4.04 In a proposition there must be exactly as many things to differentiate as there are in the state of things it represents.
Both must possess the same logical (mathematical) multiplicity. (Compare Hertz’s Mechanics on dynamic models.)
The more a proposition comes to have in common with what it represents, the less distinguishable it is from it.
2 comments:
Duncan,
Good to be reading your blog again.
Coffa has an interesting comment about multiplicity:
"The motivation for the requirement that an appropriate symbolism have the same mulitiplicty as what it symbolizes is that the other two alternatives have evident drawbacks. If the multiplicity of the symbolic system is smaller than that of what it represents, there will be possible circumstances we will not be able to describe. If the multiplicity is greater, the problem is more familiar -- it is called 'philosophy'. All of philosophy (up to, and perhaps including, Wittgenstein) had consisted of attempts to say things that cannot be said. Good philosophy attempts to say what can be shown, sinnlos; bad philosophy attempts to say what cannot even be shown, the unsinnig, the utter nonsense. Most philosophy had been bad philosophy, based on confusions concerning language. These confusions were roughly of the sort displayed by Russell's paradox: The language we use has a greater multiplicity than what it talks about. We can therefore form expressions whose syntactic appearance is like that of perfectly claims, but from them we are led to some form of chaos." (The Semantic Tradition from Kant to Carnap, 156-7)
A short while after reading Coffa's comment, I came across the following passage in Waismann's Theses that confirms it.
"Syntax hence becomes requisite where the nature of signs is not yet adjusted to the nature of things, where there are more combinations of signs than possible situations. This excessive multiplicity of language must be confined by artificial rules; and these rules are the syntax of language. The rules of syntax assign to combinations of signs the exact multiplicity they must possess in order to be pictures of reality." (LWVC, 240)
Good to hear from you again.
Yes, you want to be able to say all that there is to say and to be constrained from saying anything more than that.
Thanks for the references.
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