LANGUAGE (7) A proposition is true or false by agreeing or disagreeing with reality: it is true if the possible situation it depicts obtains in fact, and false if it does not (TLP 4.023) (8) A proposition must be independent of the actual situation, which, if it obtains, makes it true; otherwise it could never be false (TLP 3.13) (9) No proposition is a priori true (TLP 3.05) In stating these theses I have not used the word ‘picture’, because the theory is interesting and important whether or not it is misleading to encapsulate it in the slogan ‘A proposition is a picture’ Wittgenstein did in fact believe that all the theorems remain true if for ‘proposition’ one substitutes the word ‘picture’ He was also well aware that propositions not look like pictures But he believed that if a proposition were fully articulated and written out in an ideal language, then to each element of the propositional sign would correspond a single object in the world Thus its pictorial nature would leap to the eye (TLP 3.2) We should not think, however, that there is anything wrong with the unanalysed sentences we utter in ordinary life Wittgenstein insists that all the propositions of our everyday language, just as they stand, are in perfect logical order (TLP 5.5563) That is because the full analysis of them is already present in the thought of any of us who understand them, although of course we are no more conscious of how our words symbolize than we are of how our sounds are produced (TLP 4.002) Not all sentences produced by English speakers, however, are genuine propositions: many are only pseudo-propositions which analysis would reveal to lack sense The last seventeen pages of the Tractatus are devoted to a brisk demonstration of how the propositions of logic (6.1 ff.), mathematics (6.2 ff.), a priori science (6.3 ff.), ethics and aesthetics (6.4 ff.), and finally philosophy (6.5 ff.) are all in different ways pseudo-propositions The only propositions that deserve a place in logic books are tautologies, which say nothing themselves but simply exhibit the logical properties of genuine propositions, which say things (TLP 6.121) Mathematics consists of equations, but equations are concerned not with reality but only with the substitutability of signs In real life we make use of mathematical propositions only in passing from one non-mathematical proposition to another (TLP 6.2–3) In science, propositions such as the axioms of Newtonian mechanics are not really propositions; rather, they are 136