So much for elementary propositions. What about the non-elementary ones that predominate in natural language? Wittgenstein’s answer was that every non-elementary proposition is a truth-function of elementary ones. What does this mean?
A proposition p is a truth-function of propositions q1, q2, . . . , qn just in case the truth-values of the latter settle the truth-value of the former in all possible circumstances. For instance, if p says that it is raining or it is snowing, q1 says that it is raining and q2 says that it is snowing, then p is a truth-function of q1 and q2: no two possible worlds that agree over q1 and q2 are going to disagree over p. So Wittgenstein thought that the truth-value of every proposition is settled by the truth-values of the elementary ones.
Now take all the distributions of truth-values amongst elementary propositions that make a given p true: these are its truth-grounds (TLP, 5.101). Then the possible worlds where p’s truth-grounds obtain are exactly those worlds where p is true, that is, those amongst which p claims that the actual world lies. So the truth-grounds of p settle what p says in that modal sense of ‘what p says’ introduced at Section 2.
Hence to account for the truth-grounds of a proposition is to account for its content. That completes Wittgenstein’s answer to (1).
6. Consequences
Here are two consequences of the view we’ve outlined – one for meta-physics and one for logic.
The first follows from the picture theory’s generality. Wittgenstein thought (TLP, 3–3.001) that thoughts are pictures: what we can and cannot picture is just what we can and cannot think. It is no use trying to ‘get outside’ thought: if a thought is really about anything – that is, if it is a thought at all – then it must conform to the constraints on meaningful discourse that the picture theory imposes.
This means that any general formal constraints on symbolism mirror literally unthinkable features of the universe. They belong to its ‘logical form’. Thus consider the distinction between particular and universal.
We have an obscure sense – which does not qualify as a thought – that components of monadic facts somehow ‘fit together’. We cannot describe this incomparable thing in language or thought; but language and thought illustrate it. For the essence of the picture theory is that the elements of meaningful subject–predicate sentences share just that
‘fitting together’ of their elements with the reality that they depict. Or consider the number of simple objects: language cannot tell us that the world contains these and these objects; but the multiplicity of its names reflects this (TLP, 4.1272, 5.5561). The Tractatus puts it in terms of a famous distinction: these metaphysical things cannot be said; but our language shows them to us (TLP, 4.12–4.121; cf. 6.36).
The second consequence concerns logical consequence. Russell con-sidered logic a science, its job being to discover truths about actuality of the kind ‘which can be made concerning everything without mention-ing any one thmention-ing or predicate or relation’ (Russell, 2004, p. 86). For instance the logical truth of ‘If, if Mary is fat then Tom is bald, and Mary is fat, then Tom is bald’ is explained by its belonging to the generally true schema: ((p ⊃ q) p) ⊃ q.
But for Wittgenstein logic is about what follows from what (TLP, 6.1264); and it doesn’t say anything at all about the world. That one proposition follows from others is not a truth distinct from those of the non-logical sciences; it is rather an inevitable by-product of the repre-sentational mechanism that those sciences already employ, that is, that described in Section 5. More particularly, q follows from p1, p2, . . . , pn iff the truth-grounds that are common to the pi are amongst the
truth-grounds of q. Logic ‘is not a field in which we express what we wish with the help of signs, but rather one in which the nature of the natural and inevitable signs speaks for itself’ (TLP, 6.124).
7. Conclusion
This very brief account has been necessarily both lacunary and dog-matic. Some of the power of the Tractatus resides in its cosmic sweep but most of its value resides in the detailed working out of his theory of symbolism and its application to issues that I have not touched upon:
the Theory of Types (TLP, 3.33–3.333), solipsism and the self (TLP, 5.541–5.5423, 5.6–5.641), the nature of mathematics (TLP, 6.01–6.031, 6.2–6.241), and of rational mechanics (TLP, 6.3–6.3751), the theory of value (TLP, 6.4–6.45), and the nature of philosophy (TLP, 6.5–7).
Further Reading
The best short introductions to the Tractatus are still those by Anscombe (1959) and Mounce (1981). Among more demanding discussions, the best short one is Ramsey’s critical notice (1923). Two other classics are: Black, 1967; and Pears, 1987.
According to a tradition that I have not discussed, the Tractatus is not supposed to say anything. Rather it is supposed (as Pears puts it) to be a kind of emetic that purges you of itself as well as of philosophy. For more on, and by, those ‘New Witt-gensteinians’ who believe this, see Crary and Read (eds), 2000.
Notes
1 Sections 1–3 of this exposition qualify it as a realist interpretation of the Tracta-tus, according to which the structure of possibilities is the independent guarantor of linguistic meaning. This point is controversial: for an excellent discussion of both it and the alternative, on which the real possibilities of our world merely shadow the expressive possibilities of our language, see Pears, 1987, chapter 5.
2 This interpretation of TLP 3.11 is controversial; for an alternative reading see Mounce, 1981, pp. 31–3. For further discussion see Hacker, 1999.
Bibliography
Anscombe, G. E. M. (1959), An Introduction to Wittgenstein’s Tractatus. London:
Hutchinson.
Black, M. (1964), A Companion to Wittgenstein’s Tractatus. Cambridge: Cambridge University Press.
Crary, A. and Read, R. (eds) (2000), The New Wittgenstein. London: Routledge.
Hacker, P. M. S. (1999), ‘Naming, Thinking and Meaning in the Tractatus’, Philosophi-cal Investigations, 22, (2), 119–35.
Mounce, H. O. (1981), Wittgenstein’s Tractatus: An Introduction. Oxford: Blackwell.
Pears, D. (1987), The False Prison: A Study of the Development of Wittgenstein’s Philosophy, vol. I. Oxford: Clarendon Press.
Ramsey, F. P. (1923), ‘Critical Notice of the Tractatus’. Mind, 32, 465–78.
Russell, B. (1985 [1918]), The Philosophy of Logical Atomism. Chicago and La Salle, IL: Open Court.
—(2004 [1912]), ‘On Scientific Method in Philosophy’, in his Mysticism and Logic.
Mineola, NY: Dover, pp. 75–96.
Wittgenstein, L. (1961 [1921]), Tractatus Logico-Philosopicus, trans. D. F. Pears and B. F. McGuinness. London: Routledge.