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• catalog contributor b5748213.
• catalog created "1975.".
• catalog date "1975".
• catalog date "1975.".
• catalog dateCopyrighted "1975.".
• catalog description "3. Languge and logic : The complexity of vernacular language systems ; Logical language ; The limitations and capabilities of logical language ; Russell's theory of proper names and his theory of definite descriptions ; Russell's theory of types -- 4. Two basic concepts: meaning and truth : Language as meaningful ; The formation, specifically, of logical meaning: logical operations ; What is said as distinct from the saying ; The function of a concept of truth within logic ; A concept of truth sufficient for metalogic -- 5. The rigour and range of proof in formal logic : Introduction: the significance of Godel's theorem; evaluating formal logic as a body of truths ; Assessing the consistency, completeness and decidability of propositional logic ; Assessing the consistency, completeness and decidability of predicate logic ; A summary assessment of logic in general ; The concept of proof in logic -- ".
• catalog description "3. Logic and deductive systems : Introduction ; The nature of a deductive system ; The elements and structure of an axiomatic system ; Natural deduction systems ; Relating the axiomatic and the natural deduction approaches to the science of logic itself -- 4. A précis of propositional logic : A selected list of tautologies or laws in propositional logic ; An axiomatic system of the tautologies of propositional logic ; A survey of classic axiomatizations of propositional logic -- 5. Predicate logic : Introduction ; The language of predicate logic ; Discovering truths in predicate logic ; Practice in derivation by the method of supposition: a sampling of logical laws in predicate logic with their proofs ; The range of logical laws in predicate logic ; The laws of dyadic, triadic...n-adic predicates interpreted as a logical theory of relations ; Has predicate logic a decision procedure for determining whether any well-formed formula in its language is a tautology -- ".
• catalog description "6. A discussion of Russell's paradox and of the grounds for classal thought and for calculi of classes : Russell's paradox ; The impact of Russell's paradox within his own system ; The developmental influence of Russell's paradox within his own system ; Class terms in the history of traditional philosophy and logic: the problem of universals ; Perspective on Russell's paradox : The role and use of the concept, class, in contemporary mathematics ; Stanislaw Lesniewski (1886-1939) and mereology, the theory of concrete totalities ; Formal solutions to the paradoxes ; The history of paradoxes and of their solutions underlines the value, for logic, of a distinction between expressive and descriptive thought -- 7. The principles of logic and mathematics : The principles of logic: axioms or rules? ; Can a line be drawn between logic and mathematics?".
• catalog description "6. The traditional theory of the syllogism presented as a fragment of modern predicate logic : Introduction ; Axiomatizing the syllogistic ; Proving the syllogistic theses in a natural deduction system ; Conclusion: aristotles' syllogistic as a fragment of predicate logic -- 7. Class calculus : Introduction ; The symbolism of class calculus ; Boolean operations generating complex classes from simple ones ; A sampling of statements expressing relations between classes ; Diagramming statements about classes and using such diagrams as a method of displaying the validity or invalidity of arguments ; Axiomatizing the class calculus: a formalization of the Boole-Schroder algebra of classes ; Class calculus specified to a calculus of relations -- ".
• catalog description "8. Modal logic and many-valued logic : Introduction ; Modal logic : The basic history of its development ; Basic concepts and definitions in modal logic ; Modal laws in the context of Aristotle's syllogistic and the logic of modal syllogisms ; Modern systems of modal logic. Many-valued logic : The basic history of its development ; Basic observations about values, operators, proofs and theorems in many-valued systems ; The main systems of many-valued logic -- 9. The history of formal logic: a survey of creative periods : Introduction ; Aristotelian logic ; Megarian-Stoic logic ; Medieval logic ; From the end of the middle ages to the development of modern mathematical logic: a period that is not creative and in which a distorted version of logic, the so-called classical logic, developed ; Modern mathematical logic".
• catalog description "Bibliography: p. [393]-420.".
