A posteriori, 45, 47, 64

A priori, 47, 59, 64, 115, 118, 147, 150, 151, 163, 170-71, 173, 182, 188, 190, 191, 194, 205, 228, 233, 244

Abortion, 10, 91

Abstract objects. See Ideal entities; Mathematical entities

Abstraction, categorial (formal), 207, 208, 226-30, 281

Abstraction, generalizing, 226-29

Abstraction, logical, 67-94, 96

Abstraction, psychological, 67, 95-98, 103, 104, 109-32, 137, 141-43, 145, 148, 150, 154, 156, 281

Abstraction and properties, 68-71, 96-98, 111-12, 114, 115, 120,125-26, 141-43, 145, 150, 154, 155, 237

Abstractness, 60, 63-64, 65, 72, 97, 103, 115, 120, 145, 148, 173, 188, 190-91, 193, 209, 210, 225, 249-50, 263-89. See also Platonism

Absurdity, 7, 28, 71, 102, 125, 143, 148, 194, 213. See also Nonsense

Actual world. See World

Against will, 68, 146

Alexander the Great, 46, 47, 48, 49, 60, 61, 256, 259

Algebra, 3, 55, 62, 63, 128, 146, 164, 181, 184, 205, 246, 281

All, 8, 85, 86, 87, 91, 148, 236

Ambiguity, 9, 76, 89, 90, 92, 102, 128, 149, 164, 165, 168, 179, 186

Analysis, mathematical, 2, 123, 128, 139, 140, 156, 157, 166, 173, 184

Analyses, psychological, 109, 123-29, 144-45, 163-66, 173

Analytic philosophy, xi-xiv, 2, 47, 199, 265, 284,

Analyticity, 2, 3, 4, 42, 46, 59, 128, 146, 164-67, 170-75, 182, 188-91, 194, 202, 204, 212, 230-32, 235, 238, 250

Analyzing away, 81, 82, 88. See also Vanish, making

Angelelli, Ignacio, 32

Antinomies of set theory, 89, 128, 155, 166, 268. See also Russell's paradoxes

Aquinas, Saint Thomas, 138

Aristotelian logic, 162, 168, 171, 172, 180

Aristotle, 42, 46, 96, 116, 117, 120, 126, 138, 143, 149, 162, 172, 259

Arithmetization, 115, 123-24, 126, 127, 137, 139-41, 145, 152, 156, 157, 167

Assertive sentences, 23, 26, 29, 34, 35, 36, 240, 248

Associativity, 37, 258

Astronomy, 77

Attributes. See Properties

Augustine, Saint, 138

Axiom of Choice, 54, 55, 63, 210, 242-44, 249, 251, 253, 259-61, 284

Axiom of Completeness, xii, 179-80, 185, 186-87

Axiom of Reducibility, 17, 86-88

Axiomatization, 2, 161-78, 179-95, 260, 269, 271, 272

Axioms, 9, 59, 139, 153, 169, 170, 174, 175, 179, 182, 185, 186, 187, 190, 191, 200, 202, 248, 265, 272, 273

Bacon, Francis, 138

Barwise, Jon, 65

Basic Law V, 12-15, 58-59, 65, 73-77, 88, 100, 101, 201, 210-14. See also Russell's Paradox

Beauty, 88, 89, 121

Beeson, Michael, 244

Benacerraf, Paul, 243, 253, 263, 264, 269, 270-78, 284

Beth, Evert, 199

Black holes, 275

Blindness, 75, 92, 172

Boethius, 138

Bolzano, Bernard, 2, 3, 32, 121, 129, 130, 131, 151, 157, 181, 188, 189, 200

Boole, George, 8, 74

Bourbaki school, 32, 204, 272, 281

Brentano, Franz, 2-4, 103-4, 107, 109, 122-23, 127-29, 137-38, 144-45, 147, 150, 155-56, 161, 163, 166, 180-82, 192

Brouwer, Luitzen, 247

Brown, James R., 267-69, 275, 277, 286

Burgess, John, 275, 277

Calculus of variations, 185

Cantor, Georg, xi, 2-4, 67, 95-107, 109-35, 137-57, 161, 164-66, 173, 181, 185, 194-95, 200, 205, 221, 235-36, 254, 283

Cardinal numbers. See Numbers, cardinal

Cardinality spectra, 246

Carnap, Rudolf, 33, 37, 39, 203, 216-17, 232, 271

Categorial acts, 224-34, 256, 280. See also Intuition, categorial

Categorial concepts, 166, 170, 229

Categorial elements, 206, 207

Categorial objects, 35, 38, 65, 166, 224, 226, 280. See also Objectualities

Categoriality, 227-31, 246

Category theory, 205, 239, 281

Caton, Charles, 43

Cats, 97, 98

Cauchy sequences, 271

Causality, 151

Causal theory of knowledge, 221, 253, 264, 266, 269, 274-76, 278

Chang-Los-Suszko Theorem, 256

Chess, 168, 183

Church, Alonzo, 1, 28, 36, 61, 210, 211

Church's Theorem, 283-84

Cicero, 49

Classes, 9, 10, 15-17, 67-69, 76, 77, 78, 79-88, 100, 110-12, 119, 122, 141, 143, 155, 243. See also Sets

