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)

Saturday, April 5, 2008

The propositions of logic are tautologies.

Thus, propositions of logic (analytic propositions) tell one nothing. So theories that let a logical statement appear to have content are always invalid. One might think, for example, that the words 'true' and 'false' signified properties just like others. Remarkably, every proposition has one of these two properties. Now that seems nothing less than obvious, just as, for instance, the proposition, 'All roses are either yellow or red', would sound obvious if it were true. Indeed, the latter acquires all the characteristics of a proposition of natural science - a sure indication that it has been misconstrued. A valid explanation of the propositions of logic must assign them a unique status among all propositions.

It is the unique characteristic of logical propositions that one can recognize that they are true from the symbol alone. In itself, this fact contains the whole philosophy of logic. And so it is also one of the most important facts that the truth or falsity of non-logical propositions can not be recognized from the statement alone.

That the propositions of logic are tautologies, is shown by the formal, logical properties of language, of the world. That the constituents of logic, thus connected, yield a tautology, characterizes the logic of those constituents. Propositions must have certain structural properties to yield a tautology when joined in an appropriate way. When they do yield a tautology, that shows they possess these structural properties.

That, for example, the propositions (p) and (~p) yield a tautology in the combination (~(p . ~p)) shows that they contradict one another. The fact that the propositions (p⊃q), (p), and (q), combined with one another in the form ((p⊃q).(p):⊃:(q)), yield a tautology shows that q follows from p and (p⊃q). That ((x).fx:⊃:fa) is a tautology shows that (fa) follows from ((x).fx) etc.

It is clear that one would reach the same conclusions using contradictions instead of tautologies.

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