Index

Abbreviation proposals, 199, 216, 219, 221-22

Abbreviations, 135-37, 203, 217-19, 278-79, 291

Abstract entities/things, 131, 166, 227, 236—45; numbers as, 180—81, 210-11

Abstraction, process of, 154-55, 193-94

Abstract numbers, 151, 153

Ackermann, W., 199

Acquaintance, 13, 82, 93, 179, 227, 255-56

Addition, recursive definition of, 185, 186-88

Adickes, E., 46-47

Adverbial theory of sensing, 115

Aggregates, 150-53, 181, 189-91, 243-45

Aleph zero, existence of, 227-28

Algebra: Boolean, 104, 252-53; as theory of structures, 252

Analyticity, 143, 160, 257, 258, 263; for analytic philosophers, 273-74, 279-80; for Bolzano, 153-56, 160; of laws of logic, 162-63; for logical positivists, 287-94; as a matter of convention, 294-98; for Quine, 262, 263, 264

Analytic judgments, 132-37, 215-16

Analytic philosophers, 250, 273-98. See also Logical positivists

Analytic propositions, 137, 141-42, 154-55, 160, 178-79

Analytic statements, 135-37, 144, 294-98

Analytic states of affairs, 135-36

Analytic-synthetic dichotomy, 263, 273-74; for logical positivists, 287-88, 297-98

Analytic truth, 149-53, 160, 184-86, 188

A posteriori, 139-43, 145, 297

Appearance, 76-80, 84, 114; for Kant, 38, 39-40, 41

A priori, 39-40, 215-16, 281, 297; judgments, 133, 139-43; for Kant, 169, 170, 280; propositions as rules, 281. See also Necessity; Synthetic a priori

Arbitrary sets, 233-34

Arbitrary signs, 178-79

Aristotelian Tradition, 3-4, 7, 10, 11-12, 14, 20-21, 192

Arithmetic, vii-viii, 133, 241, 246, 260, 266-68; analyticity of, 273-74, 279-87; Bolzano on, 148—53; dispute between Mill and Frege concerning, 178-82; for Frege, 209-10, 215-24; Hilbert on, 182-83; for Kant, viii, 143-45, 215; Kitcher on, 183-84; and models, 253, 264-66; for Quine, 261-62, 263; as reducible to set theory and logic, 201-202, 217; viewed as a game, 294-95. See also Mathematics; Numbers

Arithmetic, laws of, 165, 172, 175, 184-88, 252; as analytic and a priori, 215-16; as matter of convention, 296-98

Arithmetic propositions, 137, 139, 140-42, 178-82, 215-16, 227

Arithmetic relations, 204, 208, 241

Arithmetic truths, 146-47, 226, 234, 292-94; for Kant, 143, 169, 226, 273; syntactic notion of, 295-97

Arithmetic vocabulary, 270-71

Armstrong, D. M., 62, 63, 198, 205

Arnauld, A., 4, 133, 139

Artificial languages, formation rules for, 174, 284-86

Aspects, theory of, 84-85

Association, law of, 178, 184-85

Association psychology, 170-71

Atomism, 30, 226-27, 256-57

Atoms, 59, 61-64

Attention, 96-98, 102-103, 106-107, 109, 115-16

Attributes, 161, 163, 165

Axioms, 234, 248-49, 264, 270; for Frege, 222, 259, 260; geometric, 255-59, 292; as implicit definitions, 259-60, 261-64, 296; for Quine, 262, 263, 264

Ayer, A. J., 65, 66, 117, 288-97

Barbara (logical rule), 163-64

Becoming, realm of, 129-31

Being, realm of, 129-31

Belief, 53, 81-82, 83, 113, 115, 116; relationship to perception, 30-33, 70-71

Benacerraf, P., 227, 233-34, 266-68

Bergmann, G., 175-76

Berkeley, G., 10-16, 19, 22-23, 34, 36-39, 44; Moore’s attempt to refute, 55-56; on perception, 58-59, 65-66

Berry, G., 247

Body, mind and, 21, 48

Bollnow, O. F., 110, 121-22, 124

Bolzano, B., 132, 148-56, 159-60, 161-64, 165-68; numbers for, 148, 149-53, 192-93; response to Kant, 148-50, 163-64, 167

Boolean algebra, 104, 252-53

Bound variables, 156

Brentano, F., 30, 58, 82-83, 99-101, 132; idealism, 48-51, 52, 54; thesis of intentionality, 25, 48, 52, 54, 67, 123

Broad, C. D., 77-78, 80, 87-88

Calculus of higher order, laws of, 160

Cantor, G., 151, 191, 200-201

Cantor’s paradox, 230

Cardinal numbers, Cantor on, 151

Carnap, R., 147, 246, 279-80, 294-98

Carroll, Lewis, 274-75

Cartesianism, 10-11, 16, 20-21, 52; and the principle of immanence, 15, 19, 91-94. See also Descartes, R.

