Ludwig Wittgenstein once said that language can’t even describe the smell of a cup of coffee – this is an interesting statement with not a small amount of truth to it. In his ‘Tractatus-Logicus-Philosophicus,’ Wittgenstein reduced language a tight logical system because he was attempting to explain one of Bertrand Russell’s big questions: what is logic? After his departure from and return to philosophy, Wittgenstein realized that what Russell tried to say about logic can’t be said with language – not because of any deficiency on the part of language but because he had misunderstood the limits of language.
What are the limits of language? Are there certain things that language can’t say? This is the idea of ‘the ineffable,’ present in a number of religious and mystical traditions – that the most deep and true things in the world can’t be said. Wittgenstein famously ends the ‘Tractatus’ with the proposition, ‘Whereof one cannot speak, thereof one must be silent.’
But should this be seen as Wittgenstein committing himself to the idea of the ineffable? It’s difficult to say – there appear to be things that can’t be said, but must rather be shown – a family resemblance, for example.
So to return to the question, what are the limits of language? How does language relate to the world?
For Wittgenstein and the ‘Tractatus,’ the answer was logic:
‘Starting with a seeming metaphysics, Wittgenstein sees the world as consisting of facts (1), rather than the traditional, atomistic conception of a world made up of objects. Facts are existent states of affairs (2) and states of affairs, in turn, are combinations of objects. Objects can fit together in various determinate ways. They may have various properties and may hold diverse relations to one another. Objects combine with one another according to their logical, internal properties. That is to say, an object’s internal properties determine the possibilities of its combination with other objects; this is its logical form. Thus, states of affairs, being comprised of objects in combination, are inherently complex. The states of affairs which do exist could have been otherwise. This means that states of affairs are either actual (existent) or possible. It is the totality of states of affairs—actual and possible—that makes up the whole of reality. The world is precisely those states of affairs which do exist.’
‘There are, first, the propositions of logic. These do not represent states of affairs, and the logical constants do not stand for objects. “My fundamental thought is that the logical constants do not represent. That the logic of the facts cannot be represented” (TLP 4.0312). This is not a happenstance thought; it is fundamental precisely because the limits of sense rest on logic. Tautologies and contradictions, the propositions of logic, are the limits of language and thought, and thereby the limits of the world. Obviously, then, they do not picture anything and do not, therefore, have sense. They are, in Wittgenstein’s terms, senseless (sinnlos). Propositions which do have sense are bipolar; they range within the truth-conditions drawn by the propositions of logic. But the propositions of logic themselves are neither true nor false “for the one allowsevery possible state of affairs, the other none” (TLP 4.462).
‘The characteristic of being senseless applies not only to the propositions of logic but also to other things that cannot be represented, such as mathematics or the pictorial form itself of the pictures that do represent. These are, like tautologies and contradictions, literally sense-less, they have no sense.’
‘Beyond, or aside from, senseless propositions Wittgenstein identifies another group of statements which cannot carry sense: the nonsensical (unsinnig) propositions. Nonsense, as opposed to senselessness, is encountered when a proposition is even more radically devoid of meaning, when it transcends the bounds of sense. Under the label of unsinnig can be found various propositions: “Socrates is identical”, but also “1 is a number”. While some nonsensical propositions are blatantly so, others seem to be meaningful—and only analysis carried out in accordance with the picture theory can expose their nonsensicality. Since only what is “in” the world can be described, anything that is “higher” is excluded, including the notion of limit and the limit points themselves. Traditional metaphysics, and the propositions of ethics and aesthetics, which try to capture the world as a whole, are also excluded, as is the truth in solipsism, the very notion of a subject, for it is also not “in” the world but at its limit.’
Propositions Wittgenstein identifies another group of statements which cannot carry sense: the nonsensical (unsinnig) propositions. Nonsense, as opposed to senselessness, is encountered when a proposition is even more radically devoid of meaning, when it transcends the bounds of sense. Under the label of unsinnig can be found various propositions: “Socrates is identical”, but also “1 is a number”. While some nonsensical propositions are blatantly so, others seem to be meaningful—and only analysis carried out in accordance with the picture theory can expose their nonsensicality. Since only what is “in” the world can be described, anything that is “higher” is excluded, including the notion of limit and the limit points themselves. Traditional metaphysics, and the propositions of ethics and aesthetics, which try to capture the world as a whole, are also excluded, as is the truth in solipsism, the very notion of a subject, for it is also not “in” the world but at its limit.’
http://plato.stanford.edu/entries/wittgenstein/#Phi
Logic represents the limits of the world for Wittgenstein. But is this true? What is logic’s relation to the world? Can meaningful things be said that don’t fit into the category of logical true/false propositions? And finally, as Bertrand Russell asked, what is logic?
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