## Thursday, November 08, 2007

5.502 Therefore I write “N(ξ) [with a line over it]” instead of “(-----T) (ξ, …..).”

N(ξ) [with a line over it] is the negation of all the values of the propositional variable ξ.

Marie McGinn (p. 232): “The operation expressed by N(ξ) [with a line over it] is not strictly equivalent to Sheffer’s stroke, which is a two-place operator. N(ξ) [with a line over it] is a multi-grade operator, which jointly negates all the propositions that are the values of the variable ξ, that is, it corresponds to the operation expressed by the sign (-----T)( ξ,…).”

#### 1 comment:

Furrowed Brow said...

Everyone I‘ve read interprets . (-----T)( ξ,…).” in light of what Wittgenstein says about the N notation. But I think this gets things back to front. We need to ask ourselves why LW has gone to such efforts in the 3s to detail the variable. Also why does he place the variable sign inside the right hand pair of brackets? I’d say the answer is that he means an operation of the following form . (-----T)( ξ, p, q).” Whereby the variable, and its values are all jointly negated together. As opposed to (---T)(p , q). If you write out the table for the first operation you will see that to keep the table consistent certain truth values will need to be omitted. As indicated by the -----T in the left hand pair of brackets.

I've read two accounts that think the five dashes work much like ellipses. The number of dashes not then significant. Frankly most just ignore LW's presentation of (-----T)( ξ,…). and go straight to the N notation.

However if the truth operation is read as I suggest then the N notation can be left in place. All that happens is that the variable recedes to the limits of the proposition.

So I guess I'm saying there is way more going on here than the literature on this point has so far dug up.