• catalog description "Intro : The science of logic: its perspective and human value ; Preliminary work done in a course on formal logic -- Section A : 1. The phenomenon of meaning : Human thought as a fabric of meaning and a context for phenomena of meaning ; Language as a fabric of meaning and a context for logical phenomena ; The structuring of meaning ; A dualism within meaning: sense and reference ; More complex meaning: propositional meaning ; The complexity of signification in predicative sentences: some elementary features ; Value as a phenomenon within meaning ; Simple relationships between predicative propositions -- 2. The phenomenon of implication : Inference and implication ; Implications within the square of opposition ; Simple operations on predicative propositions which disclose implications: conversion, obversion, contraposition and inversion ; The crux of inversion ; Some simple implications ; Complex implications: the simple categorical syllogism ; Some exercises on the rules of the simple categorical syllogism ; Is there any real inference in the simple categorical syllogism? ; Syllogisms other than the simple categorical type ; Validity and truth in argument ; Rules of inference ; How to analyse an argument -- 3. The phenomenon of unreason: antinomies (or paradoxes) and fallacies -- 4. The application of logic in life and science -- Exercises : Exercises on the general nature and structuring of meaning ; Exercises on the phenomenon of conflict: contradiction and contrariety ; Exercises on simple implications ; Exercises on the syllogism ; Exercises in analyzing vernacular arguments".
• catalog description "Section B : 1. The language of formal logic : Introduction ; The utility of variables ; Constants ; Well-formed formulae (wff's) ; Equivalent expressions ; The main notations used in propositional logic -- 2. Logical truth and methods of deciding what is logically true : The nature of logical truth ; Examples of sentences whose claim is to logical truth ; On finding a decision procedure for logical truth in propositional logic ; Drawing up truth-tables: some technical details ; Testing the validity of arguments (in propositional logic) by the truth-table method ; Decision procedures (for propositional logic) other than that of truth-tables : The normal form procedures ; The method of truth trees. Decision procedures in sections of logic other than propositional logic -- ".
• catalog description "Section C : 1. Perspective on metalogic : Introduction ; Making explicit concepts that are operational in formal logic ; Establishing metatheorems ; Perspective on metalogic -- 2. Historical survey : Modern mathematical logic in perspective : George Boole (1815-1864) ; Gottlob Frege (1848-1925) ; Bertrand Russel (1872-1970) ; Ludwig Wittgenstein (1889-1951). A broad survey of metalogical problems and interests in antiquity, the middle ages and in modern and contemporary times : Introduction ; Aristotle ; Megarian-stoic logic ; Medieval logic ; From the end of the middle ages to the development of modern mathematical logic ; Modern and contemporary metalogical problems and interests presented as a function of the development of mathematical logic -- ".
• catalog description "Section D : 1. A history of the philosophy of logic : Introduction ; The Greek period ; The medieval period ; Post-renaissance logicians ; The period of modern and contemporary mathematical logic -- 2. A definition of logic : Introduction ; Logic as a depth of grammar of human rationality ; Logic as an ontology of the possible ; Logic as the science of formal truth -- 3. The nature of logical space, of the proposition and of logical operators : The nature of logical space ; The nature of the proposition ; The nature of logical operators : Truth functional operators ; The predicator and the quantifiers ; The negator ; Operators in class-calculus and in many-valued logic ; Modal operators -- 4. Logic and subjectivity : Introduction ; Aristotle and Leibniz ; Wittgenstein ; Structuralism ; Husserl ; Subjectivity in contemporary philosophy -- 5. Logic and the ideal rational life : Introduction ; Formalization is inherent to rational living ; The limitations of formalization ; Metaformalism as an ideal for rational living ; Metaformalism and the new logic of framework transpositions within science ; General conclusion".
• catalog description "Section E : 1. The scope of applied logic : Introduction ; Limits in the purpose and functioning of applied logic ; The specific contents of applied logic -- 2. Logical forms in the Empirical science : Introduction ; An history survey of the development, structurally, of physical science and of scientific method generally ; Structure and method in the biological and human sciences ; The logical forms and logical processes within empirical science -- 3. Logical problems in empirical science : Introduction ; The general problem of contextual reasoning ; The problem of verification ; Probability values and truth values ; The problem of induction ; A general conclusion -- 4. Theoretical thought outside the empirical sciences : Introduction ; Theoretical reasoning that is not subject to control and evaluation by either observation of philosophy and philosophizing ; The use of logical techniques in formal analyses -- 5. Formal detachment: ideal or myth? : Introduction ; Michael Polanyi ; John Henry Newman (1801-90) ; Conclusion.".
• catalog extent "429 p. ;".
• catalog hasFormat "Logic.".
• catalog identifier "0717107108 :".
• catalog isFormatOf "Logic.".
• catalog issued "1975".
• catalog issued "1975.".
• catalog language "eng".