Category, viii, 13, 16, 37, 83, 211; of number, 192-210; ontological, 129, 233

Causal interaction, argument from, 236-50

Causality, 52, 236-37, 242

Causal theory of perception, 33-34, 81-84, 236-40, 250

Certainty, 91, 113

Chihara, C., 249

Chisholm, R. M., 114-15

Choice, axiom of, 159-60, 234, 296

Circular definitions/reasoning, 285-86; paradoxes as result of, 228-30, 231

Classes, logical addition of, 204-205

Coffa, J. A., 256-59, 274

Coherence, 65-66

Collective connection, 193-95

Colors, 13-14, 16-19, 36, 170, 183-84, 243; as abstract entities, 210-11, 238; for Brentano, 50-51; for Frege, 212-13, 214; identified with atomic states, 61-64; for Kant, 38-44, 45; for modern physics, 9, 58-64; perception of, 96, 210-11, 237-38, 239-40, 244; principle of reduction applied to, 60-61; as properties of sensations and of perceptual objects, 43, 51, 212; as secondary qualities, 6-7, 26-27, 28-30; as sensations, 7-9, 10-11, 14-15; as viewed in argument from the relativity of sensing, 72-76, 94-95

Common-name doctrine, 232-33, 242

Common sense, 14, 26-28, 29, 63-64, 69, 114; and idealism, 22, 23, 24

Complex entities, 198, 207, 251

Concept-correlates, 202

Conception, 129-30, 171-75

Concepts, 4, 53-54, 163, 193, 232; Bolzano on, 148, 149; for Frege, 167, 198, 201-202, 211-15, 216-17, 219, 221; for Kant, 132, 133-34, 142, 143-45, 192, 215; numbers as, viii, 192; as represented by logical terms, 155, 161

Conceptual truths about God, 249

Concrete multitudes, 193, 194

Concrete numbers, 151-52

Concrete things, 237, 241-45, 250

Conditional relations, 278

Connectives, 277-79, 290, 291

Connotation of numerals, 188-90

Consciousness, 94, 96-97, 98, 99-101, 120

Conscious states, 92, 100, 102-107, 108, 118, 119; anxiety as part of, 123; moods as, 110-11; and reflections, 107, 115

Consistency, 228, 259-60

Constructional definitions, 264-66

Content of mental act, 52-56, 92-93

Context thesis of Frege, 213-15

Contextual definitions, 199

Continuum hypothesis, truth of, 234

Contradiction, 139, 171-75, 230, 276, 279

Convention, 146, 150, 179, 294-98; truth by, 146, 263, 296

Conventionalism, 294-98

Cornman, J. W., 78-89

Dedekind, R., 186, 230, 260, 264, 270; notion of number, 208-209, 254-55, 264

Definiens: as representing a property, 262

Definitions, 208-209, 231, 263, 264-66; as abbreviation proposals, 199, 216; arithmetic propositions as, 178-80, 181; associative law as part of, 184, 185; for Ayer, 291-94; debate between Russell and Poincaré, 255-59; as equivalences, 207, 208; forms viewed as, 253-55; for Frege, 137, 146, 201-203, 215-17, 219-24; importance in logicism, 150, 215-17, 219-24; impredicative, 228-33; recursive, 185, 186—88. See also Implicit definitions

Denotation of numerals, 188-90

Descartes, R., 3-9, 20-21, 49, 112-13; mind for, 4-6, 11-12, 44, 48; wax used as example by, 8-9, 11-12. See also Cartesianism

Description expressions, 178-79, 187-88, 208-209, 216, 223-24, 231

Descriptions, 82, 144, 227-28, 254, 264; expressions connected to, 178-79, 187-88, 216; impredicative, 228-33, 286; recursive, 186-88

Desire, 25, 97, 98, 117-21, 123-24

Despair, 121-22

Ding an sich, 37-39, 41, 44-47

Dingler, H., 258

Disjunction, 278

Disjunctive syllogism, law corresponding to, 282-83

Double affection interpretation, 44-47

Double negation, law of, 281-82

Doubt, Descartes’s method of, 112-13

Dummett, M., 214

Ego, 100-101, 120

Eidetic intuition, 14, 210, 248

Elementary particles, 59-61, 82, 84, 176

Emergent properties, 61-64

Emotional states, 108-109, 110-11, 123

Emotions, 49, 108-11, 114, 116, 117-21

Empirical imagination, 149

Empirical intuition, 148

Empirical laws, arithmetic truths as, 146-47

Empiricism, vii, 130-31, 146-47, 210, 226-27, 241; alliance with realism, vii-viii, 131; dilemma of 288-89; and logical laws, 162-65; for logical positivists, 279-80

Empty sets, models of, 264-65, 269

Entities, 141, 159-60, 196-97, 200; complex, 198, 207, 251; concrete, 237, 241-45, 250; laws of logic concerning, 160, 162; mathematical, 240-41, 246

Epistemology, vii-viii, 14, 58, 250; in Platonic Tradition, 129-31. See also Knowledge

Equal (Gleich): meaning for Bolzano, 152-53

Equations, 181, 292-93

Equivalences, 203, 207, 208, 231, 278-79; in Frege’s reductive steps, 218-19, 220

