TRACTATUS LOGICO-PHILOSOPHICUS

of the meaning of propositions and functions. For Frege the propositions of logic were names and their arguments the indices of these names.

5.1 The truth-functions can be ordered in series. That is the foundation of the theory of probability.

5.101 The truth-functions of every number of elementary propositions can be written in a schema of the following kind:

(T T T T) (*p, q*) Tautology (if *p* then *p*, and if *q* then *q*) [*p* *p* *q**q*]

(F T T T) (*p, q*) in words: Not both *p* and *q*. [ (*p*.*q*)]

(T F T T) (*p, q*) „ „ If *q* then *p*. [*q**p*]

(T T F T) (*p, q*) „ „ If *p* then *q*. [*p**q*]

(T T T F) (*p, q*) „ „ *p* or *q*. [*p**q*]

(F F T T) (*p, q*) „ „ Not *q*. [*p**q*]

(F T F T) (*p, q*) „ „ Not *p* [*p**p*]

(F T T F) (*p, q*) „ „ *p* or *q*, but not both. [*p*. *q* : v : *q*. *p*]

(T F F T) (*p, q*) „ „ If *p* then *q* ; and if *q*, then *p* [*p**q*]

{T F T F) (*p, q*) „ „ *p*

(T T F F) (*p, q*) „ „ *q*

(F F F T) (*p, q*) „ „ Neither *p* nor *q*. [*p*. *q* or *p*|*q*]

(F F T F) (*p, q*) „ „ *p* and not *q*. [*p*. *q*]

(F T F F) (*p, q*) „ „ *q* and not *p* [*q*. *p*]

(T F F F) (*p, q*) „ „ *p* and *q*. [*p*.*q*]

(F F F F) (*p, q*) Contradiction (*p* and not*p* and *q* and not *q*.)[*p*. *p*.*q*. *q*]

Those truth-possibilities of its truth-arguments, which verify the proposition, I shall call its truth-grounds.

5.11 If the truth-grounds which are common to a number of propositions are all also truth-grounds of some one proposition, we say that the truth of this proposition follows from the truth of those propositions.

5.12 In particular the truth of a proposition *p* follows
from that of a proposition *q*, if all the truth-grounds of the second are truth-grounds of the
first.

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