Classical mathematics, 237, 241, 243-45, 246, 264

Cognition, 147, 191, 266, 269, 271, 276, 281

Cognitive value, 25, 42, 45-47, 250

Coincidence, 6, 11, 62, 63, 64, 70, 120-21

Columbus, Christopher, 5

Coma, 9-10, 91

Compactness Theorem, 242, 249, 266, 282

Completeness, xii, 2, 154, 156, 173, 175, 179-98, 202, 282, 285, 287

Comte, Auguste, 138

Concepts, 27, 28, 34, 41, 46-47, 67, 73-78, 81-82, 88, 97, 99, 100, 101, 103, 111-13, 115-22, 123, 124, 128, 144, 147, 150, 162, 168, 179, 187, 190, 191, 194, 203, 208, 229, 254- 55. See also Extensions

Concepts and objects, 13, 14, 27, 28, 29, 31, 34, 74, 76-77, 79, 81-82, 100, 101, 111, 112, 113, 124-25, 143, 147, 186, 254-55, 272

Concepts, general, 97, 98, 99, 112-13, 114, 116, 124, 125, 126, 141, 142, 147, 149, 154

Conceptual content, 53-56, 58-60, 65, 214-15

Conceptual formation, 110-12, 116, 117, 120, 124-26, 128, 141-44, 145, 147-48, 150, 155

Conceptual knowledge, 119, 149

Conceptual notation, 55, 213, 214

Conceptual words (Begriffswörter), 13, 14, 23, 25-31, 33-34, 41-42, 208, 254, 255, 271

Confusion, 2, 14, 17, 23, 33, 35, 38, 55, 56, 58, 60, 65, 85, 89, 90, 91, 92, 101, 104, 122, 126, 148, 149, 163, 164, 172, 174, 194, 202, 208, 210, 215, 217, 252

Consciousness, 103, 114, 116, 117, 126, 128, 131, 137, 144, 146-51, 157, 164, 166, 171-72, 234

Consistency, 79, 118, 153, 155, 156, 181-82, 185-89, 190, 212, 230, 233, 269, 277, 279, 283, 284-85, 287. See also Contradictions

Constitution, 149, 163, 172, 206-8, 222-39, 256, 257, 280, 281

Constructivism, 221, 233, 236, 244, 245, 247, 251, 284

Content, 54, 70, 85, 96, 125, 126, 127, 129, 143, 145, 147, 155, 169, 183, 184, 192, 212, 231, 261, 284

Contingency, 47-49, 269, 275, 276

Contradictions, 16 -17, 67-68, 75-80, 83-86, 88-90, 101, 118, 121, 128-29, 144-45, 148, 150, 155, 166, 170, 171, 172-73, 175, 182-83, 185-86, 187, 188, 190-91, 203, 232, 233, 236-37. See also Russell's paradox; Antinomies of set theory

Convenience, 32, 69, 82, 86, 88, 90, 92, 181, 270, 275, 276, 278

Counterfactuals, 48

Courses-of-values, 7, 13, 58-59, 73, 201, 211, 213

Couturat, Louis, 1, 114-15

da Silva, Jairo, 176, 195

Dauben, Joseph, 153

Decidability, 266, 282-84

Dedekind, Richard, 3, 96, 113, 115, 123, 129, 140, 155, 157, 271, 272

Deduction, 3, 116, 117, 144, 153, 156, 167, 168-70, 172, 174, 175, 183, 189-91, 202-3, 260, 261

Deductive systems, 153, 156, 161, 165, 169-73, 179-98

Definite article, 14-16, 18, 78, 82. See also Descriptions

Definite descriptions, theory of, 14-18, 82-83, 84

Demjanjuk, Jan, 9, 11

Democritus, 138

Denoting, 15, 16, 18, 24, 25, 27, 29, 34, 43, 183. See also Reference

Deontic contexts, 89

Descartes, René, 138

Descriptions, 12, 14-18, 24-25, 32, 36, 41-42, 46, 48, 49, 50, 68, 71, 75, 76, 78, 82-84, 271

Diabetes, 91

Doubts, 18, 77, 88, 99, 109, 127, 128, 145, 154, 155, 165, 166, 173, 188, 284

Duhem thesis, 265, 285

Dummett, Michael, 2, 3, 12, 18, 26, 38, 43, 44, 199, 212-13, 251

Eberle, Rolf, 243

Eidos, 116-17, 121, 149, 151, 157

Eleatic One, 120

Empirical considerations, 42-43, 46-47, 89-90, 101, 114, 120, 149-50, 153, 164, 168, 173, 186, 194, 206-8, 246-47, 256, 264, 268, 279

Empiricism, 2, 101-4, 114, 115, 117, 120, 144-45, 157, 221, 245, 246-47, 253, 256, 263, 265, 269, 274, 275, 276, 279, 280, 284

Epistemic contexts, 89

Epistemology, 1, 18, 116, 138, 146, 148, 164, 172, 187, 191, 192, 194, 201, 202, 206-8, 221-40, 246, 247, 250, 253-54, 264, 266, 267, 269, 273-79

Equality, 6-11, 13-14, 68-94, 101, 193

Equals sign. See Identity sign

Equiderivability. See Interderivability

Equipollency. See Interderivability

Equivalence, 7, 11, 33, 37, 39, 55, 62, 63, 68, 71, 82, 83, 86, 87, 90, 97, 111, 114, 142, 179, 189, 210, 253, 257, 259, 260, 270, 284