• catalog publisher "Dublin : Gill and Macmillan,".
• catalog relation "Logic.".
• catalog subject "160".
• catalog subject "BC108 .B28".
• catalog subject "Logic.".
• catalog tableOfContents "3. Languge and logic : The complexity of vernacular language systems ; Logical language ; The limitations and capabilities of logical language ; Russell's theory of proper names and his theory of definite descriptions ; Russell's theory of types -- 4. Two basic concepts: meaning and truth : Language as meaningful ; The formation, specifically, of logical meaning: logical operations ; What is said as distinct from the saying ; The function of a concept of truth within logic ; A concept of truth sufficient for metalogic -- 5. The rigour and range of proof in formal logic : Introduction: the significance of Godel's theorem; evaluating formal logic as a body of truths ; Assessing the consistency, completeness and decidability of propositional logic ; Assessing the consistency, completeness and decidability of predicate logic ; A summary assessment of logic in general ; The concept of proof in logic -- ".
• catalog tableOfContents "3. Logic and deductive systems : Introduction ; The nature of a deductive system ; The elements and structure of an axiomatic system ; Natural deduction systems ; Relating the axiomatic and the natural deduction approaches to the science of logic itself -- 4. A précis of propositional logic : A selected list of tautologies or laws in propositional logic ; An axiomatic system of the tautologies of propositional logic ; A survey of classic axiomatizations of propositional logic -- 5. Predicate logic : Introduction ; The language of predicate logic ; Discovering truths in predicate logic ; Practice in derivation by the method of supposition: a sampling of logical laws in predicate logic with their proofs ; The range of logical laws in predicate logic ; The laws of dyadic, triadic...n-adic predicates interpreted as a logical theory of relations ; Has predicate logic a decision procedure for determining whether any well-formed formula in its language is a tautology -- ".
• catalog tableOfContents "6. A discussion of Russell's paradox and of the grounds for classal thought and for calculi of classes : Russell's paradox ; The impact of Russell's paradox within his own system ; The developmental influence of Russell's paradox within his own system ; Class terms in the history of traditional philosophy and logic: the problem of universals ; Perspective on Russell's paradox : The role and use of the concept, class, in contemporary mathematics ; Stanislaw Lesniewski (1886-1939) and mereology, the theory of concrete totalities ; Formal solutions to the paradoxes ; The history of paradoxes and of their solutions underlines the value, for logic, of a distinction between expressive and descriptive thought -- 7. The principles of logic and mathematics : The principles of logic: axioms or rules? ; Can a line be drawn between logic and mathematics?".
• catalog tableOfContents "6. The traditional theory of the syllogism presented as a fragment of modern predicate logic : Introduction ; Axiomatizing the syllogistic ; Proving the syllogistic theses in a natural deduction system ; Conclusion: aristotles' syllogistic as a fragment of predicate logic -- 7. Class calculus : Introduction ; The symbolism of class calculus ; Boolean operations generating complex classes from simple ones ; A sampling of statements expressing relations between classes ; Diagramming statements about classes and using such diagrams as a method of displaying the validity or invalidity of arguments ; Axiomatizing the class calculus: a formalization of the Boole-Schroder algebra of classes ; Class calculus specified to a calculus of relations -- ".
• catalog tableOfContents "8. Modal logic and many-valued logic : Introduction ; Modal logic : The basic history of its development ; Basic concepts and definitions in modal logic ; Modal laws in the context of Aristotle's syllogistic and the logic of modal syllogisms ; Modern systems of modal logic. Many-valued logic : The basic history of its development ; Basic observations about values, operators, proofs and theorems in many-valued systems ; The main systems of many-valued logic -- 9. The history of formal logic: a survey of creative periods : Introduction ; Aristotelian logic ; Megarian-Stoic logic ; Medieval logic ; From the end of the middle ages to the development of modern mathematical logic: a period that is not creative and in which a distorted version of logic, the so-called classical logic, developed ; Modern mathematical logic".
