# Tractatus Logico-Philosophicus/Index

INDEX^{[1]}

(Note : Numbers in parentheses refer to paragraphs. Thus "6.2II (2)" indicates the second paragraph of section 6. 211.)

A priori

- all inference is, 5.133
- always proves to be something logical, 6.3211
- criterion of such a thought, 3.04
- geometry is, 6.35 (1)
- intuitions, scientific principles as, 6.34
- no part of experience is, 5.634
- possibility of a logical form as, 6.33
- what logic's being, consists in, 5.4731

Accident, none in logic, 2.012

Aesthetics, 6.421 (3)

Affirmation, logical property of, 6.231 (1)

Alphabet, 4.016 (2)

Ambiguity, of "property" and other words, 4.123 (3)

Analysis of propositions, 2.0201, 3.201, 3.25, 4.221 (1)

"Ambulo," a composite proposition, 4.032 (2)

Analytical propositions, 6.11

Application, successive

- defined, 5.2521 (1)
- equivalent to "and so on", 5.2523

Argument

- function cannot be its own, 3.333 (1)
- places, and generality, 4.0411 (2)

Assertion

- and deducibility, 5.124 (1)
- cannot give a sense, 4.064

Assertion sign, meaningless, 4.442 (2)

Atomic facts (*Sachverhalt*)

- are combinations of things, 2.01, 2.03
- are mutually independent, 2.061, 2.062, 4.27 (2)
- number of combinations of, 4.27 (1)
- possible infinity of, 4.2211
- possibility of, 2.012, 2.0124
- possibility of occurrence of things in, 2.0121 (2)
- relation to elementary propositions, 4.21, 4.25
- relation to facts, 2
- relation to propositions, 4.1
- structure of, 2.032

Axiom of Infinity, 5.535 (2, 3)

Axiom of Reducibility, 6.1232, 6.1233

Brackets, their importance, 5.461

Calculation

- not an experiment, 6.2331 (2)
- of logical properties of symbols, 6.126 (i) Case, the (
*der Fall*) - and substance, 2.024
- and the world, 1
- equated with fact, 2
- is existence of atomic facts, 2

Causality: no causal nexus, 5.136. 5.1361

Causality, law of

- as limit of the describable, 6.362
- cannot be said, 6.36 (2)
- is form of a law, 6.32, 6.321, 6.361

Certainty

- as limiting case of probability, 5.152 (3)
- of truth of tautology, 4.464 (1)
- opposed to possibility and impossibility, 4.464 (2)

Clarity: everything can be said and thought clearly, 4. 116

Classes, theory of, superfluous in mathematics, 6.031 (1)

Colloquial language. *See* Ordinary language

Colour

- a form of objects, 2.0251
- logical structure of, 6.3751

"Complex," a formal concept, 4.1272 (7, 8)

Complexes

- and definition, 3.24 (4)
- given only by descriptions, 324 (2)
- how perceived, 5.5423
- propositions about, in internal relation to a statement about constituents, 3.24 (1)
- statements about, analysable, 2.0201

Configuration of objects, 2.0272, 3.21. (*See also* Structure)

Constant : expression as, 3.312 (2)

Contradiction. (*See also* Denial)

- defined, 4.46 (4)
- limiting case of combination of symbols, 4.466 (4)
- not a picture of reality, 4.462
- shared by propositions, 5.143

Correspondence

- between objects and picture elements, 2.13
- of configuration of simple signs and objects, 3.21

Darwinian theory, irrelevant to philosophy, 4.1122

Death, 6.431, 6.4311

Deducibility

- and identity, 5. 141
- and obviousness, 5.1363
- and relative content, 5.14
- and structure, 5.13
- relation to form, illustrated, 5.1311 (1)

Definition

- as analysis, 3.26
- as rule of translation, 3.343
- effect upon signification, 3.261 (1)
- how symbolized, 4.241 (3)
- of a symbol for a complex, 3.24 (4)
- 'complete analysis' (of proposition), 3.201
- of 'contradiction', 4.46 (4)
- of 'expression', 3.31 (1)
- of 'feature', 4.1221
- of 'form', 2.033
- of 'form of an object', 2.0141
- of 'form of representation', 2.151
- of 'formal concept', 4.126 (1)
- of 'formal series', 4.1252 (1)
- of 'independent propositions', 5.152 (1)
- of 'logical picture', 2.181
- of 'logical place', 3.41
- of 'measure of probability', 515
- of 'name', 3.202
- of negation ' (in sense of simultaneous denial), 5.5
- of 'number', 6.022 (2)
- of numbers, 6.02
- of 'operation', 5.23
- of 'propositional sign', 3.12
- of ' propositional variable', 3.313 (3)
- of 'range', 4.463
- of 'sign', 3.32
- of 'simple sign', 3.201
- of 'structure' (of atomic facts) 2.032
- of 'successive application', 5.2521 (1)
- of 'successor', 4.1252 (4)
- of 'tautology', 4.46 (4)
- of 'truth-grounds', 5.101 (2)
- of 'truth-operations', 5.234
- of 'truth-possibilities', 4.3
- only an expedient in presentation, 4.242
- rules for, 5.451 (2)

