Syntacticism and functional completeness:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
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Newcastle upon Tyne
Cambridge Scholars Publishing
2024
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 599 Seiten 22 cm |
| ISBN: | 9781527556362 1527556360 |
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Datensatz im Suchindex
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Table of Contents 1. 1 Functional Completeness and Syntacticism: Logical-Philosophical Significance of a Metalogical Concept 1.1 Functional Completeness, Expressive Completeness, and Pathologies of Expressivity 1.2 Syntacticism and Functional Completeness 1.3 Preliminary Definitions of Concepts 2. 87 Construction of Formal Systems and Functional Completeness 2.1 Propositional Logic: Functional Completeness 2.1.1 Object Language and Metalanguage 2.1.2 Formal Construction and Syntacticism 2.1.3 Tarski’s Syntactical Reduction of Semantics 2.1.4 Formal Grammar for Propositional Logic 2.1.5 Polish Notation 2.2 Functional Completeness and Related Terms 2.2.1 Functional Compositionality, Definability, and Functional Completeness 2.2.2 Algebraic Composition 3. 123 Truth Functions 3.1 Grammar of Zprop 3.2 Monadic or Unary Connectives Definable over VAL = {T, F} 3.3 Dyadic or Binary Truth Functions Defined over VAL = {T, F} 3.4 Proof-Theoretic Definitions of Connectives 3.5 Algebraic Systems: Boolean Algebra J33, Boolean Ring Jb and its dual Boolean ring /вЪ 3.6 Logical Consequence Relations 3.6 Generation of Products and Hybrids of Logical Functions 3.6.1 Extraction of Associated Logical Consequence Relations from Truthtabular Definitions of Logical
Functions 3.7 Generation of Products and Hybrids of Logical Functions
vi Table of Contents 3.8 Non-Connectival Operations Definable Over Well-Formed Formulas 4. 169 Functional Completeness in the Standard Propositional Logic 4.1 Definability of Truth Functions 4.2 Minimality and Independence of Truth Functions 4.3 Informal Proofs of Functional Completeness and Normal Forms 4.4 Functionally Incomplete Sets: Informal Treatment 4.5 Rigorous Proofs of Functional Completeness and Incompleteness 5. 211 Minimal Functional Completeness 5.1 Maximal Reduction of Axiomatic Base 6.222 Connecting Functional Completeness to Properties of Functions 6.1 Properties and Relations of Truth Functions 6.1.1 HDuality/Self-Duality 6.1.2 ## Self-Duality 6.1.3 φ Symmetry and Self-Symmetry 6.1.4 △ Monotonicity 6.1.5 о Countability or Linearity 6.1.6 □ Truth-Preserving and Falsehood-Preserving Functions 6.1.7 ©Pairwise Locality 6.2 Testing Functional Completeness in Relation to Characteristic Properties of Truth Functions 7. 247 Syntacticism and Functional Completeness in the History of Modern Logic 7.1 Modern Logic, Syntacticism, and the Sheffer Functions 7.1.1 Royce’s Animadversions Toward the Boolean “Algebra of Logic” 7.1.2 Boole on the Laws of Thought and on the Primacy of Idempotence over Non-Contradiction 7.2
The “Estrangement” from Traditional Metaphysics and Syntacticist Projects 7.2.1 Quine’s Coaxing of Variables 7.2.2 Combinatory Vicissitudes 7.3 Wittgenstein’s Tractatus, Tarski’s Syntacticist Semantics, and Carnap’s Mea Culpa
Syntacticism and Functional Completeness vii 7.4 The Lvov-Vienna School 7.5 Frege Against the Formalists 7.6 Gödel’s Proof 7.6.1 Gödel’s Transfinitary Objectivism against Syntacticism 8.299 Higher Arities, Proof Systems, and the Case of Predicate Logic 8.1 Functionally Complete Truth Functions of Higher Arities and Some Object Lessons 8.1.1 A Failed Attempt 8.1.2 Successful Attempts 8.2 The Case of Predicate (First-Order) Logic 9.330 Functional Completeness in Alternative Truth-Functional Logics and in Non-Truth-Functional Systems 9.1 Lukasiewicz on the Principle of Contradiction 9.2 Sophie Piccard on Functional Completeness 9.3 Martin’s Test 9.4 Shipecki’s Criterion 9.5 J-Functions and Functional Completeness 9.6 An Initially Incomplete System, 53Luk, and the Remedy 9.7 Intensional Operators and Functional Completeness 9.8 Hybridization and Expressivity 9.9 Generalization of Truth-Functionality 9.10 Bochvar’s Trivalent System 10.411 Aspirations and Constraints: Lesniewski’s System and Dialogical Logic 10.1 Lesniewski’s Quantificational License 10.2 Lesniewski’s Protothetic 10.2.1 Syntactical Arrangements, Definitions of Connectives, and Reduction to One-Axiom Basis in the Protothetic Systems 10.2.2 Perspicuous Notation in the Protothetic Systems 10.3
