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Buzaglo M. Ч Logic of Concept Expansion
Buzaglo M. Ч Logic of Concept Expansion

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Ќазвание: Logic of Concept Expansion

јвтор: Buzaglo M.


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.

язык: en

–убрика: ‘илософи€, религи€ и культура/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2002

 оличество страниц: 194

ƒобавлена в каталог: 23.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
"essence" of a concept      83Ч85
"Following a rule"      144
"Inertia, Law of"      25
"Unsaturated" concepts      83
"What is Cantor's Continuum Problem?Ф (Goedel)      127
Absolutely forced expansions      56Ч57
Addition, laws of      19
Algebra      9 15Ч18 67 69
Algebra of negative numbers      106Ч109
Algebra, extension of fields      98Ч99
Alster, Gall      62n
Ambiguous sentences      142
Analogies      146Ч147 171
Analytic functions      31 51Ч52 57 130
Antinomies      ix 21 149 151Ч156 158n 166
Applications of expansions      22 65Ч66
Aristotle      27 78
Arithmetic      2 3 15 16Ч18 88Ч89
Arnauld, Antoine      10
Axioms from constraints to      103Ч109
Axioms of comprehension      167
Axioms of logic      152
Benacerraf, Paul      114
Berkeley, George      11
Bernoulli, Johann      13Ч14 60
Boole, George      19
Boolos, George      162n
Boundaries      87Ч90 150Ч153
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      146Ч147 148
Cardinality      44 49Ч50 65 125
Cauchy's integral formula      67Ч68
Chain of extension      73 75Ч76 78
Characteristics of concepts      74
Characteristics of forced expansions      54Ч59
Classifying expressions      163Ч168
Cognition      15
Cohen, Paul      50
Community and concepts      28Ч29
Commutative law      18 108
complex numbers      51 69 108 109
Complex numbers, acceptance of      10Ч12
Complex numbers, Cauchy's formula      67Ч68
Compositionality      32 34Ч35
Computability      121
Conjunction      19
Consistency after expansion      101 159 162Ч163
Constraints      103Ч109 143
Context of discovery      103
Cosine function      85
De Moivre's theorem      69
Decomposition      34Ч35 67
Dedekind, Richard      19
Deduction      3 23 54Ч57 59 60Ч63 95
Definitions and family resemblance      83Ч85
Demarcation problem      150Ч153
Denumerable sets      65Ч66
Determinacy of concepts      30Ч35
Diamond, Cora      31Ч35 145 147
Dichotomy picture (DP)      150Ч158
Differentials      11
Dilemmas      170Ч171
Disjunction      19
Dummett, Michael      30Ч31 70Ч71 101n 158n
EI (existential instantiation) law      110Ч115
Einstein, Albert      21
Embedded expansions      39Ч40
Empty expansions      70Ч71
Equabons, expansion of      100
Equality      100 105
Equivalent forms, principle of the permanence of      3 17Ч20 108
Euler, Leonhard      14 90Ч91 130n
Excluded middle, law of      20Ч21 58 173
Existenbal instanbabon (EI) law      110Ч115
Existence of concepts      116Ч118 123Ч126
Existence of expansions      86Ч87 116Ч126
Expansions, theory of      40Ч49
Extensionalism      35Ч37 80
Extensions of concepts      36 72Ч76 89Ч90
External expansions      97Ч100
Factorial function      52 75 130
Family resemblance      83Ч85
Ficbons      11 16 20 134 137 148
Fields, extension of      98Ч99
Fine, K.      111 114n
Finite cardinality      49Ч50
Forced expansions      15 22
Forced expansions and deducbon      54Ч57
Forced expansions as rational procedures      58Ч59
Forced expansions as scientific tools      61
Forced expansions, absolutely forced expansions      56Ч57
Forced expansions, characterisbcs of      54Ч59
Forced expansions, existence of      116Ч126