Denial

- as determining logical place, 4.0641
- by means of what is common to all negation symbols, 5.512 (2)
- is an operation, 5.2341 (2)
- needs a single definition, 5.451
- possibility of, presupposed in affirmation, 5.44 (4)
- occurrence of, does not characterize sense, 4.0621 (2)
- reverses sense, 5.2341 (3)

Denial, sign of

- corresponds to nothing in reality, 4.0621
- does not refer to an object, 5.44 (5)

Description

- of a fact by a proposition, 4.023 (3)
- of an object, 4.023 (4)
- of complex, 3.24 (2)
- of expressions, 3.33
- of propositions, 3.317 (2)
- of reality by a proposition, 4.023 (2)
- of states of affairs, 3.144
- of the world

Descriptions, systems of, 6.341

Distinguishability, 2.02331

"Dynamic models", 4.04 (2)

Ego, the non-psychological, 5.641

Elucidation of primitive signs, 3.263

Equality, meaning of sign of, 6.23 (1)

Equations

- as expressing substitutability, 6.24 (2)
- characterize a standpoint, 6.2323
- not needed to express synonymity, 6.232 (2)

Equiprobability, 5.154 (3)

Essence

- and general form of proposition, 5.471
- of notation, 3.342
- of pictorial nature, 4.013
- of propositions, 3.341, 4.027, 4.03, 4.016, 4.5 (2), 5.471
- of representation, 4.016
- of symbol, 3.341, 3.343. 4.465
- of the world, 5.4711

Essential property, of a thing, to be a possible constituent of atomic fact, 2.011

Eternity, 6.431 1

Ethics, 6.421, 6.422

Existence

- of atomic facts, 2.1 1, 4.1
- of logical place, 3.4

Expedients, in logic, 5.452

Exponent, of an operation, 6.021

Expressions

- all that need to be translated, 4.025 (1)

Expressions — *continued*

- guarantee existence of the logical place, 3.4

have meaning only in a proposition, 3.314 (1)

- presented by a variable, 3.313 (1)
- the proposition is a function of them, 3.318
- the term defined, 3.31 (1)

External property, 2.01231, 2.0233. (*See also* Internal property)

"Fact", a formal concept, 4.1272 (7, 8)

Facts (*Tatsache*). (*See also* States of affairs and Atomic facts)

- and pictures, 2.1, 2. 11
- compose the world, i.i, 1.2
- existence of, 2
- mutual independence of, 1.21
- negative, 2.06 (2)
- required for expression of sense, 3.142
- the world divides into, 1.2
- totality of, 1.11

Fate, and the ancients, 6.372 (1)

Feature, explained, 4.1221

Features of symbols, express formal properties, 4.125 (6)

Form. (*See also* Possibility)

- and possibility of structure, 2.033
- and substance, 2.025
- cannot be said to have properties, 4. 1 241
- general, of propositions, 4.5, 4.47
- general prepositional,
- and truth operations, 5.54
- is a variable, 4.53

- logical, 2.18. (
*See also*Prototype)- and variable, 3.315
- cannot be represented in proposition, 4.12, 4.121 (1)
- how determined by a sign, 3.327
- of propositions, 4.0031

- of a spot, 4.063
- of expressions, 3.31 (4)
- shown by substitutability, 6.23 (2)

- of functions, 3.333 (2)
- of objects, 2.0141, 2.0233, 2.0251
- of propositions, 3.311
- of reality, 2.18
- of representation
- defined, 2.151
- function of, in pictures, 2.22
- is shown forth, 2.172

- of the world consists of objects 2.022-3
- of values of a variable, 4.1271 (2)

Formal, equated with logical 6.12 (1)

Formal concept

- already given with object to which it applies, 4.12721
- as primitive idea, 4.12721
- characteristics of, 4.126 (5, 7)
- defined, 4.126 (1)
- examples of, 4.1272 (7, 8)
- expressed by variables, 4.126 (8), 4.127
- opposed to "proper" concept, 4.126 (2)
- questions about existence of,
- senseless, 4.127

Formal law, as determining formal series, 5.501 (6)

Formal properties

- connexion with structure, 5.321
- explained, 4.122 (1)
- expressed by features of symbols, 4.126 (6)

Formal series

- defined, 4.1252 (1)
- example of, 4.45 (2)
- expression for general term of, 5.2522
- general term of, 4.1273 (2)
- needs variables, 4.1273
- of truth functions, 5.1 (1)
- progress from term to term of, 5.252

Freedom of the will, 5.1362 (1)

Frege, 3.143, 3.318, 3.325, 4.063 (1), 4.1272 (8), 4-1273, 4.4431, 5.02 (3), 5.132 (4), 5.42, 5.451, 5.4733 (1), 5.521, 6.1271, 6.232 (1)

Frequency, of occurrence of events, 5.154 (1)

"Function", a formal concept, 4.1273 (7, 8)

Function

- and composition, 5.47 (3)
- cannot be its own argument, 3333. 5.251
- cannot present formal concepts, 4.126 (4)
- distinct from operation, 5.25 (3)
- elementary proposition is a, of names 4.24 (2)
- proposition is a, of names, 3.318, 4.24 (2)