Equivalence, lesser forms of, 88-92, 193. See also Equality

Equivalence classes, 36, 38, 46, 65, 237, 257, 258, 271, 272, 281

Equivalent functions, 11, 17, 80-81, 83-86, 100

Equivalent propositions, 10, 11, 225, 241-52, 257. See also Interderivability

Essence, 151, 154, 162, 190, 194

Euclid, 116, 124, 149, 154, 169-70, 189, 205, 268

Euthanasia, 9-10, 91-92

Experience, 101, 103, 114, 115, 116, 117, 118, 123, 124, 130, 144, 162, 191, 192, 206, 208, 265, 267, 268, 269. See also Sensory experience

Extensionality, 9, 13, 15, 17-18, 67-92, 95, 99-101, 155, 183-84, 188, 193, 194, 248, 250, 270

Extensions, 5, 7, 8, 10, 11, 14, 27-28, 31, 33-34, 39, 41, 46-47, 67-92, 99-101, 104, 147, 154, 184, 200-201, 208, 271-72

Fake objects, 78, 82

Fallacy, 79, 85, 87

Fatal flaws, 12, 77-78

Fiction, 81-82, 268-70, 276, 278-79

Field, Hartry, 263, 270, 271, 275, 276-79, 284-86

Fingers, 112, 124, 142, 144

First-order languages, 242, 265, 266, 267, 272-73, 282-85, 287

Føllesdal, Dagfinn, xiii, 32, 33, 194, 199

Formal logic, 92, 156-57, 161-62, 168, 169, 171-73, 182, 187-93

Formal reasoning. See Symbolic reasoning

Formalism, 179-82, 183-85, 189, 193, 243, 244, 284

Formalization, 3, 153, 169, 170, 186, 188, 190, 207, 208, 238, 265, 266, 272, 273, 274. See also Symbolic reasoning; Abstraction, categorial

Forms, 115-17, 120, 126, 143, 149, 154, 162, 168-70, 174-75, 189-90, 205, 223, 228-31, 256

Freedom, 118, 120, 146, 150, 153, 169-171, 175, 181, 189, 191, 230, 231, 246

Frege, Gottlob

abstraction, 67, 69-73, 81, 82, 84, 85, 88, 95, 96-98, 114

Basic Law V (Principle V), 12-15, 58-59, 65, 67, 73-77, 88, 100-101, 201, 210-14

concepts, 5, 7, 13, 14, 26-31, 54-55, 67, 73-74, 81-82, 99-101, 104, 200, 208, 254, 271-72

criticism of Cantor, 95-104, 114

criticism of Husserl, xiii, 1, 32, 67-68, 73, 95-104, 114, 199

descriptions, 14-15, 24, 41-42, 48, 71, 78, 82

extensions, 5, 7-8, 10, 13-14, 27-28, 31, 41, 67, 68, 73-79, 81-82, 84, 85, 88, 99-101, 104, 184, 200-201, 208, 250, 271-72

formalism, 183-85, 243

Husserl's criticisms of, 1, 4-5, 8-12, 17, 19, 92, 100, 104, 172, 183-85, 193, 199

identity, 2, 5-8, 12-15, 25, 27, 38, 41-51, 57, 58, 69-77, 79, 81, 82, 85, 87-88, 100, 101, 183, 193, 201, 211, 212, 214, 250

letters, 4, 25, 30-32, 56, 57, 67, 100, 183, 185, 200, 214

meaning, xiii, xiv, 23-40, 41-52, 53-66, 102, 183-84, 193, 199-202, 208-15, 248-50, 254-55, 258

Platonism, 200-202, 221, 247-48, 254, 284

psychologism, xiii, xiv, 4, 32-33, 67, 95-98, 101-4, 114, 199-201, 245

Russell's paradox, 1, 10, 12-15, 17, 67, 76-78, 80, 82, 84, 88, 100-101, 129, 155, 157

semantics, xiii, 38, 41-51, 58, 60-61, 210, 214, 215, 248, 250, 254-55, 258

substitution, 5-8, 11-12, 15, 17, 27, 28, 29, 30, 56, 60, 61, 65, 70, 74, 75, 77, 85, 88, 100, 201, 209, 211, 213, 214, 250

theory of number, 1, 5-15, 69-78, 98-102, 200, 201, 214

Functions, 2, 13, 26-28, 41, 58, 73-74, 80-81, 83-85, 86, 87-88, 90, 140, 146, 201, 211, 242, 272

Galileo, 269,

Gallagher, William, 132, 157

Gauss, Carl Friedrich, 115

Genealogy of logic, 163, 171, 172

Genetic engineering, 273

Geometry, 2, 72, 116, 139, 145, 149, 169-70, 171, 172, 185, 189-90, 200, 202, 236, 247, 268, 275

