Tractatus Logico-Philosophicus/Index

by Ludwig Wittgenstein

 

INDEX^[1]

(Note : Numbers in parentheses refer to paragraphs. Thus "6.211 (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)

1. 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.