Tuesday, March 27, 2007

3.315 If we convert a component of a proposition into a variable, then there is a class of propositions which are all the values of the resulting variable proposition. This class still depends in general on what we, by arbitrary agreement, mean by the parts of that proposition. But if we convert into variables all those signs whose meaning is arbitrarily determined then a class like this will still always remain. This however is now dependent on no agreement, but only on the nature of the proposition. It corresponds to a logical form – a logical prototype.

Take the proposition: Bad monkeys like good bananas. Now replace “bananas” with the variable x. We can now generate a class or set of propositions in which x is replaced by something suitable, something that fits (“apples,” say, but not “green”). This set depends on the arbitrary meanings we have given to words like “bad” (we could have used “mal” or “schlecht” instead). Now what if we replace all the arbitrary words with variables? For all m, if m is b and b is g then m likes b. Or perhaps: For all w and all y, if w is x and y is z then wLy. Something like that. Now there is still a class of propositions for which this could stand, to be generated by filling in the place of w, x, y, z, and L with grammatically appropriate words (or proposition parts of some kind). This set or class though does not depend on arbitrary agreement, the conventional meanings of words (or other symbols). Rather it depends on what I (following the later Wittgenstein) am here calling grammar, what Wittgenstein calls logic or logical form.

Mounce (p. 30): “In the Tractatus, logical form is something which, as it were, underlies the rules of language and guarantees its intelligible usage. In the Investigations, he thinks of logical form as being a kind of formalization of the rules of language and these arise out of its use; they do not underlie and guarantee its intelligibility. Common to both works, however, is the view that meaning is not some special entity or psychological process.”