God, 121, 122, 139, 149, 150

Gödel, Kurt, 18, 157, 161, 180, 202, 221, 252, 253-54, 264

Göttingen Mathematical Society, 153, 185-87

Goldman, Alvin, 275

Grassman, Hermann, 113

Grattan-Guinness, Ivor, 106, 132, 153, 157

Group theory, 241

Gupta-Herzberger-Belnap revision theory of truth, 274

Hale, Bob, 277, 279, 286

Hausdorff space, 242, 250

Helmholtz, Hermann von, 113, 115, 205

Henkin nonstandard semantics, 282-84

Henkin's theorem, 256

Hermite, Charles, 121, 138, 149

Hilbert, David, xi, xii, 4, 32, 129, 155, 173, 179-98

Hintikka, Jaakko, xiii, 89, 194,

Horizons, 157

Hume, David, 32, 166

Husserl, Edmund

abstraction, 67, 95-98, 104, 109-32, 137, 143, 154, 156, 162, 168-71, 190-91, 193

and analytic philosophy, xi-xiv, 2, 180, 193, 199-200

analyticity, 4, 128, 146, 164, 166-67, 170-75, 182, 188-90, 194, 202, 204, 230-32, 238

arithmetization, 123-24, 126, 127, 137, 139-41, 145, 152, 156, 157, 167

axiomatization, 161-76, 179-95

categoriality, 35, 38, 166, 170, 206-9, 222, 223-37, 246, 256, 280-81

epistemology of mathematics, 146, 148-49, 172, 187, 191-92, 164, 202, 206-8, 221-39, 247, 250, 254, 279-81, 287

extensionality, 9, 17, 95, 100, 155, 183, 188, 193, 194

extensions, 5, 33, 34, 67-68, 99-100, 104, 124, 147, 154, 155

formalism, 79, 180-85, 189, 192, 193

ideal entities, 162, 164, 172, 173, 180, 184, 185, 188, 190, 191, 193, 194, 203, 239

idealism, 104, 122, 123, 127-31, 137, 149, 150-51, 157, 162-63, 164, 170, 172, 182, 188

identity, 1, 8-12, 33, 92, 100, 183, 193, 194, 214

imaginary numbers, 127-28, 148, 151-54, 156, 157, 167, 168, 174-75, 180-87

letters, 4, 25, 30-32, 56-57, 167, 183, 185, 200, 204, 214

manifolds, multiplicities (Mannigfaltigkeiten), 128, 137, 154-57, 161-78, 179-98, 205

meaning, xi, xiii, xiv, 23-40, 59, 101-2, 130, 153, 169, 172, 174-75, 181-83, 184, 188-89, 191, 193, 194, 199-204, 208-10, 214, 222-23, 228, 230-35, 238, 254-58, 271

objectivity, xi, xiii, 32, 101, 103, 127, 128, 145, 162, 163, 164, 165, 166, 168, 170, 171, 172, 182, 188, 189, 191, 192, 193, 225, 232. See also Objectualities

Platonism, 109-29, 130, 131, 150-51, 157, 166, 202-20, 221, 233, 234, 247, 250, 254

psychologism, xiii, xiv, 4, 32-33, 95-98, 101-4, 109, 115, 122-29, 131, 137, 144-46, 151, 154-55, 156, 157, 163-66, 171, 172-74, 182 183, 185, 187, 192, 193, 199-201, 245

pure logic, 103, 128, 137, 146-49, 151, 154, 157, 161, 162, 164, 166, 168, 171, 172, 173, 182, 185, 189, 190, 191, 193, 232, 238

semantics, xiii, 38, 60-64, 202-3, 210, 213, 214, 215-16, 249, 250, 254-56, 258

sets, xi, 96-97, 99, 101-4, 109, 123, 124-28, 137, 138, 143, 146-48, 152, 154-57, 161, 165-66, 168, 173, 191, 202, 204, 205, 207, 224, 225, 226, 229, 235-37, 256, 280

situations of affairs, 30, 34-38, 59-60, 63-64, 65, 207, 208-15, 224-27, 249-51, 253-61, 280

states of affairs, 23, 30, 34-38, 59, 61, 63-64, 65, 168, 191, 206-15, 222-28, 248, 249, 250, 253-61, 279, 280

supposed influence of Frege, xiii, xiv, 23, 32, 33, 95, 157, 180, 183-85, 199-200, 202

Ideal entities, 50, 71, 115-16, 120, 130, 145, 147, 162-64, 172, 173, 180, 184, 185, 188, 190-91, 193, 194, 201-2, 234, 239, 243, 249. See also Mathematical entities; Numbers, ideal; Things in themselves

Idealism, 50, 103, 104, 109-24, 127-31, 137, 145, 149-51, 157, 162-64, 172, 180-81, 182, 188, 193, 194, 228, 230, 231, 239. See also Platonism

Idealization, 102, 109-32, 147

Ideas (Ideen) 103, 115, 116-22, 129-31, 144, 148-51, 157

Identity, 1-19, 25, 27, 33, 38, 41-51, 56, 58, 59, 68-94, 100, 163, 183, 193, 194, 201, 211, 212-14, 250, 257, 258, 260

Ima, Emiko, 132, 157

Imaginary concepts, 148, 152-57, 168, 174-75, 182, 183, 184, 185-87, 194. See also Numbers, imaginary

Incomplete symbols, 16, 18, 82, 84, 85

Independent entities, 5, 6, 69, 80, 81-83, 84, 168

Indeterminacy, 77, 99-100, 121-22, 124, 169, 189, 230, 231, 245, 246, 281, 282, 284