Forced expansions, generality of      57Ч58
Forced expansions, logic of      57
Forced expansions, rejecters of      59Ч63
Forced expansions, strongly forced expansions      44Ч45 see
Forced meaninglessness      46
Formalism      92Ч96 100Ч103 104
Foundations of Arithmetic (Frege)      102
Framework for expansions      40Ч49
Frege, Gottlob      1Ч2
Frege, Gottlob and formalism      100Ч103
Frege, Gottlob and Lakatos      92Ч96
Frege, Gottlob and realism      24Ч29 74
Frege, Gottlob, determinacy of concepts      30Ч35
Frege, Gottlob, extensionalism      35Ч37
Frege, Gottlob, growth of concepts      38Ч40
Frege, Gottlob, logic, laws of      148
Frege, Gottlob, mathematical proofs      19
Frege, Gottlob, names, expansion of      70Ч71
Frege, Gottlob, Peano, critique of      81Ч83 100
Frege, Gottlob, questions and answers      81Ч83 136
Frege, Gottlob, replacement of concepts      38Ч39
Frege, Gottlob, Russell's paradox      158Ч162 162Ч168
Frege, Gottlob, sense of a sentence      136 140
Frege, Gottlob, thoughts      136 137 138Ч143
Frege, Gottlob, truth, stretching of      134Ч148
Frege, Gottlob, Wittgenstein on      144 147
Fruitful expansions      63Ч71 128
Fruitful expansions, applications of      22 65Ч66
Fruitful expansions, criteria for      64 70
Fruitful expansions, empty expansions      70Ч71
Fruitful expansions, examples of      65Ч71
Fruitful expansions, interpretation of      68Ч69
Fruitful expansions, representational power      66Ч68
Functions, analytic functions      31 51Ч52 57 130
Functions, definitions of      43 81Ч82
Functions, expansion of      12Ч15 129Ч130
Functions, framework for expansions      40Ч49
Functions, recursive functions      129
Fuzzy logic      32Ч35
Games and language      83Ч84
Gauss, Johann      75 77Ч78
Generality of forced expansions      57Ч58
Gibson, J.J.      120n
Godel, Kurt      20 50 124
Godel, Kurt on theory of types      152Ч153
Godel, Kurt, arguments compared      123Ч126
Godel, Kurt, existence of concepts      116Ч118 126Ч133
Godel, Kurt, intuition      122Ч123
Godel, Kurt, paradoxes      58 154
Godel, Kurt, Parsons on      123Ч125
Godel, Kurt, perception      119Ч123 123Ч126
Grasping concepts      25 28Ч29 74Ч76 86
Grasping thoughts      134Ч138
Greek model of mathematics      9 78
Gregory, Duncan      18
groups      18
Growth of concepts      38Ч40
Gupta, H.      111
Hamilton, William      18 108
Hankel, Hermann      19 101
Hilbert, David      19 20 21 58 88n
Hinbkka, Jaakko      121
Hypotheses and expansions      69Ч70
Idealism      62
Identity criteria of extensions      36
Identity of objects      102 105
Identity relation      98Ч100
Illusions in logic      159Ч162
Illusions in paradoxes      153Ч156 161
Illusions in perception      120
Illusions in set theory      156Ч158
Imaginary names      111Ч114
imaginary numbers      11 see
Imaginary sentences      111Ч115
Inchoate expressions      165Ч168
Inchoate expressions, DP      153; 157
Inchoate expressions, set of all sets      156Ч158
Inchoate thoughts      139Ч143 '73~4
Inclination to accept      145Ч146
Indefiniteness      46
Infinite cardinality      49Ч50
Infinite sets      2 65 125 166
infinity      119Ч120
Integers      63Ч64
intelligence tests      58Ч59
Intensionalism      72Ч73 89 148
Internal expansions      41 97Ч100
Internal expansions, forced      42Ч43
Internal expansions, strongly forced      44Ч45
Interpretation of expansions      68Ч69
Intuitionism      21 117Ч118 121Ч123
Judgement of truth-value      134Ч138
Kant, Immanuel      16 62 121Ч122
Kant, Immanuel, antinomies      ix 21 149 151Ч156 166
Klein, Felix      3
Kripke, Saul      58 75Ч76
Kronecker, Leopold      109 118
Kuhn's theory      76Ч77
