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Buzaglo M. — Logic of Concept Expansion
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Íàçâàíèå: Logic of Concept ExpansionÀâòîð: Buzaglo M. Àííîòàöèÿ: Scientists and mathematicians frequently describe the development of their field as a process that includes expansion of concepts. Logicians traditionally deny the possibility of conceptual expansion and the coherence of this description. Meir Buzaglo's innovative study proposes a way of expanding logic to include the stretching of concepts, while modifying the principles which apparently block this possibility. He offers stimulating discussions of the idea of conceptual expansion as a normative process, and of the relation of the conceptual expansion to truth, meaning, reference, ontology, and paradox, and analyzes the views of Kant, Wittgenstein, Godel, and others, paying especially close attention to Frege. His book will be of interest to a wide range of readers, from philosophers (of logic, mathematics, language, and science) to logicians, mathematicians, linguists, and cognitive scientists.
ßçûê: Ðóáðèêà: Ôèëîñîôèÿ, ðåëèãèÿ è êóëüòóðà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2002Êîëè÷åñòâî ñòðàíèö: 194Äîáàâëåíà â êàòàëîã: 23.05.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
"essence" of a concept 83—85 "Following a rule" 144 "Inertia, Law of" 25 "Unsaturated" concepts 83 "What is Cantor's Continuum Problem?” (Goedel) 127 Absolutely forced expansions 56—57 Addition, laws of 19 Algebra 9 15—18 67 69 Algebra of negative numbers 106—109 Algebra, extension of fields 98—99 Alster, Gall 62n Ambiguous sentences 142 Analogies 146—147 171 Analytic functions 31 51—52 57 130 Antinomies ix 21 149 151—156 158n 166 Applications of expansions 22 65—66 Aristotle 27 78 Arithmetic 2 3 15 16—18 88—89 Arnauld, Antoine 10 Axioms from constraints to 103—109 Axioms of comprehension 167 Axioms of logic 152 Benacerraf, Paul 114 Berkeley, George 11 Bernoulli, Johann 13—14 60 Boole, George 19 Boolos, George 162n Boundaries 87—90 150—153 Brouwer, Luitzen 20 173 Calculus, differential 11 Cantor, Georg 44 127 155 Cantor, Georg, concept of number 57 75 Cantor, Georg, infinite numbers 125 Cantor, Georg, transcendental numbers 65 77 78 Cantor, Georg, Wittgenstein on 146—147 148 Cardinality 44 49—50 65 125 Cauchy's integral formula 67—68 Chain of extension 73 75—76 78 Characteristics of concepts 74 Characteristics of forced expansions 54—59 Classifying expressions 163—168 Cognition 15 Cohen, Paul 50 Community and concepts 28—29 Commutative law 18 108 complex numbers 51 69 108 109 Complex numbers, acceptance of 10—12 Complex numbers, Cauchy's formula 67—68 Compositionality 32 34—35 Computability 121 Conjunction 19 Consistency after expansion 101 159 162—163 Constraints 103—109 143 Context of discovery 103 Cosine function 85 De Moivre's theorem 69 Decomposition 34—35 67 Dedekind, Richard 19 Deduction 3 23 54—57 59 60—63 95 Definitions and family resemblance 83—85 Demarcation problem 150—153 Denumerable sets 65—66 Determinacy of concepts 30—35 Diamond, Cora 31—35 145 147 Dichotomy picture (DP) 150—158 Differentials 11 Dilemmas 170—171 Disjunction 19 Dummett, Michael 30—31 70—71 101n 158n EI (existential instantiation) law 110—115 Einstein, Albert 21 Embedded expansions 39—40 Empty expansions 70—71 Equabons, expansion of 100 Equality 100 105 Equivalent forms, principle of the permanence of 3 17—20 108 Euler, Leonhard 14 90—91 130n Excluded middle, law of 20—21 