4.0412 For the same reason the idealist’s appeal to ‘spatial spectacles’ is inadequate to explain the seeing of spatial relations, because it cannot explain the multiplicity of these relations.

4.05 Reality is compared with propositions.

4.06 A proposition can be true or false only in virtue of being a picture of reality.

4.061 It must not be overlooked that a proposition has a sense that is independent of the facts:  otherwise one can easily suppose that true and false are relations of equal status between signs and what they signify.  In that case one could say, for example, that ‘p’ signified in the true way what ‘Pp’ signified in the false way, etc.

4.062 Can we not make ourselves understood with false propositions just as we have done up till now with true ones?—­So long as it is known that they are meant to be false.—­No!  For a proposition is true if we use it to say that things stand in a certain way, and they do; and if by ‘p’ we mean Pp and things stand as we mean that they do, then, construed in the new way, ‘p’ is true and not false.

4.0621 But it is important that the signs ‘p’ and ‘Pp’ can say the same thing.  For it shows that nothing in reality corresponds to the sign ‘P’.  The occurrence of negation in a proposition is not enough to characterize 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 designatea 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.