A Manual of Intensional LogicJohan van BenthemIntroduction I. Classical Theories 1 Tense and Time 2 Modality 3 Conditionals 4 Combinations II. Recent Developments 1: Computational Applications 5 Mathematics and Computer Sience III. Recent Developments 2: Partialilty 6 Intervals and Events 7 Possibility and Information 8 The Logic of Partiality IV. Recent Developments 3: Logical Semantics 9 Denotational Constraints on Tense and Modality 10 Conditionals as Generalized Quantifiers 11 Intensions ...

Lectures on Linear LogicA.S. Troelstra1 Introduction 2 Sequent calculus for linear logic 3 Some elementary syntactic results 4 The calculus of two implications 5 Embeddings and approximations 6 Natural deduction systems for linear logic 7 Hillbert-type systemens 8 Algebraic semantics 9 Combinational linear logic 10 Girard domains 11 Coherence in symmetric monoidal 12 The storage operator as a cofree comonoid 13 Evaluation in typed calculii 14 Computation by lazy evaluation in CCC's 15 Computatio...

Metamathematics of First-Order ArithmeticPetr Hájek, Pavel Pudlák PART A I - Arithmetic as Number Theory, Set Theory and Logic II - Fragments and Combinatorics PART B III - Self-Reference IV - Models of Fragments of Arithmetic PART C V - Bounded Arithmetic

Modal Logic - An IntroductionBrian F. ChellasPART I 1 - Introduction 2 - Logical preliminaries PART II 3 - Standard models for modal logics 4 - Normal systems of modal logic 5 - Determination and decidability for normal systems 6 - Deontic Logic PART III 7 - Minimal models for modal logics 8 - Classical systems of modal logic 9 - Determination and decidability for classical systems 10 - Conditional logic

Mathematics of ModalityRobert GoldblattIntroduction 1: Metamathematics of Modal Logic 2: Semantic Analysis of Orthologic 3: Orthomodularity is not Elementary 4: Arithmetical Necessity, Provability and Intuitionistic Logic 5: Diodorean Modality in Minkowski Spacetime 6: Grothendieck Topology as Geometric Modality 7: The Semantics of Hoare’s Iteration Rule 8: An Abstract Setting for Henkin Proofs 9: A Framework for Infinitary Modal Logic 10: The McKinsey Axiom Is Not Canonical 11: Elementary Log...

An Introduction to Modal LogicG.E. Hughes, M.J. CresswellI. Modal Propositional Logic II. Modal Predicate Logic III. A Survey of Modal Logic

The Axiom of ChoiceThomas J. JechPreface 1. Introduction 2. Use of the axiom of choice 3. Consistency of the axiom of choice 4. Permutation models 5. Independence of the axiom of choice 6. Embedding theorems 7. Models with finite supports 8. Some weaker versions of the axiom of choice 9. Nontransferable statements 10. Mathematics without choice 11. Cardinal numbers in set theory without choice 12. Some properties contradicting the axiom of choice Appendix 1. Equivalents of the axiom of choice Ap...

Elements of IntuitionismMichael Dummett1. Preliminaries 2. Elementary Intuitionistic Mathematics 3. Choice Sequences and Spreads 4. The Formalization of Intuitionistic Logic 5. The Semantics of Intuitionistic Logic 6. Some Further Topics 7. Concluding Philosophical Remarks

Intuitionism - An IntroductionA. HeytingI. Disputation II. Arithmetic III. Spreads and species IV. Algebra V. Plane pointspecies VI. Measure and integration VII. Logic VIII. Controversial subjects

The Principles of Mathematics RevisedJaakko Hintikka1 - The functions of logic and the problem of truth definition 2 - The game of logic 3 - Frege's fallacy foiled: Independence-friendly logic 4 - The joys of independence: Some uses of IF logic 5 - The complexities of completeness 6 - Who's afraid of Alfred Tarski? Truth definitions for IF first-order languages 7 - The liar belied: Negation in IF logic 8 - Axiomatic set theory: Fraenkelstein's monster? 9 - IF logic as a framework for mathematica...