Dialogical Logic 11.459 Wittgenstein on Syntacticism and Functional Completeness 11.1 Wittgenstein’s Tractatus and Functional Completeness 11.2 Syntacticism in Wittgenstein’s Tractatus Logico-Philosophicus
viii Table of Contents 11.2.1 The Wissenschaft View of Logic versus the Zeichenregel View of Logic 11.3 Wittgenstein on Functional Completeness and the N-Operator 11.3.1 Wittgenstein’s Notation and Definitions 11.3.2 Wittgenstein’s N-Operator Reconstructed 12. 502 The Logical Philosophy of Syntacticism and Functional Completeness 12.1 Functional Completeness and Logicality 12.2 Functional Completeness and the Expressivity of Formal Languages 12.3 Logical-Philosophical Stakes in the Study of Functional Completeness 12.4 Non-Connectival Syntactical Operations 12.5 Non-Logical Induced Shifts in Logic 12.5.1 Generation of Products of Logical Functions 12.6 Failures of Transfer 12.6.1 Hiz’s Warning 12.6.2 The Recalcitrant Case of Zeroary Functions 12.6.3 Makinson’s Warning 12.7 Logical Consequence and Logical Truth Divided 12.8 Prior’s Ticket Out of Proof-Theoretic Expressivism 12.9 Trade-Offs Compelled by Increases in Expressivity 12.10 Otto Neurath’s Syntacticism 12.11 Peirce’s Semeiotic 12.12 Syntacticism and Functional Completeness Bibliography. 576 Index. 594 |
| adam_txt |
Table of Contents 1. 1 Functional Completeness and Syntacticism: Logical-Philosophical Significance of a Metalogical Concept 1.1 Functional Completeness, Expressive Completeness, and Pathologies of Expressivity 1.2 Syntacticism and Functional Completeness 1.3 Preliminary Definitions of Concepts 2. 87 Construction of Formal Systems and Functional Completeness 2.1 Propositional Logic: Functional Completeness 2.1.1 Object Language and Metalanguage 2.1.2 Formal Construction and Syntacticism 2.1.3 Tarski’s Syntactical Reduction of Semantics 2.1.4 Formal Grammar for Propositional Logic 2.1.5 Polish Notation 2.2 Functional Completeness and Related Terms 2.2.1 Functional Compositionality, Definability, and Functional Completeness 2.2.2 Algebraic Composition 3. 123 Truth Functions 3.1 Grammar of Zprop 3.2 Monadic or Unary Connectives Definable over VAL = {T, F} 3.3 Dyadic or Binary Truth Functions Defined over VAL = {T, F} 3.4 Proof-Theoretic Definitions of Connectives 3.5 Algebraic Systems: Boolean Algebra J33, Boolean Ring Jb and its dual Boolean ring /вЪ 3.6 Logical Consequence Relations 3.6 Generation of Products and Hybrids of Logical Functions 3.6.1 Extraction of Associated Logical Consequence Relations from Truthtabular Definitions of Logical
Functions 3.7 Generation of Products and Hybrids of Logical Functions
vi Table of Contents 3.8 Non-Connectival Operations Definable Over Well-Formed Formulas 4. 169 Functional Completeness in the Standard Propositional Logic 4.1 Definability of Truth Functions 4.2 Minimality and Independence of Truth Functions 4.3 Informal Proofs of Functional Completeness and Normal Forms 4.4 Functionally Incomplete Sets: Informal Treatment 4.5 Rigorous Proofs of Functional Completeness and Incompleteness 5. 211 Minimal Functional Completeness 5.1 Maximal Reduction of Axiomatic Base 6.222 Connecting Functional Completeness to Properties of Functions 6.1 Properties and Relations of Truth Functions 6.1.1 HDuality/Self-Duality 6.1.2 ## Self-Duality 6.1.3 φ Symmetry and Self-Symmetry 6.1.4 △ Monotonicity 6.1.5 о Countability or Linearity 6.1.6 □ Truth-Preserving and Falsehood-Preserving Functions 6.1.7 ©Pairwise Locality 6.2 Testing Functional Completeness in Relation to Characteristic Properties of Truth Functions 7. 247 Syntacticism and Functional Completeness in the History of Modern Logic 7.1 Modern Logic, Syntacticism, and the Sheffer Functions 7.1.1 Royce’s Animadversions Toward the Boolean “Algebra of Logic” 7.1.2 Boole on the Laws of Thought and on the Primacy of Idempotence over Non-Contradiction 7.2