Future, no knowledge of, 6.26311

Generality

- accidental, 6.031 (2), 6.1232
- concept of, separated from truth-function, 5.521
- essential
- needed in mathematics, 6.031 (2)
- opposed to accidental generality, 6.1232

- how shown, 5.1311 (2)
- how symbolized, 4.0411
- its notation contains a prototype, 3.24 (3). 5.522
- symbol for, occurs as an argument, 5.523
- symbolism for, makes constants prominent, 5.522
- refers to logical prototype, 5.522

Geometrical place, and possibility, 3.41 1

Geometry, as a priori, 6.35 (1)

God, 6.432, 6.372 (1)

"Green is green", 3.323 (3)

Hertz, 4.04 (2), 6.361

Hieroglyphic writing, 4.016

Idealists, their explanation of seeing spatial relations, 4.0412

Identity

- cannot be asserted, 6.2322
- criticism of Russell's definition of, 5.5302
- how expressed, 5.53, 5.531, 5.532. 5.5321
- not a property, 5.473 (2)
- not a relation between objects, 5.5301 (1)
- of sign-tokens, 3.203
- sign of
- dispensable, 5.533, 6.232 (2)
- its meaning, 4.241 (2)

Immortality, 6.4312 (1)

Inconceivability, and internality of properties, 4.123

Independence, of propositions, defined, 5.152 (1)

Index (of a name)

- explained, 5.02
- confused with argument, 5.02 (3)

Induction

- as assumption of simplicity, 6.363
- has only psychological foundation, 6.3631 (1) Induction, law of
- not a logical law, 6.31
- not a priori, 6.31

Inference

- is a priori, 5.133
- "Laws of", senseless, 5.132(4)

Internal properties. (*See also* Formal properties)

- and features, 4.1221
- and inconceivability, 4.123 (1)
- and structure, 4.122 (2)
- knowledge of, needed for knowledge of objects, 2.01231
- of a proposition, describe reality, 4.023 (4)
- of possible states of affairs, 4.124 (1), 4.125
- their holding is shown, 4.122(4)

Internal relations

- and deducibility, 5.131
- and definition of formal series, 4.1252 (1)
- between structures of propositions, 5.2
- equivalent to operations, 5.232
- of statement about a complex to a statement about constituents, 3.24 (1)
- representation as an instance, 4.014 (1)

Internal similarity, 4.0141

"Is," meanings of, 3.323 (2)

Language (*See also* Ordinary Language)

- able to express every sense, 4.022 (1)
- as supplying intuition, 6.233
- "critique of", 4.0031
- disguises the thought, 4.002 (4)
- is totality of propositions, 4.001
- limits of my, 5.6
- logic of, 4.002 (3), 4.003 (1)
- translation of, 3.343

Law of least action, 6.3211

Laws of nature, not explanations, 6.371

Life, the problem of, 6.52, 6.521

Logic. (*See also* Logical propositions)

- all is accident outside, 6.3
- all questions of, answerable off-hand, 5.551 (1)
- and mechanics, 6.342
- application of, 5.5521, 5.557
- as all-embracing, world reflecting, 5.511
- calculation in, 6.121 (1)
- cannot cross limits of world, 5.61 (3)
- deals with possibilities, 2.0121 (3). 5.555 (3)
- every proposition of, its proof, 6.1265
- expedients in, 5.452, 5.511
- impossibility of " contradicting ", 3.03-3.032, 5.4731
- impossibility of describing the world in, 5.61 (2)
- irrelevance of monism and dualism to, 4.128 (2)
- is a priori, 5.4541 (2), 5.4731, 5.551 (1)
- is transcendental, 6.13 (2)
- its propositions are tautologies, 6.1, 6.22
- laws of, do not obey further laws, 6.123 (1)
- must take care of itself, 5.454 (1)
- no classification in, 5.454 (1)
- no mistakes possible in, 5.473 (3)
- no numbers in, 5.453 (2)
- no primitive propositions in, 6.127 (1)
- no surprises in, 6.1251
- not a natural science, 6.111
- not a theory, 6.13 (1)
- nothing accidental in, 2.012
- of constituents, shown by tautologies, 6.12 (2)
- of facts, cannot be represented, 4.0312 (2)
- possibility in, 5.473 (2)
- precedes every experience, 5.552 (2)
- "primitive propositions " of, arbitrary in number, 6.1271
- problems of, concrete, (2)
- process and result equivalent in, 6.1261
- proof in, 6.126 (2-4), 6.1262
- propositions of, say nothing, 5.43 (2)
- reflects the world, 6.13 (1)
- role of postulation in, 6.1223
- searches for regularity, 6.3
- simplicity of, 5.4541
- whole philosophy of, 6.113
- why called theory of forms, 6.1224
- "zero-method" in, 6.121 (2)

Logical, equated with formal, 6.12 (1)

Logical constants

- disappearance of, 5.441
- do not represent, 4.0312 (2)
- only one of them, 5.47 (4),
- there are none, 5.4