Esse est percipe principle, 55-56

Established usage, logical laws based on, 164-65

Euclid, 193, 208

Excluded middle, law of, 291

Exemplification, 129, 197, 200, 205, 229

Existence, 25-26, 30-31, 197, 259-60; of objects of mental acts, 51-52, 54-55, 66-68

Existence, human: moods as ground of, 121-22

Existentialists, importance of moods for, 121—23

Experience, 94, 95, 100, 106-107, 121, 214; and a priori knowledge, 139-43; and arithmetic propositions, 142, 169, 180; as colored by moods, 121; of the conscious state, 92, 118; of emotional states, 108-109, 124; as equivalent to existence, 25-26; as kind of mental act, 24-26; for Mill, 170-71; misidentification of in repression, 119; relationship to reflection and perception, 73-74, 78-79, 93, 96-98, 116, 117; universality of judgments based on, 169; versus inspection for knowledge of our own minds, 91-101

Extensionality, 7-8, 26, 87-88, 166, 170

Extensions (Umfangen): for Frege, 201-202, 216, 217, 221, 224, 226

Facts, 77, 129, 173, 251, 273, 291; arithmetic statements as, 178-82; as category of ontology, 129-30, 168; causal role in perception, 239-40; involving identity, 277; and necessity, 138, 288-89; relationship to Bolzano’s propositions, 166, 167; science, mathematics, and logic as matters of, 162, 263-64, 274-279, 290-91

Factual disagreements: differentiated from semantic disagreements, 282-83

Falsity, 153-56, 173, 176

Fear, 108, 122, 123-24

Feelings, 102-104, 110-11, 114

Form, 3-4, 7, 10, 11, 153-62

Formation rules: for artificial language, 174, 284-86; for logical systems, 139

Forms, 36-37, 252-53, 262, 264; axioms as, 257-58, 260; as definitions, 253-55; as having models, 264-69; interpretation of, 269-70; in Platonic Tradition, 129-31

Fractions, existence of, 208, 209

Freedom, possibility of, 122-23, 124

Free variables, 156

Frege, G., 137, 144, 145, 167-68, 226-27, 258; context thesis, 213-15; dispute with Mill, 178-80, 181, 189, 190; on necessity, 138, 145-46, 263; on numbers, 194, 196-99, 200, 201-204, 209-10, 211-12, 213-15, 294; reduction of arithmetic to logic, 215-24; versus Hilbert on implicit definitions, 259-61

Frege sets, 265-66

Freud, S., 117-21, 123

Functional calculus, 160, 161

Functions, 148, 157, 186-88, 198

Galileo, 6-7

Games, logic and arithmetic as, 294-95

Generalities, 140-41, 162, 169, 185

Geometry, 41, 143, 234, 256, 291-92; Hilbert versus Frege on axioms of, 259-61; Poincaré versus Russell on definition of, 255-59

Geometry, non-Euclidean, 256, 292

Gleich (Equal): meaning for Bolzano, 152-53

God, 37, 249

Goedel, K., 234, 236, 245-46, 248-50, 256

Goodman, N., 150

Grammar, 277; rules of, 258-59, 280-87

Grelling’s paradox, 229

Grice, H. P., 237, 238-39

Guilt, 118-20, 124

Hallucination, argument from, 21, 31, 58, 65-71

Hallucinations, 31, 65-71

Hegel, G. W. F., 94

Heidegger, M., 48, 121

Hempel, C. G., 136, 141-42, 293

Heterological predicates, 229

Heyting, A., 193-94

Higher functional calculus, 160

Hilbert, D., 182-83, 199, 228, 259-61

Hockney, H., 270-72

Hume, D., 12, 34, 35, 106, 273; on perception, 22, 23-24, 49

Husserl, E., 48, 52, 74-75, 84-85, 146, 175; eidetic intuition, 210, 248; numbers for, 193-96

Idealism, vii, viii, 16, 21-23, 133, 135, 176-77; Berkeley’s, 10-16, 19, 36; Brentano’s, 48-51, 52, 54; Descartes’s realism as leading to, 3-4, 6-9; Kant’s treatment of, 36-47, 167; Moore’s attempt to refute, 55-56; Reid’s rejection of, 18, 20-21, 23-35; terminology of used by Bolzano and Frege, 167-68; use of argument from hallucination, 58, 65-66; use of argument from physics, 58-59; use of isomorphism to escape from, 83

Ideas, 5, 7-8, 21-23, 49, 53-54, 91-93; for Berkeley, 10-11, 14-16, 36; for Bolzano, 155, 156, 166-67; relationship to objects, 4-6, 52

Identity, 52, 62-63, 197, 219-20, 276-77; law of, 159-60; thesis of, 4-5, 6

Identity statements, 159, 181, 187, 203, 220-21, 231; definitions as, 216, 221, 224

Illusion, 39, 70

Images, 49-50, 53-54, 102-104, 105

Imaginability, 142, 162, 169-71, 177-78. See also Unimaginability

Imagination, 49, 54, 149, 171-75, 176

Immanence, principle of, 3-6, 10, 15, 19, 35, 58; rejection of, 6, 20-21, 31-32, 91-94