On Formally Undecidable Propositions Of Principia Mathematica And Related SystemsKurt GödelIn 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Gödel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will ...

Proof TheoryGaisa TakeutiPart I. First Order Systems 1. First Order Predicate Calculus 2. Peano Arithmetic Part II. Second Order and Finite Order Systems 3. Second Order Systems and Simple Type Theory 4. Infinitary Logic Part III. Consistency Problems 5. Consistency Proofs 6. Some Applications of Consistency Proofs

Structural Proof TheorySara Negri, Jan von PlatoPREFACE INTRODUCTION 1 FROM NATURAL DEDUCTION TO SEQUENT CALCULUS 2 SEQUENT CALCULUS FOR INTUITIONISTIC LOGIC 3 SEQUENT CALCULUS FOR INTUITIONISTIC LOGIC 4 THE QUANTIFIERS 5 VARIANTS OF SEQUENT CALCULI 6 STRUCTURAL PROOF ANALYSIS OF AXIOMATIC THEORIES 7 INTERMEDIATE LOGICAL SYSTEMS 8 BACK TO NATURAL DEDUCTION CONCLUSION: DIVERSITY AND UNITY IN STRUCTURAL PROOF THEORY APPENDIX A SIMPLE TYPE THEORY AND CATEGORIAL GRAMMAR APPENDIX B PROOF THEORY AND C...

Normalization, Cut-Elimination and the Theory of ProofsA.M. UngarIntroduction 1 Background 2 Comparing NJ with LJ 3 Natural Deduction Revisited 4 The Problem of Substitution 5 A Multiple-Conclusion Calculus 6 Reduction Procedures 7 Correspondence Results 8 Interpretations of Derivations Appendices A. A Strong Cut-Elimination Theorem for LJ B. A Formulation of the Classical Sequent Calculus C. Proofs and Categories

Model TheoryC.C. Chang, H. Jerome Keisler1. Introduction 2. Models constructed from constants 3. Further model-theoretic constructions 4. Ultraproducts 5. Saturated and special models 6. More about ultraproducts and generalizations 7. Selected topics A. Set theory B. Open problems in classical model theory

Set Theory - An Introduction to Large CardinalsFrank R. Drake1 Introduction: Sets and Languages 2 The Development of ZFC 3 The Léavy Hierarchy and the Reflection Principle 4 Inaccessible and Mahlo Cardinals 5 The Constructtble Universe 6 Measurable Cardinals 7 Trees and Partition Properties 8 Partition Cardinals and Model Theory: Silver's Results 9 Indescribable Cardinals 10 Infinitary Languages and Large Cardinals

Set Theory and the Continuum HypothesisPaul J. CohenI. General Background in Logic II. Zermelo-Fraenkel Set Theory III. The Consistency of the Continuum Hypothesis and the Axiom of Choice IV. The Independence of the Continuum Hypothesis and the Axiom of Choice

Set TheoryThomas JechPart I. Sets 1. Axiomatic Set Theory 2. Transitive Models of Set Theory Part II. More Sets 3. Forcing and Generic Models 4. Some Applications of Forcing Part III. Large Sets 5. Measurable Cardinals 6. Other Large Cardinals Part IV. Sets of Reals 7. Descriptive Set Theory

Introduction to Combinatorics and λ-CalculusJ. Roger Hindley, Jonathan P. Seldin1 The λ-calculus 2 Combinatory logic 3 The power of λ and combinators 4 Representing the computable functions 5 The undecidability theorem 6 The formal theories λβ and CLw 7 Extensionality in λ-calculus 8 Extensionality in combinatory logic 9 Correspondence between λ and CL 10 Simple typing, Church-style 11 Simple typing, Curry-style in CL 12 Simple typing, Curry-style in λ 13 Generalizations of typing 14 Mo...