Logical coordinates, as determining logical place, 3.41

Logical forms, are anumerical, 4.128 (1)

Logical grammar, 3.325 (1) (*See also* Logical syntax)

"Logical objects", there are no, 4.441, 5.4

Logical place (*See also* Logical space)

- denial as determining, 4.0641
- proposition determines one, 42 (1)
- relation to propositional sign and logical coordinates, 3.41

Logical properties of propositions, demonstrated by producing tautologies, 6.121

Logical propositions

- as forms of a proof, 6.1264 (1)
- as modus ponens, 6.1264 (2)
- connection with the world of, 6.124
- dispensable, 6.122
- have a peculiar place among all propositions, 6.112
- have equal rank, 6.127 (1)
- not confirmable by experience, 6.1222
- not distinguished by generality, 6.1231 (1)
- present the scaffolding of the world, 6.124
- their truth discernible in the symbol, 6.113
- "treat" of nothing, 6.124

Logical space {See also Logical place)

- and the world, 1.13
- everything is in, 2.013
- facts in, 1.13
- given with every proposition, 3.42 (1)
- pictures present facts in, 2.11, 2.202
- place in, determined by proposition, 3.4

Logical syntax

- and rules of translation, 3.344
- implies all logical propositions, 6.124
- meanings of signs plays no role in. 3.33
- need for obeying, 3.325 (1)
- rules of, 3.334

Mathematics

- has no need for theory of classes, 6.031 (1)
- intuition in, place of, 6.233
- is a logical method 6.2 (1), 6.234

Mathematics — *continued*

- method of, working with equations, 6.234 (1)
- no accidental generality in, 6.031 (2)
- proof in, significance of, 6.232 (1)
- propositions of
- all self-evident, 6.234 (1)
- are equations, 6.2 (2)
- as links in inference, 6.211
- express no thoughts, 6.21
- show logic of the world, 6.22

- uses method of substitution, 6.24 (1)

Mauthner, 4.0031

Mechanics

- its generality, 6.3432
- nature of, 6.343
- relation to logic, 6.342

Microcosm, the, 5.63

Meaning

- of names, 3.3
- of primitive signs, 3.263

Modus Ponens, 6.1264 (2)

Multiplicity

- and number of dimensions of signs, 5.474
- and symbol for generality, 4.0411 (3)
- cannot be represented, 4.04 (1)
- the same in the proposition and the state of affairs represented, 4.04

Mystical, the, 6.44, 6.45, 6.522

Names

- are primitive signs, 3.26
- are simple signs, 3.202
- are simple symbols, 4.24 (1)
- are unanalysable, 3.26
- cannot be defined, 3.261 (2)
- cannot express sense, 3.142
- dispensable in describing the world, 5.526
- elementary proposition a connexion of 4.22
- have meaning only in context of proposition, 3.3
- how they occur in propositions, 4.23
- index of, 5.02 (i)
- no composition essential, 3.3411
- resemble points, 3.144 (2)
- the " real ", 33411
- variable, 3.314 (2)

Natural sciences

- are the totality of true propositions, 4. i (1)
- do not include philosophy, 4.111

Necessity: only logical necessity, 6.37

Negation (*See Denial*)

Negation (= Simultaneous denial)

- introduced, 5.5
- symbolized, 5.502

Newtonian mechanics, 6.341, 6.342 (2)

Nonsense (*Unsinn*)

- examples of, 5.5303, 5.5351 (2)
- impossible to judge, 5. 5422

Nonsensical, logical propositions not, 4.461 (1)

Notation (*See also Language*)

- arbitrariness of, 3.342
- essence of, 3.342
- "Number", a formal concept, 4.1272 (7, 8)

Number

- concept of, 6.022
- concept of equality of, 6.1022 (3)
- general form of, 6.022 (1), 6.03

Numbers

- as exponents of operation, 6.021
- definitions of, 6.02
- ordered by internal relation, 4.1252 (2)

"Object", a pseudo-concept, 4.1272 (1)

Objects and possibility, 2.014

- are colourless, 2.0232
- are referred to by names, 3.203, 3.22
- are simple, 2.02
- are substance of world, 2.021
- are the fixed form of the world, 2.023, 2.026
- as determining bounds of empirical reality, 5.5561 (1)
- can only be named, 3.221
- cannot be asserted, 3.221
- common characteristics of, not
- shown by similarity of signs, 3.322
- configuration of, 3.21
- form of, 2.0141
- if given,
*all*are given, 5.524 (1) - independence of, 2.0122
- occurrence in atomic facts of, 2.012-2.0123
- possible infinity of, 4.2211
- possibility of connexion with other objects, 2.0121 (4)
- senseless to speak of their existence, 4.1272 (5)
- senseless to speak of their number, 4.1272 (6)

Obviousness, and deducibility,

Occam's razor, 3.328, 5.47321 (1)