Implicit definitions, 164, 253-64, 281, 296

Impredicative definitions, 228-33

Impredicative descriptions, 228-33, 286

Impressions, 22, 23-24, 49

Inconceivability, 171-73. See also Conception

Indiscernibles, law of the identity of, 204

Individual things, 17-18, 129-31, 132, 192-93, 196-201

Induction, 134, 141-42, 185-88; for Kant, 140, 142, 145, 169

Infallibility, 112-25

Inference, 73-74, 81, 227, 247-48, 249, 274-75; relationship to perception, 30-35; rules of based on logical laws, 274, 287

Infinite regress argument of Carroll, 274-75

Infinite sets, 233

Infinity, 159-60, 227-28

Inner sense, 97, 99-100, 112-25, 189

Inseparable association, 170-71

Inspection, 91-101, 102-107, 108, 112-15

Intentionality, 50, 51-54, 67-69, 93, 250; for Brentano, 48, 67, 123; in introspection, 102-103, 105, 106

Intentional nexus, 68-69, 70, 92-93, 166, 250

Introspection, vii, 102-11, 115, 147, 227

Introspective psychology, 102-106, 114

Intuition, viii, 129-30, 148-49, 247, 256; eidetic, 14, 210, 248; and impredicative descriptions, 228-33; mathematical, 193-94, 229, 241, 245-50; synthetic judgments based on, 133-34, 142-43

Intuition for Kant, 38, 39, 40, 132, 133-34, 143, 192, 215; forms of, 36-37, 40-41, 43. See also Pure intuition

Isomorphisms, 82-84, 153, 251-53, 268, 269-72; models, 264, 265, 266-69

Jealousy, 109-10

Jubien, M., 240-41

Judgments, 53, 69-70, 132, 214-15; for Bolzano, 155, 166, 167; for Kant, 132-34, 215; for Leibniz, 132-33; for Moore, 85-86; for Platonic Tradition, 129-31. See also Analytic judgments; A priori: judgments; Synthetic: judgments

Kambartel, F., 259

Kant, I., vii, viii, 86, 176-78, 192, 215, 255-56; on arithmetic truths, 215, 226, 273; Bolzano’s response to, 148-50, 163-64, 167; double affection interpretation of, 44—47; epistemological framework, 131-37, 139-40, 142-47; influence on Frege, 212; Mill’s response to, 169-70; transcendental idealism, 36-47

Kessler, G., 190-91

Kierkegaard, S., 122-23, 124

Kitcher, P., 139, 183-84, 195

Knowledge, 121, 130-31, 166; for Cartesians, 21, 91-94; of external world, vii, 1-88; fallibility of, 112-14; for Kant, 37, 131-37, 139-40, 142-47; mathematical, 37, 44-45, 129-298; of our own minds, vii, 91-125; in Platonic Tradition, 129-31. See also Epistemology

Kronecker, L., 209

Language, 54, 173-74, 273, 275, 277, 289-90; formation rules of, 174, 284-86; manipulation of in conventionalism, 294-98

Leibniz, G. W., 4, 132-33, 139, 178-79

Locke, J., 12, 15, 22, 38, 107

Logic, 113, 147, 174, 220, 227; for analytic philosophers, 273-74, 279-87; for Bolzano, 155-56, 159-60, 161, 163; conventionalism in, 294-98; and empiricism, 162-65; factual disagreements in field of, 282-83; for Frege, 145-46, 201-202, 215-24; as a game, 294-95; geometry as branch of, 260-61; and implicit definitions, 255; as matter of form, 155-62; paradoxes, 229-32

Logic, laws of, 135-37, 141, 172, 175, 274-75, 289; arithmetic propositions as, 215-16; and empiricism, 162-65; and form, 159-62; as matter of convention, 296-98; necessity based on, 138-39; rules of inference determined by, 287; for Wittgenstein, 274-80

Logical positivists, 142, 146, 147, 273, 279-87; analyticity for, 287-94; conventionalism in logic and mathematics, 294-98. See also Analytic philosophers

Logical things, Wittgenstein’s argument against, 277-79

Logical truths, 147, 150, 155, 162, 179; Ayers on, 288-93; syntactic notion of, 295-98

Logicism, 135, 145-46, 150, 186, 215-24, 263; Frege’s, 201-203, 215-24

Maddy, P., 241-42, 243-44

Mathematical entities, 240-41, 246

Mathematical induction, axiom of, 185-88

Mathematical intuition, 193-94, 229, 241, 245-50

Mathematics, 157-59, 233, 263-64, 288-93; conventionalism in, 294-98; fallibility of propositions, 112-13; knowledge of, 37, 44-45, 129-98. See also Arithmetic

Matter, 3-4, 10, 11

Meaning(s), 54, 146, 155, 165-68, 214, 298; emanating from rules of grammar, 280-87; and mathematical knowledge, 273-98; of statements, 172-75, 274; as use for Wittgenstein, 174-75, 283-87; of words and sentences, 226-27

