This log was inspired by "How to Read Wittgenstein" and "Ludwig Wittgenstein: the duty of genius" by Ray Monk. It is based on reading Tractatus Logico-Philosophicus by Ludwig Wittgenstein translated by D. F. Pears & B. F. McGuinness (Routledge and Kegan Paul:1963)

Thursday, April 3, 2008

Signs for logical operations are punctuation marks.

When logical signs are introduced properly, then one has in effect also introduced the content of all their combinations; i.e. not only (p ∨ q) but (~(p ∨ q)) as well, etc. etc. Thus it is clear that the actual general primitive signs are not (p ∨ q), ((∃x).fx), etc. but the most general ones required to form them and their combinations. The seemingly unimportant fact that, unlike real relations, the pseudo-relations of logic, such as '∨' and '⊃', need brackets is actually significant. The use of brackets with these signs already indicates that they are not really primitive. And surely no one is going to believe brackets have an independent meaning. So signs for logical operations are punctuation marks.

Clearly, whatever we can say in advance about the form of all propositions, we must be able to say all at once. In the event, an elemental proposition already contains all logical operations in itself. For (fa) says the same thing as
((∃x) . fx . x = a).

In any composite sentence, there are argument and function, and with these, all the logical constants. One could say that the sole logical constant is that which all propositions, by their very nature, must have in common with one another. But that is the general propositional form. The general propositional form is the essence of the proposition. Stating the essence of the proposition means to state the essence of all description, that is the essence of the world. The description of the most general propositional form is the description of the one and only general primitive sign in logic.

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