Operations

- assert nothing, 5.25 (2)
- basis of, 5.21, 5.24 (3), 5.25 (2), 5.251
- can cancel out, 5.253, 5.254
- characterize difference in forms, 5.24 (a), 5.241
- connexion with structure, 5.22, 6.002
- defined, 5.23
- depend upon formal properties, 5.231
- distinct from functions, 5.25 (3)
- examples of, 5.2341 (2)
- exponent of, 6.021
- not relations, 5.42 (1)
- number of basic, depends only on our notation, 5.474
- occurrence of, does not characterize sense, 5.25 (1)
- result of, can be basis of same operations, 5.251
- shown in a variable, 5.24 (1)
- signs for, are punctuations, 5.4611
- successive application of, 5.2521, 5.2523

Ordinary language

- all its propositions completely in order, 5.5563
- ambiguity of, 3.323
- as complicated as the human organism, 4.002 (2)
- needs complicated adjustments, 4.002 (5)

Philosophy

- an activity, not a theory, 4.112 (2)
- and the Darwinian theory, 4.1122
- danger of confusion with psychology, 4.1121 (3)
- demarcates natural science, 4.113
- demarcates the thinkable, 4.114
- displays the speakable, 4.115
- importance of possibility in, 3.421
- in no special relation to psychology, 4. 1121 (1)
- is full of confusions, 3.324
- its object the logical clarification of thoughts, 4.112 (1)
- makes propositions clear, 4.112 (4)
- mostly consists of senseless statements, 4.003
- not a natural science, 4.111
- results in elucidations, 4.112(3) Philosophy —
*continued* - right method of, 6.53
- value of questions about purpose of symbolism in, 6.211 (1)

Physical laws, refer to obejcts of the world, 6.3431

Pictures

- and logical space, 2.1 1
- are compared with reality, 2.223
- are facts, 2.14, 2.141
- are models of reality, 2.12, 4.01
- form of representation of, 2.15
- have form of representation in common with reality, 2.16, 2.171
- how linked with reality, 2.151, 2.1511, 2.201, 2.21
- include representing relation, 2.1513
- logical
- are thoughts, 3.
- propositions as, 4.03 (3)
- the term defined, 2. 181

- made by us, 2.1
- none a priori true, 2.224, 2.225
- possibility of, requires substance, 2.0212
- propositions are, 4.012
- propositions as, of reality, 4.021
- represent their sense, 2.221

Possibility, 2.0122-3

- and conceivability, 3.02
- and form of representation, 2.151
- and logic, 2.0121 (3), 5.473 (2)
- and logical place, 3.411
- and nature of the world, 3.3421
- of atomic facts, 2.012, 2.0124
- of connexion of things, 2.0121 (4)
- of method of symbolizing, 2.3421
- of projection, 3.13 (2)
- of propositions, 4.0312 (1)
- of states of affairs, 2.014, 2.202, 2.203
- how shown, 5.525 (2)

- of structure is form, 2.033

"Postulation" of "logical truths", 6.1223

Primitive ideas, formal concepts as, 4.12721

Primitive signs

- how their meanings are elucidated, 3.263
- names are, 3.26
- of logic
- as forms of combination, 5.46
- need to be justified, 5.45

- rules of definition apply to, 5.451 (2)
- signify differently from non-primitive signs, 3.261 (2)

Principles, scientific, as a priori intuitions, 6.34

Probability

- based on series of truth-functions, 5.1
- does not apply to isolated propositions, 5.153
- has certainty as a limiting case of, 5.152 (3)
- involves general description of propositional form, 5.156 (2)
- is a generalization, 5.156 (1)
- measure of, defined, 5.15, 5151
- needed in default of certainty, 5.156 (2)
- of elementary propositions, 5.152 (2)
- proposition
- an extract from other proposition,s 5.156 (5)

- has no special object, 5.1511
- relation of experience to, 5.154(4)
- relation to certainty, possibility, impossibility, 4.464 (2)
- unit of, 5.155

Problems, the deepest, are no problems, 4.003 (3)

Projection

- and translation, 4.0141
- method of, as thought, 3.11 (2)
- possibility of, belongs to proposition, 3.13 (2)

Proof

- in logic, a mechanical expedient, 6.1263
- of significant proposition contrasted with proof in logic, 6.1263
- of twice two, 6.241

Propositional connexion {*Satzverband*), 4.221

Propositional sign

- as determining logical place, 3.41
- cannot contain itself, 3. 332
- defined, 3.12
- elements of, 3.2
- essential nature of, 3.1431 (1)
- is a fact, 3.14, 3.143
- relation of, to proposition, 3.12
- sense of, needs no explanation, 4.02, 4.021
- truth table as, 4.44, 4.442 (1)

Propositional variable

- bar symbol for, 5.501
- defined, 3.313 (3)
- determination of values of, 3.316
- expresses a formal concept, 4.126 (8)
- every variable conceivable as, 3.314
- relation to logical form, 3.315