Meinong, A., 48, 52, 83-84

Memory, 54, 105, 107, 116

Mental acts, 43, 92-94, 96, 125, 172, 211; and attention, 97-98; for Brentano, 48-51, 54; consciousness of, 99-100; content distinguished from object of, 52-56; denial of existence of, 99, 104, 106; for Descartes, 44, 48; of emotion, 108-109, 110-11, 123, 124; as having no phenomenal duration, 107, 108, 109; Hume’s impressions as, 23-24; intentionality of, 48, 50, 51-54, 67-69, 250; introspection of, 106-107; judgment and perception as distinct kinds of, 69-70; Kant’s intuition as kind of, 143; objects of, 24-26, 66-67; reflection on, 107, 115-17; self-consciousness of for Sartre, 100-101; sensations as for Reid, 27-30, 32

Mental contents, 103-106, 107, 110, 112-15, 125

Mental phenomena, 48-51, 124

Mental states, 94-96, 100

Mental things, 50-51, 96, 102-104

Metaphysics, 63-64, 226-27, 274

Mill, J. S., 146-47, 170-73, 178-83, 184-85, 188-90; Ayer’s response to, 288-89; numbers for, 192-93, 210

Mind(s), 6-7, 68, 118, 212, 213, 281; in Aristotelian and Platonic traditions, 3-4, 7, 10-11, 129, 212, 213; in Berkeley’s idealism, 10-11, 15, 23, 58-59; and Dedekind on abstraction, 254-55; for Descartes, 4-9, 11-12, 44, 48; ideas in, 22, 166; and immanence principle, 91-94; and intentionality, 48, 50, 51; for Kant, 36-42; knowledge of our, 91-124; for Reid, 20-21, 27; relationship of sensations to, 14-18; role in perception, 3-4, 7, 33, 67

Misidentification of emotion, 118-21

Modal logic, 178

Models, 251-53, 255, 260, 264-71

Modus ponens, 164-65, 274-75

Modus tollens, 273

Moods, 101-11, 121-22

Moore, G. E., 16, 18, 24, 48, 55-56, 78; version of theory of aspects, 85-88

Multitudes, numbers as, 193-96

Nagel, E., 164

Natural numbers, 143, 178, 207-10, 226, 261-62, 264-66; category of, 192-210; for Frege, 218, 220, 226; principle of mathematical induction concerning, 185-86; progression of, 254-55, 265, 267-69; relations among, 186-88, 252-53

Necessity, 55, 143, 160, 175, 176-78, 297; for analytic philosophers, 280-87; of a priori judgments, 139-40, 142-43; of arithmetic and logic, 145-47, 162, 165, 169, 273-74; of arithmetic truths, 226, 263, 273, 280; as emanating from lawfulness, 138-39; of geometric axioms, 258; for logical positivists, 287-88; for Mill, 170-71; of non-analytic judgments, 133, 139; unimaginability as, 169-71, 177

Negation, 172-73, 174-75, 177, 284, 288, 290; for Wittgenstein, 278, 281-82, 284-87

Neither-nor as connective, 278-79

Neurosis, 119-20, 123, 125

Nominalism, 130-31, 242, 250

Non-existence proofs as paradoxical, 229, 230

Nonexistent objects, 51-52, 54-55, 68-71, 159

Nothingness, 122-23, 124

Notion of all numbers, 231-32

Number, 83, 232, 286; category of, 192-210; as common name, 232-33

Numbers, 131, 159, 204, 221, 246, 264; acquaintance with, 210-15, 227; for Benacerraf, 266-69; Bolzano on, 148, 149-53, 192-93; for Cantor, 199-200; for Frege, 178-82, 194, 196-99, 200, 201-204, 209-10, 211-12, 213-15, 217, 294; for Hockney, 270-72; for Husserl, 193-96; Kant’s concept of, 143—45, 192; Kessler on, 190-91; for Mill, 178-82, 188-90, 192-93; notion of all, 231-32; perception of, 236-38, 239-40, 241, 272; in Platonic Tradition, 192; postulation of, 246-47; as properties, 192-93, 196-99; as quantifiers, 205-207, 210, 211, 224, 226; as relations, 205; satisfactory theory of, 246; as sensible things, 190, 211-12, 213; as sets, 188, 201-205, 233; structures formed by relations among, 252-53; as used in Frege’s reductive steps, 218-20. See also Natural numbers; Real numbers

Numerals, denotation and connotation of, 188—90

Objective things, 212-14

Objects, 24-26, 98, 108, 143, 213, 216, 276-77; of anxiety, 122-24; for Bolzano, 152-54, 166-67; as distinct from mental acts, 23-24; of inspection, 106-107; material, 10-11, 13, 14-16; mind’s intentionality toward, 48, 50, 51-54; moods as not having, 110; nonexistent, 68-71; numbers as, 198, 215, 266; of reflection, 115-16; relationship to ideas, 4-6, 52; relationship to mental acts, 51-56, 67-69; as states of affairs, 70

