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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 scheme 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 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
also: 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 - 5.15
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