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

We can do without logical propositions.

The propositions of logic demonstrate the logical properties of propositions in that they combine them to form propositions without content. This could also be called a null method. In a logical proposition, propositions are brought into equilibrium with one another, and that equilibrium then indicates what the logical constitution of these propositions must be.

It follows from this that we can even do without logical propositions because a suitable notation enables one to recognize the formal properties of propositions by inspection. If, for example, two propositions (p) and (q) in the compound proposition (p⊃q) yield a tautology, then it is clear that (q) follows from (p). That (q) follows from (p⊃q.p) is seen from the two propositions themselves, but it is also possible to show it by combining them to form (p⊃q.p:⊃:q), and then showing that this is a tautology.

Logical propositions cannot be confirmed by experience any more than they can be refuted by it. Not only must a proposition of logic be irrefutable by any possible experience, but it must also be unconfirmable by any possible experience. We can postulate the truths of logic in sthat we can postulate an adequate notation. Clearly: the laws of logic cannot themselves be subject to laws of logic. (There is not, as Russell thought, a special law of contradiction for each 'type'; one law is enough instead, since it is not applied to itself.)

The mark of a logical proposition is not general validity, since that only means to be valid for all things by happenstance. An ungeneralized proposition can just as well be tautological as a generalized one.

We could call logical generality essential, in contrast with the accidental generality of such propositions as 'All men are mortal'. Propositions like Russell's 'axiom of reducibility' are not logical propositions, and this explains our feeling that, even if they were true, their truth could only be the result of a fortunate accident.

One can imagine a world in which the axiom of reducibility is not valid. But it is clear that logic has nothing to do with the question of whether our world is really so or not.

Logical propositions describe the structural skeleton of the world. They have no content on their own, but presuppose that names have meaning and elementary propositions make sense; and that connects them to the world. Clearly, it must show something about the world that certain conjunctions of symbols—that in essence have a specific character—are tautologies. This is a decisive point.

Some things are arbitrary in the symbols that we use and some things are not. In logic, only the latter express. That does not mean we express what we wish with the help of signs, but rather that one in which the nature of the absolutely necessary signs speaks for itself. If we know the logical syntax of any symbolic language, then we have already been given all the propositions of logic.

No comments:


Blog Archive