Individuals, 69, 85, 88, 143, 169, 243

Inference, 7, 59, 71, 75, 79, 88, 97, 192

Infinite, paradoxes of, 2, 129

Infinity, 2, 3, 85, 110-13, 118-19, 121, 127, 129, 140, 142, 146-49, 152, 153, 157, 158, 170, 171, 175, 184, 189, 190, 239, 244. See also Infinite sets

Informativeness, 38, 75, 83, 244, 250, 251

Intellectual crisis, 67-68, 78-79, 127-29, 137, 146, 149, 154, 157, 161, 164-68, 171

Intensionality, 2, 89, 90-92, 194

Intensions, 11, 39, 88, 89, 92, 194

Intentionality, 2, 144, 156, 162, 180, 192

Interderivability, 55-57, 63, 210, 214, 241-52, 253, 260, 261, 284, 285

Intuition, 101, 103, 115-16, 144-45, 147-49, 156-57, 162, 170, 191-92, 207-8, 222, 223-24, 228-29, 233, 238-39, 249, 257, 269, 277. See also Mathematical intuition; Objects and intuition; Sensory experience

Intuition, categorial, 207, 208, 222-27, 229, 230-33, 235-37, 269, 280-82

Intuition sensible, 101, 207, 208, 222-31, 234, 280-82

Intuitionism, 244, 247, 251

Invariance, 30, 35, 36, 37-38, 40, 61, 62, 63, 65, 201, 209-11, 225

Irvine, A. D., 277

Jourdain, Philip, 77

Judgeable content, 54-55, 58

Kant, Immanuel, 138, 166, 167, 182, 189, 200, 201, 205, 208, 232, 247, 251, 254

Kantianism, 115, 144, 145, 201, 205, 208

Kennedy, Jackie, 10, 11

Kennedy, John, 10, 11, 72, 74-75

Kersey, Ethel, xiii

Khatchadourian, Haig, 43, 48

Kienzle, Bertram, 45

Kitcher, Philip, 246, 263

Klein, Felix, 185

Kripke, Saul, 43, 47-49, 271, 274

Kronecker, Leopold, 113-14

L-equivalency, 33, 37, 39

Landgrebe, Ludwig, 233, 239

Lattices, 63, 242, 243, 245, 246

Leibniz, Gottfried, 1, 6, 8, 9, 10, 12, 15, 70, 74, 87, 88, 138, 166, 182, 189

Lesniewski, Stanislaw, 243

Letters, 4, 25, 30-32, 56, 57, 67, 112, 113, 116, 121, 138, 139, 149, 150, 183, 185, 200, 204, 214

Lindström, Per, 282, 284

Locke, John, 96, 126, 138, 143

Löwenheim-Skolem Theorem, 265-66, 282

Löwenheim-Skolem-Tarski Theorems, 242, 244-45, 282

Löwenheim-Skolem-Tarski Theorems, Upward and Downward, 63, 260

Logic, two sides, 162-63

Logicism, 200-202, 247, 248, 271

Lotze, Hermann, 32, 109, 129-31, 151, 157, 200

Maddy, Penelope, 263

Magic, 76, 81, 84, 98, 114

Manifolds (Mannigfaltigkeiten), 116, 119-21, 128, 137, 146, 149, 151, 154-56, 161-78, 179-98, 205, 273

Mannigfaltigkeitslehre, Cantor's, 102, 103, 110-11, 113, 115-18, 121, 138, 141, 146, 149, 154, 155-56, 165-66, 173

Mannigfaltigkeitslehre, Husserl's, 151, 154, 156-57, 161-78, 179-98, 205

Many-one relation, 25, 27, 35

Marcus, Ruth Barcan, 89-91

Mathematical entities, 50?, 62, 116, 145, 201, 206, 221, 222, 229-37, 243-50, 263-64, 267, 269-79, 281, 284. See also Numbers as objects

Mathematical intuition, 228-30, 236-37, 281, 282

Mathematical statements, 22, 3?, 55, 63, 188, 210, 221, 241-52, 253, 258-61, 267, 273, 274, 276-77, 279, 284-85

Maximal ideals, 24, 53-54, 62-63, 242, 248-49, 259

Meaning, xi, xiii, 16, 101, 169, 172, 174-75, 181, 182, 183-87, 188-90, 200, 201, 202, 203, 208, 209, 194, 203-4, 222-23, 228, 230-33, 235, 238, 258-59, 268-69. See Sense; Reference; Denotation

Medicine, 10, 89, 91-92

Meinong, Alexius, 104, 107

Mereology, 243-44

Metaphysics, 103, 115, 116, 121-23, 129, 131, 137-38, 149-50, 156-57, 188, 222. See also Idealism

Mikton, 116, 121, 149

Mill, John Stuart, 32, 96, 126, 245

Mittag-Leffler, Gösta, 110, 116, 138, 141

Modality, 49, 89, 286

Models, 241, 242, 245, 246, 256, 260, 264-68, 272-73, 282, 285, 287

Mohanty, J. N., xiii, 199

Monroe, Marilyn, 10

Moore, G. E., 2

Moral issues, 10, 89, 91

Multiplicities (Vielheiten). 96, 99, 110, 121, 124, 125, 143, 147, 154, 165, 169. See also Classes; Sets; Manifolds

Mutual subordination, 74, 81-83

Mystery, 57, 79, 103, 115, 148, 149, 181, 186, 189, 199, 222, 245, 264, 269, 281

Mysticism, 103, 121, 129, 138-39, 156

Names, 12, 23, 24, 29, 31, 34, 43, 75, 82, 84, 85, 111, 126, 143, 154, 208, 212, 274