Propositions

- accidental features of, 3.34
- about complexes, 3.24
- all of equal value, 6.4
- always complete pictures, 5.156 (4)
- analysis of, 3.201, 3.25, 4.221 (1)
- and truth possibilities of elementary prepositions, 4.4
- are articulated, 3.141 (2), 3.251, 4.032 (1)
- are compared with reality, 4.05
- are composite, 4.032 (2), 5.5261 (1)
- are descriptions of facts, 4.023 (3)
- are expressions, 3.31 (2)
- are expressions of their truth conditions, 4.431 (2)
- are generalizations of elementary propositions, 4.52
- are pictures of reality, 4.021
- are truth-functions of elementary propositions, 5(1)
- as configurations of objects, 2.0231
- as functions of expressions, 3.318
- as logical pictures, 4.01 (1), 4.03 (3)
- as models of reality, 4.01 (2)
- can say nothing about themselves, 3.332
- cannot assert their own truth, 4.442 (3)
- cannot be given sense by assertion, 4.064
- cannot represent logical form, 4.12 (1), 4.121
- completely generalized, 5.526 (1), 5.5261 (1)
- content of, 3.13 (4)
- denial of, 4.0641
- determine one logical place each, 3.42
- elementary
- are truth-arguments of proposition, 5.01
- assignment of truth-values to, describes the world, 4.26

- cannot be given a priori, 5.5571

Propositions — *continued*

- cannot contradict other elementary propositions, 4.211
- composition of, cannot be given, 5.55 (2)
- concept of, 5.555 (1)
- consist of names, 4.22, 5.55 (2)
- contain all logical operations, 5.47 (2)
- forms of, no hierarchy of, 5.556
- if given,
*all*are given, 5.524 (2) - importance of, for understanding other propositions, 4.411
- how symbolized, 4.24 (2, 3)
- logically independent, 5.134
- possible forms of, 5.55
- purely logical grounds for there being, 5.5562
- range allowed by, 5.5262 (1)
- relation of truth possibilities of, to other propositions, 4.4
- relation to atomic facts, 4.21, 4.25
- relation to tautology and contradiction, 6.3751(3)

- essential features of, 3.34

expression of thoughts in, 3.2

- follow from elementary propositions, 4.52
- general form of, 5.47 (5)
- have elementary propositions as truth-arguments, 5.01
- have sense independent of facts, 4.061
- have truth-value because pictures of reality, 4.06
- how understood, 4.024
- in them names stand for objects, 3.22
- logical (
*See*Logical propositions) - logical form of, 4.0031
- most general form of, 4.5, 6
- need only 'yes' or 'no' to fix reality, 4.023 (1)
- neither probable nor improbable in themselves, 5.153
- number of possibilities of agreement with truth-possibilities of elementary propositions, 4.42, 4.45 (1)
- opposition of, 5.513 (2)
- present existence and non-existence of atomic facts, 4.1
- presuppositions of, 5.5151 (3)

"primitive", 5.43 (1) probability, have no special object, 5.1511

- psychological, 5.541, 5.542
- reach through whole logical space, 3.42 (3)
- relation of, to propositional sign, 3.12
- resemble arrows, 3.144 (2)
- say how, not what a thing is, 3.221
- sense of, unchanged by adjoining tautology, 4.465
- show their sense, 4.022
- show what they say, 4.461 (1)
- significant
- are thoughts, 4
- content of, 3.13 (4, 5)

- what is common to, illustrated, 5.513 (1)
- what they say, 4.022 (2)
- what logical space given with, 3.42 (1)

Prototype

- and logical form, 3.315
- and symbolism for generality, 5.522
- and variable, 3.315
- examples of, 3.333 (1), 5.5351 (1)
- in notation for generality, 3.24 (3), 5.522

Pseudo-concept, 4.1272 (1)

*proposition*and*thing*as, 5.5351 (1)

Pseudo-propositions, 5.535 (1)

- arising from use of pseudo-concepts, 4.1272 (4)
- mathematical propositions are, 6.2 (2)

Psychology, and philosophy, 4.1121

Range, defined, 4.463

Reality

- as existence of atomic facts, 2.06 (1)
- completely described by proposition, 4.023 (2)
- described by internal properties of proposition, 4.023 (4)
- empirical, bounded by totality of objects, 5.5561 (1)
- form of, 2.18
- how linked to pictures, 2.1511-2.15121
- logical features of, 4.023 (5)
- not pictured by tautology or contradiction, 4.462
- pictures are models of, 2.12
- pictures compared with, 2.21, 2.223
- proposition as picture of, 4.01 (1), 4.021
- propositions are compared with, 4.05
- total, is the world, 2.063

Representation, logic of, 4.015 (See also Form of representation)

Representing relation, belongs to the picture, 2.1513

Right and left hand, Kantian problem of, 6.361 11

Rules, as equivalent to symbols, 5.514

Russell, 3.318, 3.325, 3.331, 3.333, 4.0031, 4.12721, 4.1272 (8), 4.1273, 4.241 (3), 5.02 (2), 5.132 (4), 5.252, 5.4, 5.42, 5.-452 (2), 5.513 (3), 5.521, 5.525. 5.5302, 5.535, 5.541 (4), 5.5422, 5.553 (1), 6.123 (2), 6.1232

Russell's paradox, 3.333 (4)

Saying

- by propositions, 4.022 (2)
- impossibility of, what we cannot think, 5.61 (4)

Scaffolding, logical, 3.42 (3), 4.023 (5), 6.124

Scepticism, 6.51 (1)

Self-evidence (*See also* Obviousness)