• catalog tableOfContents "Intro : The science of logic: its perspective and human value ; Preliminary work done in a course on formal logic -- Section A : 1. The phenomenon of meaning : Human thought as a fabric of meaning and a context for phenomena of meaning ; Language as a fabric of meaning and a context for logical phenomena ; The structuring of meaning ; A dualism within meaning: sense and reference ; More complex meaning: propositional meaning ; The complexity of signification in predicative sentences: some elementary features ; Value as a phenomenon within meaning ; Simple relationships between predicative propositions -- 2. The phenomenon of implication : Inference and implication ; Implications within the square of opposition ; Simple operations on predicative propositions which disclose implications: conversion, obversion, contraposition and inversion ; The crux of inversion ; Some simple implications ; Complex implications: the simple categorical syllogism ; Some exercises on the rules of the simple categorical syllogism ; Is there any real inference in the simple categorical syllogism? ; Syllogisms other than the simple categorical type ; Validity and truth in argument ; Rules of inference ; How to analyse an argument -- 3. The phenomenon of unreason: antinomies (or paradoxes) and fallacies -- 4. The application of logic in life and science -- Exercises : Exercises on the general nature and structuring of meaning ; Exercises on the phenomenon of conflict: contradiction and contrariety ; Exercises on simple implications ; Exercises on the syllogism ; Exercises in analyzing vernacular arguments".
• catalog tableOfContents "Section B : 1. The language of formal logic : Introduction ; The utility of variables ; Constants ; Well-formed formulae (wff's) ; Equivalent expressions ; The main notations used in propositional logic -- 2. Logical truth and methods of deciding what is logically true : The nature of logical truth ; Examples of sentences whose claim is to logical truth ; On finding a decision procedure for logical truth in propositional logic ; Drawing up truth-tables: some technical details ; Testing the validity of arguments (in propositional logic) by the truth-table method ; Decision procedures (for propositional logic) other than that of truth-tables : The normal form procedures ; The method of truth trees. Decision procedures in sections of logic other than propositional logic -- ".
• catalog tableOfContents "Section C : 1. Perspective on metalogic : Introduction ; Making explicit concepts that are operational in formal logic ; Establishing metatheorems ; Perspective on metalogic -- 2. Historical survey : Modern mathematical logic in perspective : George Boole (1815-1864) ; Gottlob Frege (1848-1925) ; Bertrand Russel (1872-1970) ; Ludwig Wittgenstein (1889-1951). A broad survey of metalogical problems and interests in antiquity, the middle ages and in modern and contemporary times : Introduction ; Aristotle ; Megarian-stoic logic ; Medieval logic ; From the end of the middle ages to the development of modern mathematical logic ; Modern and contemporary metalogical problems and interests presented as a function of the development of mathematical logic -- ".
• catalog tableOfContents "Section D : 1. A history of the philosophy of logic : Introduction ; The Greek period ; The medieval period ; Post-renaissance logicians ; The period of modern and contemporary mathematical logic -- 2. A definition of logic : Introduction ; Logic as a depth of grammar of human rationality ; Logic as an ontology of the possible ; Logic as the science of formal truth -- 3. The nature of logical space, of the proposition and of logical operators : The nature of logical space ; The nature of the proposition ; The nature of logical operators : Truth functional operators ; The predicator and the quantifiers ; The negator ; Operators in class-calculus and in many-valued logic ; Modal operators -- 4. Logic and subjectivity : Introduction ; Aristotle and Leibniz ; Wittgenstein ; Structuralism ; Husserl ; Subjectivity in contemporary philosophy -- 5. Logic and the ideal rational life : Introduction ; Formalization is inherent to rational living ; The limitations of formalization ; Metaformalism as an ideal for rational living ; Metaformalism and the new logic of framework transpositions within science ; General conclusion".
• catalog tableOfContents "Section E : 1. The scope of applied logic : Introduction ; Limits in the purpose and functioning of applied logic ; The specific contents of applied logic -- 2. Logical forms in the Empirical science : Introduction ; An history survey of the development, structurally, of physical science and of scientific method generally ; Structure and method in the biological and human sciences ; The logical forms and logical processes within empirical science -- 3. Logical problems in empirical science : Introduction ; The general problem of contextual reasoning ; The problem of verification ; Probability values and truth values ; The problem of induction ; A general conclusion -- 4. Theoretical thought outside the empirical sciences : Introduction ; Theoretical reasoning that is not subject to control and evaluation by either observation of philosophy and philosophizing ; The use of logical techniques in formal analyses -- 5. Formal detachment: ideal or myth? : Introduction ; Michael Polanyi ; John Henry Newman (1801-90) ; Conclusion.".
• catalog title "Logic : depth grammar of rationality : a textbook on the science and history of logic / Patrick K. Bastable.".
• catalog type "text".