The “Estrangement” from Traditional Metaphysics and Syntacticist Projects 7.2.1 Quine’s Coaxing of Variables 7.2.2 Combinatory Vicissitudes 7.3 Wittgenstein’s Tractatus, Tarski’s Syntacticist Semantics, and Carnap’s Mea Culpa
Syntacticism and Functional Completeness vii 7.4 The Lvov-Vienna School 7.5 Frege Against the Formalists 7.6 Gödel’s Proof 7.6.1 Gödel’s Transfinitary Objectivism against Syntacticism 8.299 Higher Arities, Proof Systems, and the Case of Predicate Logic 8.1 Functionally Complete Truth Functions of Higher Arities and Some Object Lessons 8.1.1 A Failed Attempt 8.1.2 Successful Attempts 8.2 The Case of Predicate (First-Order) Logic 9.330 Functional Completeness in Alternative Truth-Functional Logics and in Non-Truth-Functional Systems 9.1 Lukasiewicz on the Principle of Contradiction 9.2 Sophie Piccard on Functional Completeness 9.3 Martin’s Test 9.4 Shipecki’s Criterion 9.5 J-Functions and Functional Completeness 9.6 An Initially Incomplete System, 53Luk, and the Remedy 9.7 Intensional Operators and Functional Completeness 9.8 Hybridization and Expressivity 9.9 Generalization of Truth-Functionality 9.10 Bochvar’s Trivalent System 10.411 Aspirations and Constraints: Lesniewski’s System and Dialogical Logic 10.1 Lesniewski’s Quantificational License 10.2 Lesniewski’s Protothetic 10.2.1 Syntactical Arrangements, Definitions of Connectives, and Reduction to One-Axiom Basis in the Protothetic Systems 10.2.2 Perspicuous Notation in the Protothetic Systems 10.3
Dialogical Logic 11.459 Wittgenstein on Syntacticism and Functional Completeness 11.1 Wittgenstein’s Tractatus and Functional Completeness 11.2 Syntacticism in Wittgenstein’s Tractatus Logico-Philosophicus
viii Table of Contents 11.2.1 The Wissenschaft View of Logic versus the Zeichenregel View of Logic 11.3 Wittgenstein on Functional Completeness and the N-Operator 11.3.1 Wittgenstein’s Notation and Definitions 11.3.2 Wittgenstein’s N-Operator Reconstructed 12. 502 The Logical Philosophy of Syntacticism and Functional Completeness 12.1 Functional Completeness and Logicality 12.2 Functional Completeness and the Expressivity of Formal Languages 12.3 Logical-Philosophical Stakes in the Study of Functional Completeness 12.4 Non-Connectival Syntactical Operations 12.5 Non-Logical Induced Shifts in Logic 12.5.1 Generation of Products of Logical Functions 12.6 Failures of Transfer 12.6.1 Hiz’s Warning 12.6.2 The Recalcitrant Case of Zeroary Functions 12.6.3 Makinson’s Warning 12.7 Logical Consequence and Logical Truth Divided 12.8 Prior’s Ticket Out of Proof-Theoretic Expressivism 12.9 Trade-Offs Compelled by Increases in Expressivity 12.10 Otto Neurath’s Syntacticism 12.11 Peirce’s Semeiotic 12.12 Syntacticism and Functional Completeness Bibliography. 576 Index. 594 |
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| spelling | Makridis, Odysseus Verfasser (DE-588)1326938061 aut Syntacticism and functional completeness by Odysseus Makridis Newcastle upon Tyne Cambridge Scholars Publishing 2024 viii, 599 Seiten 22 cm txt rdacontent n rdamedia nc rdacarrier Logik (DE-588)4036202-4 gnd rswk-swf Analytische Philosophie (DE-588)4001869-6 gnd rswk-swf Logic Analysis (Philosophy) Philosophie analytique Logik (DE-588)4036202-4 s Analytische Philosophie (DE-588)4001869-6 s DE-604 Erscheint auch als Online-Ausgabe 9781527556379 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034954835&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Syntacticism and functional completeness |
| title_auth | Syntacticism and functional completeness |
| title_exact_search | Syntacticism and functional completeness |
| title_exact_search_txtP | Syntacticism and functional completeness |
| title_full | Syntacticism and functional completeness by Odysseus Makridis |
| title_fullStr | Syntacticism and functional completeness by Odysseus Makridis |
| title_full_unstemmed | Syntacticism and functional completeness by Odysseus Makridis |
| title_short | Syntacticism and functional completeness |
| title_sort | syntacticism and functional completeness |
| topic | Logik (DE-588)4036202-4 gnd Analytische Philosophie (DE-588)4001869-6 gnd |
| topic_facet | Logik Analytische Philosophie |
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