- how discarded in logic, 5.4731
- not a criterion of logical propositions, 6. 1 271
- of mathematical propositions, 6.2341

Sense

- and deducibility, 5.122
- cannot be supplied by assertion, 4.064
- characterized by expressions, 3.31 (1)
- connexion with method of projection, 3. 11 (2)
- equated with representation of state of affairs, 4.031 (2)
- expressible only by facts, 3.142
- new, how communicated, 403 (1)
- objects occurring in, 4.1211 (1)
- of propositional sign, needs no explanation, 4.02, 4.021
- of propositions
- and possibilities of existence of atomic facts, 4.2
- contained in sense of other propositions, 5.122
- expressed by spatial position, 3.1431 (2)
- form only of, contained in proposition, 3.13 (4)

Sense — *continued*

- how determined, 4.063 (2)
- independent of facts, 4.061 (1)

- of truth-functions as a function, 5.2341 (i)
- only propositions have it, 3.3
- opposite, 4.0621 (3)
- postulate of determinateness of, 3 23
- requires substance, 2.021 1
- reversed by denial, 5.2341 (3)
- what a picture represents is its, 2.221

Senseless (*Sinnlos*)

- distinct from nonsensical, 4.461 (3), 4.4611
- examples of the, 4.1272 (9), 4.1274, 5.1362 (2)
- "laws of inference" are, 5.132 (4)
- tautology and contradiction are, 4.461 (3)

Series, formal {See Formal series)

Showing

- by tautologies and contradictions, 4.461 (1)
- by structure, 4.1211 (2)
- correctness of solipsism, 5.62 (2)
- examples of, 4.1211, 6.12, 6.1201, 6.127 (2), 6.36 (2)
- excludes saying, 4. 1212
- generality, 5.1311 (2)
- logic of the world, 6.22
- logical form, 4. 121 (4)
- needed for form of representation, 2.172
- of operations, 5.24 (i)
- of sense, 4,022
- that a formal concept applies, 4.126 (3)
- that internal properties hold, 4.122 (4)
- that one proposition follows
- from another, 4.1 211 (2)
- that the world is my world, 5.62 (3)
- the inexpressible, 6.522
- what it says, by proposition, 4.461 (1)

Sight, field of, 5.633, 5.6331

Sign

- and symbol, 3.326
- application of, 3.262
- as likeness of the signified, 4.012
- as perceptible part of symbol, 3.12 3.32
- cannot receive a wrong sense, 5.4732
- complex, 3.1432
- equivalence of, 5.47321 (2)
- how it determines a logical form, 3.327
- identity of tokens of, 3.203
- possible, 5.473 (2)
- primitive (
*See*Primitive signs) - propositional (
*See*Propositional sign) - simple, 3.201, 3.202
- the same, may belong to different symbols, 3.321
- unused, 3.328 (1)

Similes, 4.015

Simplicity of objects, 2.02, 2.021

"Socrates is identical", 5.473 (2), 5.4733 (3)

Solipsism

- coincides with realism, 5.64
- correct in intention, 5.62

Soul, 5.5421 {*See also* Subject)

Space

- a form of objects, 2.0251
- congruence in, 6.36111
- geometrical figures cannot contradict laws of, 3.032
- logical (
*See*Logical space) - spatial objects must lie in, 2.0131 (1)
- spatial objects unthinkable apart from, 2.0121 (4)
- symmetry in, 6.3611 (3)
- visual, 2.0131 (2)

"Spatial spectacles", 4.0412

States of affairs (*Sachlage*)

- can be described, not named, 3.144 (i)
- connexion of object with, 2.0122
- possibility of, 2.014

Structure

- and form, 2.033
- and internal property, 4.122(2)
- connexion with operation, 5.22
- logical, 4.014 (2)
- logical relations shown by, 4.1211 (2)
- of a picture, 2.15 (2)
- of atomic fact, 2.032, 2.034
- of propositions, and deducibility, 5.13
- of propositions, stand in internal relations, 5.2
- properties of, and tautology, 6.12 (3)

Subject, the

- and the body, 5.631 (2)
- does not belong to the world, 5.632
- is a limit of the world, 5.632, 5.641 (3)
- no such thing exists, 5.542 (1), 5.631 (1)

Substance

- of the world, identified with objects, 2.021
- exists independently of what is the case, 2.024
- is form and content, 2.025

Successor, definition of, 4.1252(4)

Superstition, 5.1361 (2)

Symbolizing, methods of, 3.322

Symbols

- and signs, 3.326
- as equivalent to rules, 5.541
- composite, criterion of, 5.5261 (2)
- difference of, 3.323 (3)
- different, may have common sign, 3.321
- equated with expressions, 3.31
- essential features of, 3.34
- for complexes, how defined, 3.24 (4)
- have sign for perceptible part, 3.32
- presuppositions of, 5.5151 (3)
- what signifies in, 3.344