Names, universal, 33-35, 208, 255

Napoleon, 24, 25, 32, 36, 48

Necessity, 42, 43, 45, 47, 48, 49, 58, 63, 68, 76, 78, 81, 88, 99, 111, 113, 121, 123, 125, 140, 141, 142, 147, 175, 179, 182, 190, 191, 247, 253, 275, 276, 277, 278, 279

Negative squares, 167, 181, 184

Newtonian mechanics, 274

Nicolas von Cusa, 138

Noemata, 38, 157

Nominalism, 243-44, 263, 267, 275, 277, 279, 284

Nonabelian group, 37

Nonsense, 7, 29, 45, 49, 71, 72, 75, 81, 89, 153, 174, 181, 186, 203, 232, 238

Notation, 55, 58, 69, 88, 95, 98, 99, 100, 101, 201, 214

Number, theory of, 1, 2, 5-15, 67, 69-78, 95, 96-104, 109, 110-30, 139-57, 163-68, 173-75, 200, 214, 241, 263-65, 270-73

Numbers as objects, 5, 6, 69, 110, 141, 179, 223, 227, 248, 264, 270, 272, 273, 276, 278. See also Mathematical entities

Numbers, cardinal, 97, 98, 103, 111-15, 119, 120, 124, 128, 129, 141, 142, 146, 147, 148, 150, 152, 155, 164, 165, 167, 168, 174, 175, 200-201, 203-5, 232, 236-37

Numbers, ideal (eidetikoi), 116, 117, 120, 121, 150, 180, 184-85

Numbers, imaginary, 119, 124, 127, 131, 151-54, 156, 157, 167-68, 174-75, 180-83, 184, 185-87, 194

Numbers, new, 110, 111, 116, 119, 123, 137, 139, 141, 146-47, 153, 156

Numbers, ordinal, 124, 128, 146, 152, 164, 167, 168, 174, 203-4, 205, 232, 236

Numbers, whole, 100, 110, 116, 118, 119, 120, 121, 122, 124-28, 131, 140-42, 147, 149, 150, 152, 170, 174-75, 181, 183, 187

Objectivity, xi, 60, 103, 127, 128, 145, 149, 162-66, 168, 170-72, 182, 188, 189, 191-93, 232, 234, 248, 264

Objectualities (Gegenständlichkeiten), 23, 24, 25, 33-34, 65, 205, 207-9, 222-26, 228, 230-37, 239, 256-57, 280-81

Observational sentences, 268

One and the Many, 120-22

Ontology, 41, 80, 81, 88, 173, 191, 201-4, 229-30, 236-37, 243, 264, 270-73, 276-78

Organ transplants, 11, 91-92

Organic whole, 119-20,

Oswald, Lee Harvey, 72, 75

Paradoxes. See Russell's paradoxes

Particulars, 9, 69, 79, 99, 118

Peano, Giuseppe, 3, 4, 96, 113, 116, 149, 272

Perception. See Sensory experience

Perry, John, 65

Phenomenology, xi, xii, xiii, 109, 131-32, 137, 138, 149, 151, 157, 171, 172, 187, 192, 194, 202, 217, 233

Plato, 46, 47, 60, 61, 116-22, 130, 138, 149, 150, 200, 254

Platonic Ideas, 103, 109, 117, 118, 121, 129, 130, 131, 149, 151, 157

Platonic theory of recollection, 116, 117, 118, 150

Platonism, 103, 109, 116-22, 129, 130-31, 149-51, 157, 166, 199-220, 221, 233-34, 247-51, 253-54, 263-85

Positivism, 115, 144, 156,

Pragmatic considerations, 36, 37, 88, 265

Predicates, 8, 9, 11, 12, 28, 34, 68-69, 71, 79, 86-87, 90, 92, 111, 162, 168, 274, 280, 283, 284

Presentations (Vorstellungen), 101-4, 111, 115, 117, 119, 129-30, 144, 147, 192

Prime ideal theorem, 259-61

Principle V. See Basic Law V

Proper names, 14, 23-26, 28-35, 38, 41-42, 48-50, 78, 82, 184, 208-9, 250, 254-55

Properties, 8, 10, 44, 68-69, 71, 78, 80, 84-86, 87, 88, 91, 102, 111-15, 194, 206, 245, 250, 272, 273, 279-80. See also Abstraction and properties

Propositions, 8, 9, 10, 34, 35, 37, 59, 65, 130, 168, 171, 175, 179, 181, 185, 186-89, 200, 203, 205, 222, 249, 255, 256, 257, 279

Psychologism, xiii-iv, 4, 32, 33, 95, 98, 101-4, 114-15, 123, 126-27, 129, 131, 137, 143-46, 151, 157, 164-66, 171-72, 174, 182-83, 185, 187, 199-201. See also Empiricism

Psychology, 10, 11, 95, 98, 102, 103, 109, 111, 114, 123, 128, 129, 142, 145, 155, 163, 164, 166, 170, 172-73, 187, 192

Pure logic, 103, 114, 128, 130, 137, 145-49, 151, 154, 157, 161-62, 164, 166, 168, 171-73, 182-83, 185, 189-91, 229, 232