Lakatos, Imre      90Ч96
Language and community      28Ч29
Language and games      83Ч84
Language and mathematics      22Ч23
Language and thought      160Ч162
Language, changes in      22Ч23 90Ч91
Language, inter subjectivity of      27
Language, logic of      82Ч83
Language, nature of      16
Language, philosophy of      22 90 91
Laws that force expansions      52
Laws, expansions of      58Ч59 168
Laws, preservation in expansions      2 17Ч19 103Ч109 127Ч128
Lebesgue, Henri      57 65 127Ч128
Leibniz, Gottfried, n      13Ч14 66n 106
Liouville, Joseph      65
Logarithm function      13Ч14 130n 157
Logic      19 20Ч21
Logic of expansion      40Ч53 58 59
Logic, consistency of      158Ч162
Logic, illusions in      159Ч162
Logic, inchoate expressions      165Ч168
Logic, partially defined predicates      30Ч35 147Ч148
Logic, philosophy of      58 169
Lorenz transformations      79
Maddy Penelope      12
Maimon, Solomon      15Ч16 155
Manders, K.      22
Mass, change in concept of      78Ч80
Mathematical objects      20 97Ч115 102Ч106 129 132
Mathematics and language      22Ч23
Mathematics, analytical continuation      31
Mathematics, debates in      9Ч15
Mathematics, fiction      11 16 20
Mathematics, Kuhn's theory      76Ч77
Mathematics, logic of      147
Meaningful sentences      142Ч143 150Ч158 see
Meaninglessness metaphysics      16 27
Model theory      98Ч100 108
Modern mathematics      2 57
Modern mathematics and physics      22 76
Modern mathematics, revolutions in      21 76Ч80 see
Momentum      78Ч80
Monads      12
Multiplication, laws of      19
Names      82 160
Names and sentences      70Ч71
Names, imaginary      111Ч114
Names, new      110Ч115
Names, unique references for      162Ч164
Natural numbers      109
Nature      62 148
negative numbers      10 106Ч109
Newtonian concept of mass      78Ч80
Normativity of expansions      62Ч63 62Ч63
Notation      19 81Ч82
NUMBER      50
Number, expanding the system      101Ч103
Number, fruitful expansions, rule for      66
Number, uniqueness of expansion      120 127
Number, very large numbers      88Ч89
Number, Wittgenstein on      83 171
Objectivity of concepts      25Ч28
Objects      see mathematical objects
Occam's razor      86
Ordinals      120
Ordinals as expansion of predicate calculus      109Ч115
Paradigm shifts      12 76Ч80
Paradoxes      14 58
Paradoxes, axioms and      165Ч166
Paradoxes, dichotomy picture (DP)      149Ч158
Paradoxes, illusions in      153Ч156
Paradoxes, set theory      21 168
Parsons, Charles      123Ч125
Pascal, Blaise      10 107
Peacock, George      3 17Ч20 52
Peano, Giuseppe      19 81Ч83 100
Perception of propositions      124
Perception ofconcepts      119Ч123 123Ч126 131Ч132
Philosophy      20Ч23
Philosophy of language      22 90 91
Philosophy of logic      58 169
Philosophy of mathematics      12 119 133
Physics      1 22 76
Polyhedra, theory of      90Ч91 95
Positional system of numbers      67
Positivist principle      151
Power function      2 51 73 88Ч89 98
Predicate calculus      40Ч51 111Ч115
predicates      82
Predicates, partially defined      30Ч35 147Ч148
Principle of the permanence of equivalent forms      3 17Ч20 52
Procedure of expansions      3 12Ч15 19Ч20
Products of expansions      3 9Ч15 97Ч115
Proofs      19Ч20 22Ч23 65Ч68 173
Proofs and Refutations: The Logic of Mathematical Discovery (Lakatos)      90
Proofs of propositions, sense and      143Ч148
Proofs, Lakatos      90Ч96
Proper names      see names
Propositions      123Ч124
Putnam, Hilary      21Ч22 75Ч76
Quadratic equations      10
Quaternions      18 108
Questions and answers, sense of      136Ч138
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