HOME TOP UP PREV NEXT GERMAN MAP      Tractatus Logico-Philosophicus 5.101


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

(T T T T)(p, q) Tautology (if p then p, and if q then q) [p  HOOK  p . q  HOOK  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  HOOK  p]
(T T F T)(p, q)     ''    ''    If p then q. [p  HOOK  q]
(T T T F)(p, q)     ''    ''    p or q. [p v q]
(F F T T )(p, q)     ''    ''    Not q. [~q]
(F T F T)(p, q)     ''    ''    Not 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.


HOME TOP UP PREV NEXT GERMAN MAP      Tractatus Logico-Philosophicus 5.101