Pure mathematics, 146, 148, 150, 163-64, 229-30, 281

Putnam, Hilary, 263-71, 273-79, 284

Putnam's skolemization argument, 264-67, 278, 282

Puzzles, 14, 15, 18, 83, 89, 90, 103, 131, 146, 149, 174, 214, 271, 243, 246-47, 284

Quine, Willard van Orman, xiii, 10, 68, 76, 78-79, 245, 246, 263, 265, 267-70, 272, 275-79, 284-85

Radical, 2, 87, 102, 109, 123, 129, 139-40, 144, 151, 162, 163, 164, 172-73, 180, 183, 191, 227, 271, 276

Realism, 103, 117, 119, 149, 264-67, 269-70, 275-79. See also Platonism

Reality, 17, 45, 89, 92, 110, 112, 113, 114, 117, 118-19, 121, 125, 126, 130, 141-42, 149, 150, 156, 164, 173, 191, 194, 226, 246, 263-64

Reality, immanent, 118-19

Reality, transient, 118-19

Reduction, 35, 202, 204-5, 207, 223, 271, 272, 280

Reference, xiv, 2, 10, 23-40, 41-51, 53-66, 82?, 83, 90, 102, 181-84, 186, 188, 193, 199-202, 208-14, 222, 226, 232, 248, 249, 250, 254-56, 258-60, 264, 266, 271, 274. See also Denoting

Reform, 2, 172, 180, 182

Reinach, Adolf, 238

Relativity theory, 268, 274, 275

Resnik, Michael, 64, 275

Riemann, Bernhard, 156, 166, 189, 200, 205, 273

Resnik, Michael, 64

Rigid designators, 47-50

Rigor, 2, 3, 113, 123, 139, 140, 168, 192-93, 194

Russell, Bertrand, xi, 1, 2, 3, 4, 9-12, 14-18, 24, 67, 78-88, 96, 100, 104, 139, 155, 157, 166, 180, 192, 194, 199, 235, 270

Russell's paradoxes, 1, 2, 3, 10, 12-18, 67, 76-78, 89, 100-101, 129, 155, 166, 232, 235-36

Salva veritate, 6, 8, 11, 70, 83, 232, 238

Sartre, Jean-Paul, 192

Schirn, Matthias, 43, 44, 45, 212, 213

Schröder, Ernst, 30-32, 155, 200, 208

Science, theory of (Wissenschaftslehre), 190, 192

Sciences, natural, 89, 90, 123, 144, 150, 172, 173, 265, 268, 275, 281

Sciences, physical, 162, 171, 210, 245-46, 263, 265, 267-70, 273, 275, 276-77, 279, 281, 286

Scott, Sir Walter, 15, 16, 18, 24, 82-83, 210

Second-order languages, 262, 266, 267, 272-73, 282-84, 287

Semantics, xiii, 38, 41-51, 58, 60-64, 202-3, 210, 213-16, 247-50, 253-55, 258-59, 266, 273-74, 282-83, 287

Sense, xiv, 2, 23-40, 41-51, 53-66, 84, 130, 184, 193, 199-202, 208-12, 214-15, 250, 254-55, 258, 259, 260, 271

Sensory experience, 101-4, 114-16, 118, 120-21, 223, 144-45, 147, 150, 206-9, 221-24, 227, 228, 229, 238, 246, 256-66, 267-70, 274-75, 279-81

Set theory, xi, 2, 3, 12-15, 18, 55, 63, 67-94, 110, 123-24, 137-41, 146, 154-56, 157, 165-66, 168, 172-73, 202, 204, 205, 235-36, 239, 243, 244, 260, 261, 265, 266, 271. See also Zermelo-Fraenkel set theory

Sets, 30, 67-68, 96, 99, 100, 103, 109, 111-13, 115-17, 120-21, 124-26, 128, 137, 142, 146-50, 157, 165-66, 173, 191, 204, 207, 224-25, 227, 229, 235-36, 239, 241-43, 245, 263-65, 267, 270-72, 280-81

Sets, infinite, 111, 121, 146-48, 152, 167, 242

Shwayder, David, 53

Signs, 25-27, 32, 33, 43, 90, 111, 127, 147, 168-70, 182, 184

Simons, Peter, 217

Situations of affairs, 30, 34, 35-38, 59-60, 63-65, 207-11, 214-15, 224-26, 249-51, 253-62, 280

Skolem, Albert, 265, 266, 267, 273. See also Löwenheim-Skolem Theorem; Löwenheim-Skolem-Tarski Theorems; Löwenheim-Skolem Theorems, Upward and Downward

Skolem's paradox, 264-67, 285

Sluga, Hans, 59, 199, 212-14

Socrates, 24, 32, 28, 48, 116, 118, 120, 122, 150

Solomon, Robert, 32

Species, 113, 116, 142, 147, 149, 169, 226-27, 229, 272. See also Universals

Spinoza, Baruch, 138

Statements, 201, 202, 206-12, 222, 223, 225, 228, 230, 279, 280, 284. See also Identity statements; Interderivability; Mathematical statements; True statements

States of affairs, 23, 30, 34-38, 59, 61-65, 168, 191, 206, 207-11, 214-15, 222-28, 248-50, 252, 253-62, 279-80