58 173 Existenbal instanbabon (EI) law 110—115 Existence of concepts 116—118 123—126 Existence of expansions 86—87 116—126 Expansions, theory of 40—49 Extensionalism 35—37 80 Extensions of concepts 36 72—76 89—90 External expansions 97—100 Factorial function 52 75 130 Family resemblance 83—85 Ficbons 11 16 20 134 137 148 Fields, extension of 98—99 Fine, K. 111 114n Finite cardinality 49—50 Forced expansions 15 22 Forced expansions and deducbon 54—57 Forced expansions as rational procedures 58—59 Forced expansions as scientific tools 61 Forced expansions, absolutely forced expansions 56—57 Forced expansions, characterisbcs of 54—59 Forced expansions, existence of 116—126 Forced expansions, generality of 57—58 Forced expansions, logic of 57 Forced expansions, rejecters of 59—63 Forced expansions, strongly forced expansions 44—45 see Forced meaninglessness 46 Formalism 92—96 100—103 104 Foundations of Arithmetic (Frege) 102 Framework for expansions 40—49 Frege, Gottlob 1—2 Frege, Gottlob and formalism 100—103 Frege, Gottlob and Lakatos 92—96 Frege, Gottlob and realism 24—29 74 Frege, Gottlob, determinacy of concepts 30—35 Frege, Gottlob, extensionalism 35—37 Frege, Gottlob, growth of concepts 38—40 Frege, Gottlob, logic, laws of 148 Frege, Gottlob, mathematical proofs 19 Frege, Gottlob, names, expansion of 70—71 Frege, Gottlob, Peano, critique of 81—83 100 Frege, Gottlob, questions and answers 81—83 136 Frege, Gottlob, replacement of concepts 38—39 Frege, Gottlob, Russell's paradox 158—162 162—168 Frege, Gottlob, sense of a sentence 136 140 Frege, Gottlob, thoughts 136 137 138—143 Frege, Gottlob, truth, stretching of 134—148 Frege, Gottlob, Wittgenstein on 144 147 Fruitful expansions 63—71 128 Fruitful expansions, applications of 22 65—66 Fruitful expansions, criteria for 64 70 Fruitful expansions, empty expansions 70—71 Fruitful expansions, examples of 65—71 Fruitful expansions, interpretation of 68—69 Fruitful expansions, representational power 66—68 Functions, analytic functions 31 51—52 57 130 Functions, definitions of 43 81—82 Functions, expansion of 12—15 129—130 Functions, framework for expansions 40—49 Functions, recursive functions 129 Fuzzy logic 32—35 Games and language 83—84 Gauss, Johann 75 77—78 Generality of forced expansions 57—58 Gibson, J.J. 120n Godel, Kurt 20 50 124 Godel, Kurt on theory of types 152—153 Godel, Kurt, arguments compared 123—126 Godel, Kurt, existence of concepts 116—118 126—133 Godel, Kurt, intuition 122—123 Godel, Kurt, paradoxes 58 154 Godel, Kurt, Parsons on 123—125 Godel, Kurt, perception 119—123 123—126 Grasping concepts 25 28—29 74—76 86 Grasping thoughts 134—138 Greek model of mathematics 9 78 Gregory, Duncan 18 groups 18 Growth of concepts 38—40 Gupta, H. 111 Hamilton, William 18 108 Hankel, Hermann 19 101 Hilbert, David 19 20 21 58 88n Hinbkka, Jaakko 121 Hypotheses and expansions 69—70 Idealism 62 Identity criteria of extensions 36 Identity of objects 102 105 Identity relation 98—100 Illusions in logic 159—162 Illusions in paradoxes 153—156 161 Illusions in perception 120 Illusions in set theory 156—158 Imaginary names 111—114 imaginary numbers 11 see Imaginary sentences 111—115 Inchoate expressions 165—168 Inchoate expressions, DP 153; 157 Inchoate expressions, set of all sets 156—158 Inchoate thoughts 139—143 '73~4 Inclination to accept 145—146 Indefiniteness 46 Infinite cardinality 49—50 Infinite sets 2 65 125 166 infinity 119—120 Integers 63—64 intelligence tests 58—59 Intensionalism 72—73 89 148 Internal