Objects, perceptual, 24, 33, 48, 87, 96-97, 246, 255-56; in argument from hallucination, 65-71; in argument from the relativity of sensing, 76-84; in Aristotelian Tradition, 3-4; for Berkeley, 10-11, 14-16, 36; for Brentano, 49-51; causal interaction between perceiver and, 236-38; colors as properties of, 43, 51, 212, 213; as consisting of elementary particles, 59; as consisting of physical objects, 48; existence of, 25, 31, 55-56; for Frege, 215; for Goedel, 245-46, 247-48; for Husserl, 75; for idealists, 21-24; for Kant, 37-42, 45-47; knowledge of, 91-94, 247-49; for Moore, 78, 85-88; properties of, 12-17, 36, 58-64; for Reid, 20-21, 26-35; relationship to content of mental act, 92-93; for Russell, 72-74, 81-82, 246-47; as states of affairs, 70

Objects, physical, 45-47, 48, 51, 82-84, 247-48, 261-62

Observation, 99-100, 290, 292

Ontology, 66-69, 132, 175, 207, 232, 238; for Berkeley, 16, 36, 37; for Brentano, 51; categories of, 129-30, 165-66, 192, 205, 233; complex entities in, 251; functions as relations in, 186; and identity, 159, 220; laws of, 159-60, 172-75, 220, 284, 287; necessities of, 55, 138-39, 146; Platonic, 241; status of form, 156-59

Pain, 2-4, 24-26, 28-29, 50, 114

Paradoxes, 228-33

Partially identical propositions, 156-57

Peano forms, 268

Peano’s axioms, models of, 264-65

Perception, 41, 100, 116, 131, 147, 227, 246-47; of abstract entities, 236-45; acquaintance with geometric terms given to us by, 255-56; acquisition of concepts through, 232; for Aristotelian and Platonic tradition, 3-4, 129-31; for Brentano, 49-51, 99-100; causal theory of, 33-34, 81-84, 236-40, 250; of colors, 96, 210-11, 237-38, 23-40, 244; for Descartes, 112; for Goedel, 245-46, 248-49; for Husserl, 84-85; in idealism, 13, 21-24; knowledge of existence of numbers as resting on, 209-10; knowledge of external world based on, vii, 1-88; of material substances, 11-14; for Mill, 192-93; for Moore, 85-88; of numbers, 179, 188, 190, 211, 226, 236-38, 239-40, 241, 272; paying attention to, 106-107; for realism, 14-15; reflection and consciousness compared to, 96-97, 98; Reid on, 18, 20-21, 29, 30-35; as true by accident, 237, 238. See also Objects, perceptual; Sensations

Perception as propositional, 14, 30, 53, 131, 239, 248-49; and nonexistent objects of hallucination, 68, 69-70

Phenomenalism, 23, 24, 58, 65-66

Philosophy: replaced by set theory, 233, 234-35

Physicalism, 63, 250

Physics, vii, 9, 41, 46, 47, 234; external world for, 82-83, 84; laws of, 61-64, 146; made true by convention, 296-97; perceptual properties for, 58-64

Physics, argument from, 15, 20, 24, 26-30, 58-64, 212-13

“Place holders,” 253-54, 257, 260

Platonic dogma, 212, 236-38, 240-41, 243

Platonic Tradition, 11, 14, 129-32, 192, 210, 240-41

Plurals, 197, 200, 206-207

Poincaré, H., 229, 231, 255-59, 286

Points of view, 72-73, 76-77, 86, 94-95

Predicate concepts, 132-33, 134-35, 142-43, 148

Predicates, 197, 199, 229, 261-62

Presentations, 49, 53-54, 215

Price, H. H., 77, 113-14

Primary qualities, 14-15, 36-37, 38, 39-42. See also Space; Time

Primary qualities, distinction between secondary qualities and, 6-9, 19, 50-51, 58-64; Kant’s invocation of, 40-42, 45, 47; Reid’s acceptance of, 20, 24, 26-30, 35

Primitive terms of the geometric axioms, 255-59

Progressions, 254-55, 264-69, 271

Properties, 49, 58-64, 140-41, 175-77, 242, 244-45; for Berkeley, 10-11, 13, 14-16, 36; colors as, 43, 211, 212-13; concepts as, 132, 133, 144, 212; dubbing of, 242-43; emergent, 61-64; in Frege’s reductive steps, 217-20; general theory of, 160, 161; Goedel on, 245-46; laws of logic concerning, 160-62, 163, 164; numbers as, 144-45, 192-93, 196-99, 203-204; of numbers, 231-32, 266-68; perception of, 87, 131, 232, 240; for Reid, 18, 27-30, 32; for Russell, 18-19, 73-74, 81-82, 84; of sensations, 16-19, 74, 77, 78-79, 213

Properties of properties, 14-15, 59-64; numbers as, viii, 191, 198-201

Propositional calculus, 160, 161, 178

Propositions, 164-65, 174, 234, 260; for Bolzano, 151, 153-56, 165-68; forms of, 153-59, 160; for Frege, 215-16, 222; logical, 253, 276, 279. See also Analytic propositions; States of affairs

