But the use of this sign is the result of arbitrary
convention and it would be quite possible to choose a simple sign instead
of '+c'; in 'Pp' however, 'p' is not an affix but an argument: the sense of
'Pp' cannot be understood unless the sense of 'p' has been understood
already. (In the name Julius Caesar 'Julius' is an affix. An affix is
always part of a description of the object to whose name we attach it: e.g.
the Caesar of the Julian gens.) If I am not mistaken, Frege's theory about
the meaning of propositions and functions is based on the confusion between
an argument and an affix. Frege regarded the propositions of logic as
names, and their arguments as the affixes of those names.
5.1 Truth-functions can be arranged in series. That is the foundation of
the theory of probability.
5.101 The truth-functions of a given number of elementary propositions can
always be set out in a schema of the following kind: (TTTT) (p, q)
Tautology (If p then p, and if q then q.) (p z p . q z q) (FTTT) (p, q) In
words : Not both p and q. (P(p . q)) (TFTT) (p, q) " : If q then p. (q z p)
(TTFT) (p, q) " : If p then q. (p z q) (TTTF) (p, q) " : p or q. (p C q)
(FFTT) (p, q) " : Not g. (Pq) (FTFT) (p, q) " : Not p. (Pp) (FTTF) (p, q) "
: p or q, but not both. (p . Pq : C : q . Pp) (TFFT) (p, q) " : If p then
p, and if q then p. (p + q) (TFTF) (p, q) " : p (TTFF) (p, q) " : q (FFFT)
(p, q) " : Neither p nor q.
Pages:
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55