expansions 41 97—100 Internal expansions, forced 42—43 Internal expansions, strongly forced 44—45 Interpretation of expansions 68—69 Intuitionism 21 117—118 121—123 Judgement of truth-value 134—138 Kant, Immanuel 16 62 121—122 Kant, Immanuel, antinomies ix 21 149 151—156 166 Klein, Felix 3 Kripke, Saul 58 75—76 Kronecker, Leopold 109 118 Kuhn's theory 76—77 Lakatos, Imre 90—96 Language and community 28—29 Language and games 83—84 Language and mathematics 22—23 Language and thought 160—162 Language, changes in 22—23 90—91 Language, inter subjectivity of 27 Language, logic of 82—83 Language, nature of 16 Language, philosophy of 22 90 91 Laws that force expansions 52 Laws, expansions of 58—59 168 Laws, preservation in expansions 2 17—19 103—109 127—128 Lebesgue, Henri 57 65 127—128 Leibniz, Gottfried, n 13—14 66n 106 Liouville, Joseph 65 Logarithm function 13—14 130n 157 Logic 19 20—21 Logic of expansion 40—53 58 59 Logic, consistency of 158—162 Logic, illusions in 159—162 Logic, inchoate expressions 165—168 Logic, partially defined predicates 30—35 147—148 Logic, philosophy of 58 169 Lorenz transformations 79 Maddy Penelope 12 Maimon, Solomon 15—16 155 Manders, K. 22 Mass, change in concept of 78—80 Mathematical objects 20 97—115 102—106 129 132 Mathematics and language 22—23 Mathematics, analytical continuation 31 Mathematics, debates in 9—15 Mathematics, fiction 11 16 20 Mathematics, Kuhn's theory 76—77 Mathematics, logic of 147 Meaningful sentences 142—143 150—158 see Meaninglessness metaphysics 16 27 Model theory 98—100 108 Modern mathematics 2 57 Modern mathematics and physics 22 76 Modern mathematics, revolutions in 21 76—80 see Momentum 78—80 Monads 12 Multiplication, laws of 19 Names 82 160 Names and sentences 70—71 Names, imaginary 111—114 Names, new 110—115 Names, unique references for 162—164 Natural numbers 109 Nature 62 148 negative numbers 10 106—109 Newtonian concept of mass 78—80 Normativity of expansions 62—63 62—63 Notation 19 81—82 NUMBER 50 Number, expanding the system 101—103 Number, fruitful expansions, rule for 66 Number, uniqueness of expansion 120 127 Number, very large numbers 88—89 Number, Wittgenstein on 83 171 Objectivity of concepts 25—28 Objects see mathematical objects Occam's razor 86 Ordinals 120 Ordinals as expansion of predicate calculus 109—115 Paradigm shifts 12 76—80 Paradoxes 14 58 Paradoxes, axioms and 165—166 Paradoxes, dichotomy picture (DP) 149—158 Paradoxes, illusions in 153—156 Paradoxes, set theory 21 168 Parsons, Charles 123—125 Pascal, Blaise 10 107 Peacock, George 3 17—20 52 Peano, Giuseppe 19 81—83 100 Perception of propositions 124 Perception ofconcepts 119—123 123—126 131—132 Philosophy 20—23 Philosophy of language 22 90 91 Philosophy of logic 58 169 Philosophy of mathematics 12 119 133 Physics 1 22 76 Polyhedra, theory of 90—91 95 Positional system of numbers 67 Positivist principle 151 Power function 2 51 73 88—89 98 Predicate calculus 40—51 111—115 predicates 82 Predicates, partially defined 30—35 147—148 Principle of the permanence of equivalent forms 3 17—20 52 Procedure of expansions 3 12—15 19—20 Products of expansions 3 9—15 97—115 Proofs 19—20 22—23 65—68 173 Proofs and Refutations: The Logic of Mathematical Discovery (Lakatos) 90 Proofs of propositions, sense and 143—148 Proofs, Lakatos 90—96 Proper names see names Propositions 123—124 Putnam, Hilary 21—22 75—76 Quadratic equations 10 Quaternions 18 108 Questions and answers, sense of 136—138
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