Tautology

- a limiting case of combinations of symbols, 4.466 (4)
- an ungeneralized proposition can be, 6.1231 (2)
- and properties of structure, 6.12 (3)
- as showing logic of the world, 6.22
- defined, 4.46 (4)
- derivation of tautology from, 6.126 (3)
- effect of adjoining, to a proposition, 4.465
- follows from all propositions, 5.142
- has no truth conditions, 5.461 (2)
- how used in demonstrating logical properties, 6. 121
- is analytical proposition, 6. 11
- is without sense, 4.461 (3)
- its truth certain, 4.464 (1)
- logical proposition is, 6.1
- method for recognizing, 6.1203
- not a picture of reality, 4.462
- not nonsensical, 4.4611
- probability of, 5.152 (4)
- says nothing, 4.461 (1), 5.142, 6.11
- shared by propositions, 5.143 (1)
- shows that it is a tautology, 6.127 (2)

Theory of knowledge, how related to psychology and philosophy, 4.1121 (2)

Theory of types, 3.33i-3.333, 5.252, 6.123 (2)

Things (See Objects)

Thinkable

- and picturable, 3.001
- and possible, 3.02
- is demarcated by philosophy, 4.114
- only uniform connexions are, 6.361

Thought

- a priori, criterion of, 3.04
- as a logical picture, 3
- as method of projection, 3.11 (2)
- contains possibility of a state of affairs, 3.02 (1)
- disguised by language, 4.002(4)
- expressed by signs, 3.1
- form of, 4.002 (4)
- how expressed in propositions, 3.2
- is applied propositional sign, 3.5
- is the significant proposition, 4

Time

- a form of objects, 2.0251
- "passage" of, 6.3611 (i)
- sequence of events in, 6.3611 (1, 2)
- temporal objects unthinkable apart from, 2.0121 (4)

Totality of atomic facts, 2.05

Translation

- and projection, 4.0141
- as criterion for "what is common" to symbols, 3.343

Truth

- and falsity, not coordinate relations, 4.061
- concept of, explained, 4.063
- concept of, Frege's account false, 4.431 (3)
- its connexion with pictorial nature of proposition, 4.06
- not a property, 6.111

Truth-arguments, elementary propositions are, 5.01

Truth-conditions

- groups of, can be ordered in a series, 4.45
- how expressed, 4.442 (4)
- of propositions, and truth possibilities of elementary propositions, 4.41
- symbolism for, 4.43
- relation to truth-possibilities, 4.431 (1)

Truth-functions

- and truth-operations, 5.3 (2, 3)
- are results of operations, 5.234
- can be ordered in series, 5.1 (1)
- general form of, 6 (1)
- not material functions, 5.44 (1)
- notations for, 3.3441
- of two variables, itemized, 5.101 (1)
- result from application of simultaneous denial, 5.5 (1)
- the term introduced, 5.

Truth-grounds

- and deducibility, 5.11, 5.12, 5.121
- as measure of probability, 5.15, 5.151
- defined, 5.101 (2)

Truth-operations

- and truth-functions, 5.3 (2, 3)
- defined, 5.234

Truth-possibilities

- defined, 4.3
- of combinations of elementary propositions, 4.28
- schemata for, 4.31

Understanding

- depends on understanding elementary propositions, 4.411
- of general propositions depends on understanding elementary propositions, 4.411
- of names, 4.243
- of propositions, 4.02, 4.024 INDEX
- of synonyms, 4.243

Unspeakable, the, and philosophy, 4. 1 15

Value, 6.4, 6.41

Variable {See also Propositional variable)

- an expression presented by, 3.313
- is sign of formal concepts, 4.1271
- can be regarded as propositional variable, 3.314
- determination of values of, 3.317
- form of, 4.1271 (2)
- general propositional, 5.242
- general propositional form is a, 4.53
- in expression of general term of series, 5.2522
- names, as sign for pseudo-concept,
*object*, 4.1272 (1) - name, can be conceived as propositional variable, 3.314 (2)
- needed for expressing general term of formal series, 4.1273 (1)
- propositional {See Propositional variable)
- used for operations, 5.24 (1)
- values of, 3.315, 5.501 (6)

Whitehead, 5.452 (2), 5.252

Will, the, 6.423, 6.43

Words, cannot occur both in and out of propositions, 2.0122

World, my

- I am, 5.63
- limits of, 5.62 (3)

World, the

- and life are one, 5.621
- and logical space, 1.13
- and what is the case, 1
- completely described by totality of true elementary propositions, 4.26
- composed of facts, not things, 1.1
- connexion with logical propositions, 6.124
- divides into facts, 1.2
- independent of my will, 6.373, 6.374
- information about, given by simplicity of description, 6.342 (2)
- is total reality, 2.063
- is totality of atomic facts, 2.04
- its form consists of objects, 2.023
- limits of, 5.61 (i)
- logic of, shown in tautologies and equations, 6.22
- logical properties of, 6.12, 6.124
- names not needed for description of, 5.526
- nature of, revealed by possibility, 3.3421
- objects its substance, 2.021
- projective relation of propositional sign to, 3.12
- sense of, 6.41 (i)
- the subject does not belong to it, 5.632

"Zero-method", in logic, 6.121 (2)

- ↑ The Editor is indebted to Professor Max Black for providing this Index, which was originally prepared for the use of his students at Cornell University.