st.
4.28 There correspond to these combinations the same number of
possibilities of truth--and falsity--for n elementary propositions.
4.3 Truth-possibilities of elementary propositions mean Possibilities of
existence and non-existence of states of affairs.
4.31 We can represent truth-possibilities by schemata of the following
kind ('T' means 'true', 'F' means 'false'; the rows of 'T's' and
'F's' under the row of elementary propositions symbolize their
truth-possibilities in a way that can easily be understood):
4.4 A proposition is an expression of agreement and disagreement with
truth-possibilities of elementary propositions.
4.41 Truth-possibilities of elementary propositions are the conditions
of the truth and falsity of propositions.
4.411 It immediately strikes one as probable that the introduction of
elementary propositions provides the basis for understanding all other
kinds of proposition. Indeed the understanding of general propositions
palpably depends on the understanding of elementary propositions.
4.42 For n elementary propositions there are ways in which a proposition
can agree and disagree with their truth possibilities.
4.43 We can express agreement with truth-possibilities by correlating
the mark 'T' (true) with them in the schema. The absence of this mark
means disagreement.
4.431 The expression of agreement and disagreement with the truth
possibilities of elementary propositions expresses the truth-conditions
of a proposition. A proposition is the expression of its
truth-conditions. (Thus Frege was quite right to use them as a starting
point when he explained the signs of his conceptual notation. But the
explanation of the concept of truth that Frege gives is mistaken: if
'the true' and 'the false' were really objects, and were the arguments
in Pp etc., then Frege's method of determining the sense of 'Pp' would
leave it absolutely undetermined.)
4.44 The sign that results from correlating the mark 'I' with
truth-possibilities is a propositional sign.
4.441 It is clear that a complex of the signs 'F' and 'T' has no object
(or complex of objects) corresponding to it, just as there is
none corresponding to the horizontal and vertical lines or to the
brackets.--There are no 'logical objects'. Of course the same applies to
all signs that express what the schemata of 'T's' and 'F's' express.
4.442 For example, the following is a propositional sign: (Frege's
|