No More Learning

, 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. existence), 53fT. , 107fT. , 249f. ,
254
Thinking, 35, 105, 127, 136fT. , 142fT. , 174,
185, 206, 269f. rules for-, 128
Thought, 95f. , 99, 116f. , 119, 167f. , 174, 185fT. , 188f. , 197fT. , 206fT. , 216, 243, 251f. , 253f. , 256, 258f.
actuality of-(s), 138
analysis of -(s), 107f. , 187, 253
colouring of a - , 198
combination of-(s), 150f.
conjunction of -(s), 200
grasping of -(s), 137f. , 198, 206, 25 3, 267 independence of - from thinking, 127,
133fT. , 206
laws of-, 4f. , 145fT.
mock-, v. mock
opposed -(s), 149f. , 185, 198 part of a-, 243, 253
cement for- 191
saturated/unsaturated - 116f. , 187fT. ,
190f. , 201f. , 243, 254f.
predicative component of -/subject com-
ponent of-, 185
- proper, 129, 148f.
separating - from its trappings, 138! 1'. timelessness of -(s), 135
Time, 266, 274 - instants, 15
Transfinite, 68
Translation, 6, 129, 131, 141,206
Triangles, similarity of, congruence of, 280f. True, 2fT. , 48, 51, 122, 126fT. , 144, 168f. ,
174f. , 186f. , 188f. , 194, 233, 251f. the-, 195, 233, 255
' ' contrasted with 'beautiful', v.
'beautiful'
'-'as predicate, 251f.
recognize a thought as -, 2, 7, 131fT. ,
138f. , 168, 185f. , 197, 251, 267 Truth (v. true),
eternal --(s), 15
Series (v. hereditary property), 22, 25, 38 Set (v. paradoxes of- theory), 181fT. , 269
Sign (v. concept-script, concept, relation), 17, 21 Of.
function,
ambiguous -(s), 213,227, 237
-and what is designated, 158f. , 224f. - and content of-, 85f. , 167 designating -/indicating -
249f. , 272 number--, v. number primitive-, 37,46
Signification (Peano's use of), 153fT. Similarity, v. triangle
Simple (v. meaning), 89, 271 Singular
- hypothetical thought, 189 -judgement, 107, 187, 201
- content of possible judgement, 107 -thought, 187fT.
-term (v. proper name), 118
-sinnig, 123f.
SneU, K. , 280
Some (v. particular), 60fT. , 120,213 Something, 190, 260
Sorites, 155
Speech (v. ordinary language)
indirect-, 130, 256 Spinoza, 84
Statement (v. assertion)
possibility of a -, 214
Subject-predicate, 17, 59f. , 90fT. , 96fT. ,
! 07f. , 120, 141ff. , 178, 185 Subjective, 148
130f. , 138,
233f. ,
Subsumption, v. concept, faUing of an object under
Subtraction sign (logical), 48f. , 52
Successor relation between natural numbers,
v. foUowing in a series Supplementation, v. saturated/unsaturated SyUogism, 35
Symmetrical (points), 280f.
System, 205fT. , 211, 241fT.
(v.
letter),
? 288 Index
Truth-continued
laws of-, and laws of holding to be true, 128, 145f. , 148f.
-(s) in mathematics, 78, 168f. primitive-, 204f.
--value, 99, 195, 233, 243
Un-[prefix], 150
Unit (v. one(s)), 73fT. , 79, 86, 218fT. , 226fT. Univocal, 123f.
Universe ofdiscourse, 15
Unknown (in algebra), 236f.
Unsaturated, v. saturated/unsaturated
Variable (v. letter, lettre variable), 159fT. 164, 235f. , 237f.
Variation, 159f. , 236 Verbal
- definitions, 215 -language [prose], 12f. , 39 -script, 13
Weierstrass, 215fT.