No More Learning

and), 188f. , 191 Consequence, v. condition Consequent, v. condition Consistency
Index 283
? 284 Index
Extension? , v. concept
Extensionalist logicians v. intensionalist/
extensionalist logicians
Factor (common), 22 Fallacy, 34f. , 143, ! 55
False (v. true), 127, 138, 149
the-, 195, 233, 255
reject as-, 8, 149, 185, 197f.
Feeling, 129, 198
Fick, A. , 17
Fiction, 118, 122, 129f. , 191fT. , 225, 232,
269 Fischer, K. , 84
Following (in a series), 22, 38
Formal arithmetic, 165, 215, 273f. , 275 Formula-language
- of algebra, 2, 6
- of arithmetic, 13f. , 142
- Boole's logical-, 13fT. , 47fT. - ofgeometry, 13
- o f mathematics, 13f. , 47, 270
Function, 24fT. , 119, 155f. , 157fT. , 184, 195, 234f. , 238fT. , 270fT.
argument, argument-place, of a -, 119, 121, 154fT.
- of one, of two, of three arguments, 240fT. , 244, 250
continuous -, 24f.
--letter (v. letter), 121, 154, 156,272 --sign (--name) 119, 234, 239fT. , 243f. ,
271f.
unsaturatedness of a -, 97fT. , 119, 156,
254,272
value of a-, 119, 235, 238f.
Gauss, 280
Generality, 11, ! BIT. , 52, 153fT. , IG2, 187fT. ,
194f. , 199fT. , 230f. , 236fT. , 258fT. , 272 - of an equation between functions, 121 notation for -, 18fT.
Generalization, 191
Geometry (v. sources of knowledge), 170fT. ,
273f. , 277, 278fT. Euclidean/non-Euclidea'l-, 167fT.
God, v. ontological proof of the existence of-
Good, 252
Grammar, 6f. , 141fT. , 146f. Grassmann, R. , 34 Ground, liT. , 147
Heine, E. , 164
Here, 135
Hereditary property, 28 Hilbert, 170fT. , 247fT. History, 258
historical/ahistorical -, 3 Husserl, 123f. ' Hypothetical
-judgement, 15, 52, 185, 198
- sentence [conditional sentence], 153f. ,
185, 188, 198fT. , 258fT. -thought, 188f. , 200,258, 261
I (v. affectionoftheego), 127,135
Idea (v. image, representation, association of - s ) , 54fT. , 73fT. , 104f. , 126fT. , 139f. ,
143fT. , 148, 174, 198 act of forming an -, 57 object of an-, 56fT. , 64f. -ofan-, 57
Idealism, 105, 130, 143f. , 232 Identity (v. equals sign, equation)
If
law of-, 62
relation of-, l2lf. , 182 sign of-, 10,226, 237, 240
. . . then . . . (v. hypothetical sentence), 153, 189fT.
Illustrative examples, 207, 214, 235 Image, 58, 74
Indefinitely indicating (v. letter)
- sentence-part, v. sentence-part
-sign, v. sign
Individual (thing), 213
Induction (mathematical), 31, 203
Inference (v. fallacy), 15, 27, 34f. , 118, 175,
180, 203fT. , 212, 244fT. , 261
chain of-(s), 204
- from the general to the particular,
258fT. , 272
laws of actual- /laws of correct-, 3fT.
Infinite, 273f. , 279 absolute-, 68f. actual-, 68f. potential-, 68f.
Inner perception, 58
Integral, definite, 15 7f. lntensionalist/Extensionalist logicians, 118,
122f. Interjection, 135, 140
Intuition, 32, 58, 2 78 Is, v. copula
[as expression of existence], 53, 62, 63f.
[as expression of identity], 90fT. , 113fT. It,62, 190,260
Jevons, W. S. , 10, 35f. , 48
Judgement, ! IT. , 7, 11, 16f. , 45f. , 47, 51f. ,
59f. , 119, 139, 149, 151, 185, 194,
197fT. , 251, 253f. , 267 aesthetic-, 126f. , 131f.
content of possible-, v. content hypothetical-, v. hypothetical particular-, v. particular singular-, v. singular --stroke,! ! , 18fT. , 51f. , 195,198
1urisprudence, 203
Justification (v. judgement, ground), 2ff. ,
147, 175
? Kant, 203
Kerry, B. , 87fT.