Psychology: association, 170-71; introspective, 102-106, 114

Pure intuition, 134, 142-45, 148-49, 150, 255-56

Putnam, H., 227, 233-34

Quantifiers, 196, 205-206, 229-30; numbers as, 205-207, 210, 211, 224, 226

Quine, W. V. O., 136, 155, 261-64, 296-98

Rationalism, vii, viii, 130-31, 147, 210; Frege as forced to embrace, 210, 213, 215

Realism, 11, 14-15, 58-59, 241, 246, 270, 281; alliance with empiricism, vii-viii, 131; alliance with rationalism, vii, 130-31; Des-cartes’s, 3-9; elusiveness for Reid, 18, 20-21, 23-35; Kant’s, 38, 45-47; Moore’s commitment to, 24, 55-56

Real numbers, 207-10, 231-32

Recursive definitions, 185, 186-88

Recursive descriptions of relations, 186-88

Reduction, 23, 59-64, 202, 264-65; of arithmetic to logic, 215-24; of connectives, 278-79; of definitions, 207, 208

Reflection, 93, 96-98, 101, 103, 115; on mental acts, 107, 108-109, 115-21; on sensations, 96, 114-15

Reid, T., 12, 18, 72, 76, 96-97, 98; elusiveness of realism for, 20-21, 23-25; quoted, 1

Relational properties, 198-99, 218

Relational proposition, 140-42

Relations, general theory of, 160, 161

Relations, recursive descriptions of, 186-88

Representation, 4-6, 7, 39-42, 52-53

Representationalism, 10, 15

Repression, 118-21, 123-24

Resnik, M. D., 268-69

Rules of use, meaning as, 146

Russell, B., 19, 48, 173, 227, 245-47; formulation of argument from the relativity of sensing, 72-74, 75, 81-82, 83-84, 94-95; on implicit definitions, 255-59; on logic and mathematics, 157-59, 204-205, 206-207; on numbers, 179, 188; on paradoxes, 229-31; quoted, 127

Ryle, G., 105-106

Sadness, 121-22

Saetze an sich, 151, 166-68. See also Propositions

Sartre, J.-P., 48, 100-101, 120, 124

Saying: as distinct from showing, 276-77

Schematic letters (in propositions), 156-57, 158-59, 161

Schlick, M., 261, 279, 295-96

Scholz, H., 259

Science, 139, 146, 260, 263-64, 297-98; distinction between primary and secondary qualities, 6-7, 9, 63-64; and knowledge of physical objects, 45-46, 47, 82. See also Physics; Physics, argument from

Science, philosophy of, 246, 255, 259

Scientific realism, 46-47

Secondary objects, 25, 99-101

Secondary qualities, 10, 36-37, 58-64. See also Colors; Primary qualities, distinction between secondary qualities and

Self-identity, 197, 276; law of, 159-60, 220, 276

Sellars, W., 59-61

Semantic analyticity, 273

Semantic atomism, 226-27, 257

Semantic disagreements: differentiated from factual disagreements, 282-83

Semantic nihilism, 269-72

Semantic paradoxes, 229-32

Semantic theory, 146, 281

Semantic truths, 146

Sensations (Sense-impressions), 6, 53-54, 55-56, 83, 113-15, 213; and the argument from hallucination, 21, 65-67, 69, 70-71; for Berkeley, 10-11, 13, 14-16; for Brentano, 49-51; of colors, 43, 51, 75-76, 94-96, 211, 212; for Descartes, 7-9; distinguished from sensible properties, 14-15, 16-19; for Frege, 211-13, 214; for Goedel, 245-46, 248, 249-50; for Husserl, 75; inspection of, 102-104; for Kant, 37, 38-40, 42-44, 47; for Moore, 18-19, 55-56, 85-88; for Reid, 18, 24-34; relationship to appearance, 77-80; relationship to minds, 15-16, 24; relationship to perception, 32-34, 69-70; relationship to perceptual objects, 21-24, 80-84, 213, 249; for Russell, 18-19, 73-74, 75, 81-82, 246-47; as sense-data, 73-74

Sense: for Frege, 214, 221, 222-23

Sense-data, 73-74, 78-79, 81-82, 86

Sense-reference distinction, 214, 221, 222, 223

Sensibility, 131, 214; for Kant, 36, 41-42, 131, 132, 143, 176-77

Sensible things, 210-12, 213

Sensing, acts of, 73-74, 78-79

Sensing, adverbial theory of, 115

Sensing, argument from the relativity of, 15, 19, 41-42, 58, 72-88, 94-96; Reid’s response to, 20, 24, 30, 34-35

Sentences, 214, 253, 254, 269-70, 275-76, 281; axioms as, 257-58, 259-60; meaning of, 226-27

Series, sums as, 150-51, 152-53

Set of all real numbers, 231-32

Set of sets, 219, 230

Sets, 131, 201-202, 204, 209, 227, 251; as abstract or concrete things, 241-45; aggregates as, 150, 151, 153, 243-45; Frege’s use of, 217-19; Goedel on, 245-46; multitudes as, 193-96; numbers as, 188, 201-205, 233; perception of, 243-44; properties of, 165, 200-201, 229, 230; relations among, 205, 251-53

