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)

Sunday, April 6, 2008

One can describe all true logical propositions in advance.

It is possible, even according to the old conception of logic, to describe all true logical propositions in advance. Hence there can never be surprises in logic.

One can calculate whether a proposition belongs to logic, by calculating the logical properties of the symbol. This is how one proves a logical proposition. For, without bothering about sense or meaning, we construct the logical proposition out of others using only rules that deal with signs. One proves logical propositions by generating them from logical propositions by successively applying certain operations that always generate further tautologies out of the initial ones. (And in fact only tautologies follow from a tautology.) Of course this way of showing that the propositions of logic are tautologies is not at all essential to logic, if only because the propositions from which the proof starts must show without any proof that they are tautologies.

In logic process and result are equivalent. (Hence no surprise.) Proof in logic is merely a mechanical expedient to facilitate the recognition of tautologies in complicated cases. It would be altogether too remarkable if a proposition that had sense could be proved logically from others, and so too could a logical proposition. It is clear from the start that a logical proof of a proposition that makes sense and a proof in logic must be two entirely different things.

A proposition that makes sense states something, which is shown by its proof to be so. In logic every proposition is the form of a proof. Every proposition of logic is a modus ponens represented in signs. (And one cannot express the modus ponens by means of a proposition.) It is always possible to construe logic so that every proposition is its own proof.

All the propositions of logic are of equal status: it is not the case that some of them are essentially derived propositions. Every tautology itself shows that it is a tautology.

The number of primitive propositions of logic is arbitrary, since one could derive logic from a single primitive proposition, e.g. by simply constructing the logical product of Frege's primitive propositions. (Frege would perhaps say that we should then no longer have an immediately self-evident primitive proposition. But it is remarkable that a thinker as rigorous as Frege appealed to the degree of self-evidence as the criterion of a logical proposition.)

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