Sterility, 7, 71-73, 75, 81, 89

Strangeness, 29, 49, 110, 141, 146, 148, 153, 164, 171, 243, 267, 275, 278

Stumpf, Carl, 2-4, 152, 167, 182, 204

Subjectivity, 101-2, 127, 128, 145, 149, 162-64, 171-73, 180, 182, 191-93. See also Consciousness

Substitution, 1-18, 27, 28, 29, 30, 34-37, 56, 60, 61, 65, 70, 74, 75, 77, 83, 85, 88, 90-92, 100, 201, 209, 211, 213-14, 259-60, 281

Surrealism, 132

Symbolic reasoning, 127, 128, 147, 149, 153, 164, 167-69, 181, 182, 184, 186, 194, 196, 233, 246

Syntax, 18, 41, 56, 202-3, 214, 216, 223, 226, 228, 256, 287

Synthetic a priori, 173, 202, 208

Synthetic statements, 42, 45, 47, 166, 189, 212, 250

Tannery, Jules, 116

Tannery, Paul, 117

Tarski, Alfred, 53, 54, 60, 61, 63, 202-3, 259, 266, 274. See also Ultrafilter Theorem

Tarski's theorem on maximal dual ideals. See Maximal ideals

Terminology, xii, 1, 23-24, 54, 60, 65, 101, 116, 117, 138, 154, 155-56, 158, 165-66, 195, 203, 204, 205, 206, 212, 250, 252, 254, 256, 269

Terra incognita, xiv, 146

Tertium non datur, 190

'The'. See Definite article

Thiel, Christian, 64, 199

Things in themselves, 119, 121, 129, 130, 131, 150, 162, 164, 172, 188

Thoughts, 29-30, 34, 35, 37, 54-57, 60-63, 65, 184, 201, 209, 211, 214-15, 222-32, 233, 248, 249, 255, 256-58, 268, 269

Topological spaces, 241-43, 245-46, 248, 260, 271, 287

Topology, 55, 62, 63, 205, 241, 244, 260, 281

Toposes, 205, 245

Transcendental logic, 161, 162, 171, 172, 188, 190-93

Transfinite, 85, 110-13, 116, 120, 125, 127, 129, 138, 140-42, 145-46, 150, 155, 157-58, 236

Trichotomy of cardinals, 63, 260, 284

Triviality, 10, 16, 37-38, 59, 62, 212, 213, 249, 250, 257, 258, 260, 277

Trotsky, Leon, 271

True statements, 46, 47, 48, 56, 58, 59, 75, 76, 90, 100, 183, 186-87, 190, 201, 202, 203, 206, 209, 212, 230, 244, 246, 248, 249, 250, 257, 259, 263, 264, 267, 269, 274, 275, 276, 277, 279, 284, 285

Truth, 5, 6, 10, 11, 12, 15, 16, 29, 44, 46, 59, 82-84, 86, 92, 119, 127, 129, 149, 162, 170, 175, 179, 185, 192, 203, 206, 223, 228, 244, 246, 248, 250, 253, 263, 264-67, 273-77, 279-80, 282

Truth value, 8, 26-30, 34-38, 41, 54-55, 57-63, 65, 184, 201, 206, 208-11, 213-14, 230, 248-50, 254-60, 272, 284

Tully, 48, 49

Tychonoff's Theorem, 63, 210, 242, 245, 249, 260, 284, 287

Types, 17, 76, 79-80, 85-86, 88, 207, 228, 237

Ultrafilter Theorem, 24, 53-54, 60, 61, 62-63, 66, 241, 259, 260

Ultrafilters, 66, 243, 245, 248-49, 251, 259, 261

Ultraproducts, 245-46, 250

Understanding, 35, 192, 206, 223-37, 256, 257

Universals, 69, 97, 113, 124, 130, 142, 227, 208, 255

Unsaturated expressions, 27, 28. See also Incomplete symbols

van Heijenoort, Jean, 271

Vanish, making, 6, 68, 70, 75, 81, 83, 84, 87, 88-90, 96, 97, 102-3, 114, 126

Vector spaces, 63, 241, 242-43, 245, 246

Verificationism, 264-67

Vérités de fait, vérités de raison, 166

Veronese, Giuseppe, 121, 150,

Vivanti, Giulio, 112

von Neumann, John, 270, 271

Wang, Hao, 161

Weidemann, Hermann, 65

Weierstrass, Karl, xi, 2-4, 96, 113, 123, 127, 129, 139-41, 145, 152, 156, 161, 167, 180-81, 185

Whitehead, Alfred N., 180-81

Wholes and parts, 119, 120, 121, 124, 125, 156, 193, 204, 224, 225, 236, 239, 244, 256. See also One and the Many

Willard, Dallas, 1

Wittgenstein, Ludwig, 4, 180

World, 9, 28, 38, 48, 49, 72, 110, 115, 119, 120, 128, 144, 146, 148, 162, 164, 171, 187, 190, 191, 246, 253, 264, 268, 277-78, 279, 281

Worlds, possible xiii, 28, 37, 43, 45, 48, 248, 267-69

Wright, Crispin, 286

Zeller, Eduard, 117-21

Zermelo, Ernst, 4, 270, 271

Zermelo's Well-Ordering Principle, 55, 63, 242, 260

Zermelo-Fraenkel set theory, 55, 241-42, 251, 260, 265

Zorn's lemma, 55, 63, 242, 245, 260