Knowledge (v. recognition)
-a priori, 277
geometrical source of-, 277, 278fT. sources of- (v. sense perception), 266fT. temporal source of-, v. time
Korselt, A. , I77
Language (v. meta-, formula-language), 67, 192f. , 213, 225,243, 259fT. , 269fT.
changes in-, 141
logic and-, v. logic
logical imperfections of-, 117, 143, ! 49,
177fT. , 190,193,252,266 being misled by-, 263, 266, 269fT. ordinary-, 136f. , 207, 213
poetic use of-, 139f. printed/spoken-, 13, 46,260 verbal-, v. verbal
Law (v. associative-), 145ff. , 258.
-(s) of being true/holding true, v. true
-(s) of correct inference/actual inference
v. inference
- o f excluded middle, 155, 186, 195, 198 - o f identity, 62
-(s) ofjudgement, 145fT.
-(s) of logic, v. logic
natural-(s), v. natural
primitive -(s) (of the concept-script), v.
concept-script
-(s) of thought, v. thought
Leibniz, 9f. , 13, 33, 35, 47f. , 203,253
Letter (v. function, object), 152fT. , 162fT. ,
188, 193, 199fT. , 260fT.
use of -(s) in arithmetic and mathematics
162fT. , 194f. , 200f. , 235fT. , 272 , Lettre variable, 152fT.
Limit, 25 receding-, 69
Line, 280f.
intersection of two -(s), 281
Lingua characterica, 9, 12f.
Locke, 105
Logic (v. psychology, intensional/exten-
sional), 1fT. , 96, 125, 126fT. , 136, 141fT. ,
174f. , 179, 185, 198, 203,252, 253f.
- and language, 6f. , 13, 94fT. , 136f. ,
141fT. , 188, 190,252, 266, 269fT. Aristotelian -, 15
laws of-, 3fT. , 47, 122, 145fT. Peano's mathematical-, ! 52
psychological 147fT.
conception
o f
- ,
142fT. ,
Logical
- analysis, 208fT.
- source of knowledge, 267fT.
Mathematics (v. analysis, arithmetic, formula-language, geometry), 157fT. ,
16. 5, 203fT. ? 242, 253, 277
Index 285 -in education, 221f.
functions in-, 254, 270fT.
use of letters in-, v. ? ~tter
-and philosophy, 203,216, 273f. psychological considerations in-, 76fT.
sources of knowledge of-, 267fT. , 278fT. - as a system, 205f. . 211, 242fT.
McColl, H. , 15
Mean [bedeuten], 91,96
Meaning [reference], 90, 99, 113fT. , 118fT. ,
192fT. , 229fT. , 243, 255f. simplicity of-, 49
Mer. ningless, v. concept, proper name Meeting of minds, 207, 271 Meta-language/object-language, 260fT. Mill, J. S. , 79
Mock
- assertion, 126, 130 - propername,130
- thought, 130
Multiple
COII'mOn-, 22
least common-, 24 -of a number, 22fT. , 27
Multiplication (product), logical, 33f. , 38, 46,49
-sign (logical), 48, 52
Name (v. concept, function, proper name) 123f. ,
Natural
-laws, 4f. , 127, 129, 131, 133, 137f. , 145,
258, 268
- sciences, 3, 130, 267fT.
Negation (denial), 15, 48fT. , 55, 149fT. , 185 198,253 ,
double-, 149
--stroke, 11, 20f. , SOfT.
Negative concept, v. concept
Neither . . . nor . . . , 51
Newton, 203
No, ISO, 213
Nomen appellativum, v. concept-word Nomen proprium, v. proper name
None, 63
Nonsense, 182
Normal human being, 132, 147f.
Now, 135
Number, 34, 55, 57, 70f. , 72fT. , 106f. , 215fT. ,
253, 256f. , 263f. , 265f. , 273f. , 275fT. ,
279fT.
complex -(s), 279fT. determinate/indeterminate-, 160fT. existence ofa-, 55, 57
Gaussian - plane, 280 kindergarten -(s), 276f.
logical foundation for -(s), 269 natural -, 72
positive rational -, 23
? 286
Number-continued
positive whole-, 22
real-, 279
-(s) as sets, 269
- -signs, v. numeral statement of-, 275f. , 278 variable-(s), 159fT. , 235fT. --word, v. numeral
Numeral [number-sign, -word], 16 7, 263, 265f. , 273f. , 275
Object, 87fT. , 118fT. , 176fT. , 187, 243f. , 254f. , 263, 269f.