Tense LogicRobert P. McArthur1. An Overview of Tense Logic 2. Linear Tense Logics 3. Branching Tense Logic and Temporal Modality 4. Quantificational Tense Logics 5. Soundness and Completeness Theorems for Tense Logic

Introduction to higher order categorical logicJ. Lambek, P.J. ScottPart O. Introduction to Category Theory Part I. Cartesian Closed Categories and λ-Calculus Part II. Type Theory and Toposes Part III. Representing Numerical Functions in Various Categories

Logica, etiketten en vleesStefan ThemersonVertaling door Nicolaas Matsier Literaire, logische en vaak satirische bespiegelingen over onderwerpen uit de moderne angelsaksische filosofie.

De grondslagen der arithmeticaGottlob FregeTer inleiding Beknopte biografie Noten De grondslagen der arithmetica - Inhoudstafel - Inleiding - Tekst

Filosofische grondslagen van de wiskundeD. van Dalen1. Verzamelingsleer, een platonisch paradigma/ Infinitesimaalrekening 2. Intuïtionisme / Negatieloze wiskunde 3. Logica 4. Formalisme 5. Logicisme 6. Zijn er constanten van het wiskundig denken?

Logica voor alfa's en informaticiJan van Eijk, Elias Thijsse1. Algemene inleiding 2. Kernbegrippen uit de naïeve verzamelingenleer 3. Eindige, oneindige en beslisbare verzamelingen 4. Logica, de leer van het correct redeneren 5. Propositielogica 6. Predikatenlogica 7. Uitbreidingen van de predikatenlogica 8. Informatica-toepassingen van de logica

Logica en modelDoede Nauta1. Historisch overzicht. Een introductie tot het model in de formele wetenschappen 2. Mathematische standaardbegrippen. Verzameling, afbeelding, groep, isomorfie 3. Symbolische logica. Een inleiding tot de logica aan de hand van het modelbegrip 4. Elementen der modeltheorie 5. Formele wetenschap en model

Frege and Gödel - Two Fundamental Texts in Mathematical LogicJean van Heijenoort (ed.)Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought (1879), by G. Frege Some metamathematical results on completeness and consistency; On formally undecidable propositions of Principia mathematica and related systems I; and On completeness and consistency (1930b, 1931, and 1931a), by K. Gödel

Perspectives on the History of Mathematical LogicThomas Drucker (ed.)The Problem of Elimination in the Algebra of Logic - Judy Green Peirce and the Law of Distribution - Nathan Houser The First Russell Paradox - Irving H. Anellis Principia Mathematica and the Development of Automated Theorem Proving - Daniel J. O’Leary Oswald Veblen and the Origins of Mathematical Logic at Princeton - William Aspray The Löwenheim-Skolem Theorem, Theories of Quantification, and Proof Theory - Irving H. Anellis...

A Mathematical Introduction to LogicHerbert B. Enderton0. Useful Facts about Sets 1. Sentential Logic 2. First-Order Logic 3. Undecidability 4. Second-Order Logic

Popular Lectures on Mathematical LogicHao WangA noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. Author Hao Wang surveys the central concepts and theories of the discipline in a historical and developmental context, and then focuses on the four principal domains of contemporary mathematical logic: set theory, model theory, recursion theory and constructivism, and proof theory. Topics include the pl...

Handbook of Mathematical LogicJon Barwise (ed.)Part A. Model Theory (Contributors: J. Barwise, P.C. Eklof, H.J. Keisler, A. Kock, A. Macintyre, M. Makkai, M. Morley, G.E. Reyes, K.D. Stroyan) Part B. Set Theory (Contributors: J.P. Burgess, K.J. Devlin, T.J. Jech, I. Juhász, K. Kunen, M.E. Rudin, J.R. Schoenfield) Part C. Recursion Theory (Contributors: P. Aczel, M. Davis, H.B. Enderton, A. Kechris, D.A. Martin, Y.N. Moschovakis, M.O. Rabin, R.A. Shore, S.G. Simpson) Part D. Proof Theory an...

