathematics. Meno -- A priori -- Relevance -- What are we talking about? -- How do we know? -- Modality -- Cogency -- Deduction -- Whence the premises? -- Geometry. Euclid -- Fifth postulate -- Non-Euclidean geometries -- Formal and physical geometry -- Conceptual constraints -- Which geometry? -- The theory of groups -- Pythagorean geometry has a better metric -- Desargues -- Formalism. More geometrico -- Formalising -- Maximum cogency -- Theory of formal systems -- Meaning and interpretation -- Epistemological formalism -- Logicist programme -- Numbers : the cardinal approach. Etymology -- Uses of numbers -- How many? -- Nought -- Quotifers and quotities -- Flege's extensions and sets -- Paradigm sets -- Numbers : the ordinal approach. Superlative approach -- Dedekind's successors -- And so on -- Grounding the ordinals -- How to count -- Ordinals and cardinals -- Numbers : the abstract approach. Third approach -- Peano -- ".
• catalog tableOfContents "Realism revisited. Existence and reality -- Self-subsistent objects -- Meaning and impredicativity -- Bivalence and determinacy -- Competing truths -- Contingency and structure -- Coherence and depth -- Laws of the laws of nature -- Chastened isms.".
• catalog title "Conceptual roots of mathematics ; an essay on the philosophy of mathematics / J.R. Lucas.".
• catalog type "text".