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 [Pg 207] 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;