• 1 The world is all that is the case.
  • 1.1 The world is the totality of facts, not of things.
  • 1.2 The world divides into facts.
• 2 What is the case--a fact--is the existence of states of affairs.
  • 2.1 We picture facts to ourselves.
  • 2.2 A picture has logicopictorial form in common with what it depicts.
• 3 A logical picture of facts is a thought.
  • 3.1 In a proposition a thought finds an expression that can be perceived by the senses.
  • 3.2 In a proposition a thought can be expressed in such a way that elements of the propositional sign correspond to the objects of the thought.
  • 3.3 Only propositions have sense; only in the nexus of a proposition does a name have meaning [Bedeutung].
  • 3.4 A proposition determines a place in logical space. The existence of this logical place is guaranteed by the mere existence of the constituents--by the existence of the proposition with a sense.
• 4 A thought is a proposition with a sense.
  • 4.1 Propositions represent the existence and non-existence of states of affairs.
  • 4.2 The sense [Sinn] of a proposition is its agreement and disagreement with possibilities of existence and nonexistence of states of affairs.
  • 4.3 Truth-possibilities of elementary propositions mean [bedeuten] possibilities of existence and non-existence of states of affairs.
  • 4.4 A proposition is an expression of agreement and disagreement with truth-possibilities of elementary propositions.
  • 4.5 It now seems possible to give the most general propositional form: that is, to give a description of the propositions of any sign-language whatsoever in such a way that every possible sense can be expressed by a symbol satisfying the description, and every symbol satisfying the description can express a sense, provided that the meanings of the names are suitably chosen.
    It is clear that only what is essential to the most general propositional form may be included in its description--for otherwise it would not be the most general form.
    The existence of a general propositional form is proved by the fact that there cannot be a proposition whose form could not have been foreseen (i.e. constructed). The general form of a proposition is: This is how things stand.
• 5 A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)
  • 5.1 Truth-functions can be arranged in series.
    That is the foundation of the theory of probability.
  • 5.2 The structures of propositions stand in internal relations to one another.
  • 5.3 All propositions are results of truth-operations on elementary propositions.
    A truth operation is the way in which a truthfunction is produced out of elementary propositions.
    It is of the essence of truth-operations that, just as elementary propositions yield a truth-function of themselves, so too in the same way truth-functions yield a further truth function. When a truth-operation is applied to truth-functions of elementary propositions, it always generates another truth-function of elementary propositions, another proposition. When a truth-operation is applied to the results of truth-operations on elementary propositions, there is always a single operation on elementary propositions that has the same result.
    Every proposition is the result of truthoperations on elementary propositions.
  • 5.4 At this point it becomes manifest that there are no "logical objects" or "logical constants" (in Frege's and Russell's sense).
  • 5.5 Every truth-function is a result of successive applications to elementary propositions of the operation
    "(-----T)( ,....)".
    This operation negates all the propositions in the right-hand pair of brackets, and I call it the negation of those propositions.
  • 5.6 The limits of my language mean [bedeuten] the limits of my world.
• 6 The general form of a truth-function is [p, , N(X )].
  This is the general form of a proposition.
  • 6.1 The propositions of logic are tautologies.
  • 6.2 Mathematics is a logical method.
    The propositions of mathematics are equations, and therefore pseudo-propositions.
  • 6.3 The exploration of logic means the exploration of everything that is subject to law. And outside logic everything is accidental.
  • 6.4 All propositions are of equal value.
    • 6.41
    • 6.42
    • 6.43
    • 6.44
    • 6.45
  • 6.5 When the answer cannot be put into words, neither can the question be put into words.
    The riddle does not exist.
    If a question can be framed at all, it is also possible to answer it.
    • 6.51
    • 6.52
    • 6.53
    • 6.54
• 7 What we cannot speak about we must pass over in silence.