--letter, (v. letter) ! 54
Index
Proper name (nomen proprium, object-
name), 90fT. , 97fT. , 109, 118fT. , 129f. , 154fT. , 159f. , 176fT. , 187fT. , 201f. , 213f. , 225, 234fT. , 243? . , 254? . , 269f.
apparent -, 269f.
complete part of a-, 243f. , 255 meaningless - (v. mock), 179fT. unsaturated part of a-, 195f. , 243f.
Property, 101, 103, I lifT. hereditary -, 28
Proposition, primary/secondary, 14, 17, 46, 4 7 , 5 2
Psychology, 2fT. , 76, 130, 142fT. , 253 Piinjer, 53fT.
Quantifier, v. generality, notation for Question, 7f.
Quotation marks, 158, 261
Realism (epistemological), 144 Recognize, v. true
- as the same again, 141fT.
Reflect, 69f.
Reject, v. false
Relation, 116f. , 177, 240f. , 244, 249f. , 254
first level-, 120, 182
second level-, 120, 182, 254 sign for a-, 240f.
-with three terms, 249
Representation (v. idea), 58, 74 Riemann, 157f.
Russell (v. paradox), 176
Same, 122
Saturated/unsaturated, v. complete, con?
cept, function, proper name, sense,
sentence-part, thought Sayee, A. H. , I7
Scheefer, L. , ! 57
Schliitel, W. , 49
Schoenflies, A. , 176fT.
Schriider, ! Of. , 19f. , 37fT. , 48f. , 91, 123f. Science [discipline], 5, 118, 122f. , 127f. ,
133, 136, 168f. , 203,243
distinction between history of - and
system of-, 24lf.
fruitful definitions in-, 33f. , 46 language of-, 207
most important discoveries in-, 142
Script, 13
Sense, 95f. , 118fT. , 154, 191fT. , 209fT. , 215,
225, 231fT. , 255f. complete/unsaturated-, 116
Sense-perception, 267fT. , 274, 278f. illusions of-, 267fT.
Sentence (v. clause), 119, 129, 138f. , 167(,1 174, 193fT. , 197f. , 20 I, 206, 225, 2341 243, 2. 5. 5f.
affirmative- 10. 5
--name, v. proper name
Objective (objectivity), 7, 105, 137, 144,
148, 198
One(s) (v. unit), 73fT. , 79, 86, 218fT. , 226fT. One-ness, I0I
Onomatopoeia, 13I, 139
Ontological proof (of the existence of God),
101
Or, 36f. , 48fT.
Origin (point of), 280f.
Paradox,
Russell's- 176, 182
-(es) of set theory, 176fT. , 269
Parallel, 281
Part, 181tT. Particular (v. some)
-facts, 258
-judgement, 14, 20, 61, 63, 108,254 -sentence, 105, 254
-thought, 107, 187, 254
Passive, v. active
Peano, 152fT. , 165
Perception (v. sense perception)
a-, 131
Personal suffix, 174
Philosophy (v. mathematics), 64, 67, 270
empirical-, 2f. Physics, 258
sources of knowledge of-, 278 Physiology, 144
Plane, base, 280
Plato, 203, 253
Plus sigii (v. addition, and) 86, 223, 226fT. Point, 280f.
Postulate, 204, 206f.
Potential, v. infinite
Predicate, v. subject-predicate Predicative, v. saturated/unsaturated Premises, 180, 204f. , 244fT. , 261 Prime number, 23, 229
Primitive, v. truth
Product, v. multiplication
Proof, 3, 32, 204fT. , 212, 278
use of auxiliary objects in-, 206f. indirect -, 180, 245fT.
191fT. ,
? Sentence-continued
assertoric - , 126f. , 243
Index 287 Subordination, v. concept
conditional-, v. hypothetical
-(s) expressing command, question, re-
quest, wish, 129
general -, v. generality
hypothetical-, v. hypothetical
meaning of a -, 119, 195, 232fT. , 243,
255f.
negative -, 105
particular-, v. particular
-proper, 190, 192, 195,199
quasi--, 190f. , 193, 199
sense of a -, (v. thought) 126, 129fT. ,
167f. , 216, 243
- a s series of sounds, 129, 139 'true'-, 168, 178, 233
Sentence-part, 192fT. , 225
complete-, v. saturated, unsaturated - designating-, 259f.
indicating- (v. letter), 259f.
- in need of supplementation, v.
Taste, 126, 132
Technical term, 5, 136f. , 207 Temporal, v. time
T ertium non datur , v. law
o f
excluded
saturated/unsaturated - saturated/unsaturated -, 177,
195f. , 20lf. , 228, 243f. Sentence-word, 17
187f. ,
middle
Theorem, 168, 204fT. , 209
'There is' (v.