INDEX
Aggregates, 12
Alephs, 83, 92, 97, 125
Aliorelatives, 32
All, 158 ff.
Analysis, 4
Ancestors, 25, 33
Argument of a function, 47, 108
Arithmetising of mathematics, 4
Associative law, 58, 94
Axioms, 1
Between, 38 ff., 58
Bolzano, 138 n.
Boots and socks, 126
Boundary, 70, 98, 99
Cantor, Georg, 77, 79, 85 n., 86, 89,
95, 102, 136
Classes, 12, 137, 181 ff.;
reflexive, 80, 127, 138;
similar, 15, 16
Clifford, W. K., 76
Collections, infinite, 13
Commutative law, 58, 94
Conjunction, 147
Consecutiveness, 37, 38, 81
Constants, 202
Construction, method of, 73
Continuity, 86, 97 ff.;
Cantorian, 102 ff.;
Dedekindian, 101 ff.;
in philosophy, 105;
of functions, 106 ff.
Contradictions, 135 ff.
Convergence, 115
Converse, 16, 32, 49
Correlators, 54
Counterparts, objective, 61
Counting, 14, 16
Dedekind, 69, 99, 138 n.
Deduction, 144 ff.
Definition, 3;
extensional and intensional, 12
Derivatives, 100
Descriptions, 139, 144
Descriptions, 167
Dimensions, 29
Disjunction, 147
Distributive law, 58, 94
Diversity, 87
Domain, 16, 32, 49
Equivalence, 183
Euclid, 67
Existence, 164, 171, 177
Exponentiation, 94, 120
Extension of a relation, 60
Fictions, logical, 14 n., 45, 137
Field of a relation, 32, 53
Finite, 27
Flux, 105
Form, 198
Fractions, 37, 64
Frege, 7, 10, 25 n., 77, 95, 146 n.
Functions, 46;
descriptive, 46, 180;
intensional and extensional, 186;
predicative, 189;
propositional, 46, 144;
propositional, 155;
Gap, Dedekindian, 70 ff., 99
Generalisation, 156
Geometry, 29, 59, 67, 74, 100, 145;
analytical, 4, 86
Greater and less, 65, 90
Hegel, 107
Hereditary properties, 21
Implication, 146, 153;
formal, 163
Incommensurables, 4, 66
Incompatibility, 147 ff., 200
Incomplete symbols, 182
Indiscernibles, 192
Individuals, 132, 141, 173
Induction, mathematical, 20 ff., 87, 93,
185
Inductive properties, 21
Inference, 148
Infinite, 28; of rationals, 65;
Cantorian, 65;
of cardinals, 77 ff.;
and series and ordinals, 89 ff.
Infinity, axiom of, 66 n., 77, 131 ff.,
202
Instances, 156
Integers, positive and negative, 64
Intervals, 115
Intuition, 145
Irrationals, 66, 72
Kant, 145
Leibniz, 80, 107, 192
Lewis, C. I., 153, 154
Likeness, 52
Limit, 29, 69 ff., 97 ff.;
of functions, 106 ff.
Limiting points, 99
Logic, 159, 65, 194 ff.;
mathematical, v, 201, 206
Logicising of mathematics, 7
Maps, 52, 60 ff., 80
Mathematics, 194 ff.
Maximum, 70, 98
Median class, 104
Meinong, 169
Method, vi
Minimum, 70, 98
Modality, 165
Multiplication, 118 ff.
Multiplicative axiom, 92, 117 ff.
Names, 173, 182
Necessity, 165
Neighbourhood, 109
Nicod, 148, 149, 151
Null-class, 23, 132
Number, cardinal, 10 ff., 56, 77 ff., 95;
complex, 74 ff.;
finite, 20 ff.;
inductive, 27, 78, 131;
infinite, 77 ff.;
irrational, 66, 72;
maximum? 135;
multipliable, 130;
natural, 2 ff., 22;
non-inductive, 88, 127;
real, 66, 72, 84;
reflexive, 80, 127;
relation, 56, 94;
serial, 57
Occam, 184
Occurrences, primary and secondary,
179
Ontological proof, 203
Order 29ff.; cyclic, 40
Oscillation, ultimate, 111
Parmenides, 138
Particulars, 140 ff., 173
Peano, 5 ff., 23, 24, 78, 81, 131, 163
Peirce, 32 n.
Permutations, 50
Philosophy, mathematical, v, 1
Plato, 138
Plurality, 10
Poincaré, 27
Points, 59
Posterity, 22 ff., 32; proper, 36
Postulates, 71, 73
Precedent, 98
Premisses of arithmetic, 5
Primitive ideas and propositions, 5, 202
Progressions, 8, 81 ff.
Propositions, 155; analytic, 204;
elementary, 161
Pythagoras, 4, 67
Quantity, 97, 195
Ratios, 64, 71, 84, 133
Reducibility, axiom of, 191
Referent, 48
Relation numbers, 56 ff.
Relations, asymmetrical 31, 42;
connected, 32;
many-one, 15;
one-many, 15, 45;
one-one, 15, 47, 79;
reflexive, 16;
serial, 34;
similar, 52;
squares of, 32;
symmetrical, 16, 44;
transitive, 16, 32
Relatum, 48
Representatives, 120
Rigour, 144
Royce, 80
Section, Dedekindian, 69 ff.;
ultimate, 111
Segments, 72, 98
Selections, 117
Sequent, 98
Series, 29 ff.; closed, 103;
compact, 66, 93, 100;
condensed in itself, 102;
Dedekindian, 71, 73, 101;
generation of, 41;
infinite, 89;
perfect, 102, 103;
well-ordered, 92, 123
Sheffer, 148
Similarity, of classes, 15 ff.;
of relations, 83;
of relations, 52
Some, 158 ff.
Space, 61, 86, 140
Structure, 60 ff.
Sub-classes, 84 ff.
Subjects, 142
Subtraction, 87
Successor of a number, 23, 35
Syllogism, 197
Tautology, 203, 205
The, 167, 172 ff.
Time, 61, 86, 140
Truth-function, 147
Truth-value, 146
Types, logical, 53, 135 ff., 185, 188
Unreality, 168
Value of a function, 47, 108
Variables, 10, 161, 199
Veblen, 58
Verbs, 141
Weierstrass, 97, 107
Wells, H. G., 114
Whitehead, 64, 76, 107, 119
Wittgenstein, 205 n.
Zermelo, 123, 129
Zero, 65
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