terize its sense (PPp = p). The propositions 'p' and 'Pp' have
opposite sense, but there corresponds to them one and the same reality.

4.063 An analogy to illustrate the concept of truth: imagine a black
spot on white paper: you can describe the shape of the spot by saying,
for each point on the sheet, whether it is black or white. To the fact
that a point is black there corresponds a positive fact, and to the fact
that a point is white (not black), a negative fact. If I designate
a point on the sheet (a truth-value according to Frege), then this
corresponds to the supposition that is put forward for judgement, etc.
etc. But in order to be able to say that a point is black or white, I
must first know when a point is called black, and when white: in order
to be able to say,'"p" is true (or false)', I must have determined in
what circumstances I call 'p' true, and in so doing I determine the
sense of the proposition. Now the point where the simile breaks down is
this: we can indicate a point on the paper even if we do not know
what black and white are, but if a proposition has no sense, nothing
corresponds to it, since it does not designate a thing (a truth-value)
which might have properties called 'false' or 'true'. The verb of a
proposition is not 'is true' or 'is false', as Frege thought: rather,
that which 'is true' must already contain the verb.

4.064 Every proposition must already have a sense: it cannot be given a
sense by affirmation. Indeed its sense is just what is affirmed. And the
same applies to negation, etc.

4.0641 One could say that negation must be related to the logical
place determined by the negated proposition. The negating proposition
determines a logical place different from that of the negated
proposition. The negating proposition determines a logical place
with the help of the logical place of the negated proposition. For it
describes it as lying outside the latter's logical place. The negated
proposition can be negated again, and this in itself shows that what
is negated is already a proposition, and not merely something that is
preliminary to a proposition.

4.1 Propositions represent the existence and non-existence of states of
affairs.

4.11 The totality of true propositions is the whole of natural science
(or the whole corpus of the natural sciences).

4.111 Philosophy is not one of the natural sciences. (The word
'philosophy' must mean something whose place is above or b