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In the Tractatus, Wittgenstein mentions the following:

"3.03 Thought can never be of anything illogical, since, if it were, we should have to think illogically."

"3.032 It is as impossible to represent in language anything that 'contradicts logic' as it is in geometry to represent by its coordinates a figure that contradicts the laws of space, or to give the coordinates of a point that does not exist."

Later he states

"6.54 My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)"

So first he states that all thoughts and language are logical, since an (ideal) language can't represent anything illogical. Presumably his own writing is clear and grammatically correct and so it is logical. He then claims that his own propositions are senseless. So his own writing is logical but senseless.

  • What is then, the difference for Wittgenstein (and later the Logical Positivists) between an illogical statement and a senseless statement?
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You can go back to Frege. There are two kinds of meaning to any proposition, sense (Sinn) and interpretability (Beweis). Something only has sense if the interpretability can find a reference (Bedeutung). This is kind of like the propositional logic vs model theory approach to validity. An argument can be valid in construction, but if the system lacks a model that instantiates its arguments it still does not mean anything.

So we can think a lot of things that have interpretability but lack sense. It is questionable whether something that lacks interpretability is a genuine thought, or a mere instance of symbol manipulation. The Tractatus is coming down in the latter camp. Since propositions that cannot be instantiated are not really thoughts, their expression is not really language. They cannot contradict anything because they cannot get leverage on meaning.

The latter sentiment does not seem logically connected to the earlier ones. In my interpretation, he is making a functional interpretation of Plato's position behind anamnesis, that truly important thoughts cannot be stated, but must be conveyed by manipulating one's interlocutor into a position where the meaning will be recognized (as, in Plato's theory, all important thoughts are already in the mind). (This is arrogating the contents of his work to the status of 'truly important thoughts', which is a bit excessive, to my mind.)

One can make interpretable arguments that basically lack sense, if the referent is simply not available to the listener. But you can still lead someone to that a sensible thought by means of the nonsense. (You can grow the accessible models by intension, not just construction.)

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The first two propositions are a reflection in logic and language of a proposition in philosophy, which is closer to an article of faith: that the world is intelligible; it is for this reason that one finds in Plotinus that a principle of the world is nous; or in the Gospel of St John logos.

Can I write an illogical sentence? Well, following Chomsky I could write:

Dangerously didactic jaguars are - in; what? Kin? Nor kin nor in but in-kin.

Which discursively has no logic; but if my intention is taken into account; which is to write a sentence that had no logic to it then sentence still, by itself has no logic, nor sense; and nor can one understand it; but one can understand why I wrote it.

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To be logical is to follow the rules of the language (which is why any proper sentence in a language must be logical; it is properly only a sentence if it follows the rules). But plenty of sentences follow the logical rules don't have a sense. In the tractatus, sentences which have no real subject will be of this kind, for example "the present king of France is bald" might very well be senseless (since it's not clear how it would be true or false).

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