Proofs and Refutations - The Logic of Mathematical DiscoveryImre LakatosChapter 1 1. A problem and a conjecture 2. A proof 3. Criticism of the proof by counterexamples which are local but not global 4. Criticism of the conjecture by global counterexamples 5. Criticism of the proof-analysis by counterexamples which are global but not local. The problem of rigour 6. Return to criticism of the proof by counterexamples which are local but nog global. The problem of content 7. The problem of content ...

L.E.J. Brouwer -Een biografieDirk van Dalen1. Jeugd en schooljaren 2. Studie en studententijd 3. Mystiek 4. De dissertatie 5. Naar de wiskundige top 6. De universitaire carrière 7. Ontwikkeling in isolement 8. Wetenschap en politiek 9. Het onderzoekscentrum Blaricum 10. Dimensietheorie en grondslagenstrijd 11. Götterdämmerung 12. Verloren jaren 13. Universiteit in oorlogstijd 14. Zuivering en reorganisatie 15. Strijd en erkenning

LeibnizDr. C.A. van PeursenContour van Leibniz' leer en leven De binnenkant der werkelijkheid: de monaden De buitenkant der werkelijkheid: organisatie, evolutie, perceptie, harmonie De logica der beste wereld: waarheid, vrijheid, God Wegen de toekomst in: de actualiteit van Leibniz' filosofie Literatuuropgave

Mersenne and the Learning of the SchoolsPeter Dear1. Introduction 2. Humanism and the Implications of Rhetoric 3. Dialectic, Probabilism, and “Mitigated Scepticism” 4. Aristotelian Science and the Metaphysics of Mathematics 5. Saint Augustine and Universal Harmony 6. Mechanics, Music, and Harmony 7. Philosophical Systems, Essentialism, and the Language of Philosophy 8. Mersenne’s Later Career: A Philosophical Agenda and Its Limitations 9. Summary and Conclusions

Introduction to Mathematical LogicJ. MalitzI. An Introduction to Set Theory II. An Introduction to Computability Theory III. An Introduction to Model Theory

Robot op zeePieter AdriaansPieter Adriaans - filosoof, wiskundige, ondernemer, musicus, beeldend kunstenaar en avonturier - verkocht zijn met succes opgebouwde onderneming Syllogic om een jongensdroom te realiseren: meedoen met een transatlantische solozeilrace. Altijd op zoek naar mogelijkheden om zijn talenten te combineren wordt het project Robosail geboren. Zijn passie voor zeilen verbindt hij met zijn wetenschappelijk specialisme: het ontwerpen van intelligente autonome computersystemen. Na...

De stelling van GödelE. Nagel, J.R. NewmanDe stelling van Gödel uitgelegd en begrijpelijk gemaakt - Inleiding - Het consistentieprobleem - Absolute consistentiebewijzen - De systematische codificatie van de formele logica - Een voorbeeld van een geslaagd absoluut consistentiebewijs - Het begrip afbeelden en het gebruik ervan in de wiskunde - Gödels bewijzen; Gödel-getallen; De aritmetisering van de meta-mathematica; De kern van Gödels redenering - Slotbeschouwing

The Elements of Mathematical LogicPaul RosenbloomI. The Logic of Classes II. The Logic of Propositions III. The Logic of Proposional Functions IV. The General Syntax of Language

Een nacht vol opwinding - Een keuze uit de filosofische essaysHenri Poincaré1. Selectie van feiten 2. De toekomst van de wiskunde 3. Uitvinding in de wiskunde 4. Wiskundige definities en onderwijs 5. Toeval 6. Over de aard van wiskundig redeneren 7. Wiskundig concept en ervaring 8. Intuïtie en logica bij wiskunde 9. De evolutie van de wetten