Set theory, vii-viii, 161, 204, 233-35, 246, 253; axioms of, 248-49; factual disagreements in field of, 283; laws of, 172, 175, 296; paradoxes concerning, 229-32, 233; philosophy replaced by, 233, 234-35; propositions about, 113, 227; reduction of arithmetic to, 217, 224

Shame, 118-20, 123-24

Shape, 9, 13, 39, 54, 77; as idea, 7-9, 36; perception of, 34-35, 40-41, 42, 43-44, 74, 76; as primary quality, 6-7, 26-27, 28, 29-30; as sensation, 10-11, 14, 17-18

Showing: as distinct from saying, 276-77

Signs, 32, 222-23, 276-78

Similarity, 52, 217-18, 221

Skepticism, 3-6, 16, 18, 31-32, 70; argument from relativity of sensing as leading to, 15, 35, 73, 75, 76, 81, 83, 85, 88, 95; Berkeley’s avoidance of, 10, 15; and the infallibility of mental contents, 112, 114; principle of immanence as leading to, 20, 58; as triumph over Cartesianism, 91-92, 93

Smart, J. J. C., 63

Solipsism, 15, 68

Space, 41, 50, 82, 148-49, 176, 195; for Kant, 36-37, 39-44, 131, 142

Spatial part-whole relation, 185, 189

Spatio-temporal entities, 189-90, 210, 236

Square root of 2, 230-32

States of affairs, 132, 135, 139, 250, 253; general theory of, 160, 161; imaginability as property of, 177-78; perceived, 70, 131. See also Proposition

Steiner, M., 236, 238, 240

Structure, 251-72, 268-69; of the mind, 280-81; of the world, 82-84, 277, 280-81

Subject concepts, 132-33, 142-43, 148, 149

Subject ideas, 153-54

Subjective ideas, 166-67

Subjective realm, 213-15

Substance, 3-4, 6-7, 10-14, 23, 37; arguments against existence of, 12, 13, 16; for Descartes, 4, 7-9, 11-12, 48

Substitutivity, Leibnizian law of, 88

Successor relation, 187-88, 267, 268

Sum relation, 141, 144, 169, 185, 195, 205, 267; analogy with union relation, 204; for Bolzano, 150-53; for Mill, 189-90; perception of, 241; and recursive descriptions, 186-88; as unique, 181

Sums, 184, 192-93

Syncategorematic signs, 278

Syntax: as rules of the games of logic and arithmetic, 295-96

Synonymity, 136-37, 292-94

Synthetic, 215, 257, 258, 273, 288; judgments, 132-37; propositions, 139, 178-79, 290, 295-96. See also Analytic-synthetic dichotomy

Synthetic a priori, 36, 37; conventionalism as alternative to doctrine of, 296-97; judgments, 134, 142-43, 148-49; rejection of by logical positivists, 279-80; truths, 139, 143, 171, 175-78

Synthetic truth, 163, 185-86, 188

Tarski, A., 298

Taste, 39, 41, 45

Tautologies, 147, 174, 273-80, 289, 291

Temporal things, 129-31

Thoughts: for Frege, 167-68, 215

Time, 82, 148-49, 150, 176; for Kant, 36-37, 39, 40, 131, 142, 143, 145

Transcendental idealism, 36-47

Transfinite numbers, theory of, 228

Truth, 133, 140-41, 146, 222, 227, 234; analytic, 149-53, 160, 184-86, 188; empirical as opposed to conventional, 146; implied by consistency, 259-60; not implied by necessity, 175, 177; of propositions, 133, 153-56, 234; syntactic notion of, 295-98; synthetic, 139, 143, 163, 171, 175-78, 185-86, 188. See also Logical truths

Truth tables, 277, 279, 291

Twardowski, K., 52-53, 54

Two-place relations, abbreviations concerning, 217-18

Types, Russell’s theory of, 173, 229-30

Umfangen. See Extensions

Unconscious, Freud’s theory of, 117-21

Understanding, 11, 37, 54, 212, 214; for Descartes, 8, 11-12

Unimaginability, 169-71, 172-75, 176, 177, 288. See also Imaginability

Union relation: analogy with sum relation, 104

Universality, 139-43, 169, 176, 226

Universals, 11, 14, 19, 131, 237

Uses, meaning of words as, 174-75, 283-87

Vaihinger, H., vii, viii

Value-ranges, 201-202

Variables, 156, 158-59, 161, 162, 196, 260

Veridical perception, 65-71

Verificationists, 227

Vesey, G. N. A., 77

Vicious circle, 285-86; paradoxes as result of, 228-30, 231

Vienna Circle. See Logical positivists

Von Neumann progression and sets, 264—65, 267-68, 269

Well-formedness, 173-74, 284-86

Wittgenstein, L., 146, 147, 173, 274-87, 294-95; on geometric terms, 258-59; on meaninglessness, 174-75

Zermelo, E., 231

Zermelo progressions and sets, 264-66, 267-68, 269, 270-71, 272

Zero, 200, 220-21, 222-24