Saturday, November 10, 2007

Kremer's point on the Tractatus

I'm participating in a TLP reading group this term. We're going to make it through the end of the 3's by winter break. One point that I've made several times to individuals, and which came up again in discussion on Friday, is something that I thought would be worth putting online. It is originally due to Michael Kremer, in his excellent "Mathematics and Meaning in the Tractatus." Many people think that in TLP, there is a very strict two part distinction: sentences have sense while names have meaning (Bedeutung). Names have no sense; they just mean the objects to which they refer. The objects are the meaning of the names. This is a pretty natural reading to get out of the 3's. However, sentences also have meaning. Wittgenstein uses "meaning" in two ways throughout TLP. Sometimes he means the stricter sense to characterize the relation between names and objects, and sometimes he uses it in a more general way to talk about whatever significance linguistic units have. The textual evidence for this comes from 4.4241: "When I use two signs with one and the same meaning, I express this by putting the sign '=' between them. So 'a = b' means that the sign 'b' can be substituted for the sign 'a'." The signs used there are the ones normally used as names, lower case letters from the early part of the alphabet. However, combine this with 5.254: "An operation can vanish (e.g. negation in '∼∼p' : ∼∼p = p)." We clearly have propositional signs flanking the '='. This means the two signs have the same meaning. However, they aren't names. Therefore, Wittgenstein has two senses of meaning in place in TLP. This is a fairly straightforward point but it is missed by a lot of people.

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