Lexicon of Arguments

 

Geach I 320ff
Relation/Principia Mathematica⁽¹⁾/Russell/Geach: sentences of the form "Fab" must be treated as individual copies of the form "Ya", i.e. a sentence that says how A is related to B is a particular type of the predication of a.
Quine: E.g. Edith envies everyone who is happier than Edith - Herbert is not happier than anyone who envies Herbert; so we prove that Herbert is not happier than Edith.
Solution: addition of assumptions: either
A "Edith envies Herbert" or
B ..."does not".
Problem: in A "envies Herbert" it is a term, in B "happier than Edith".
We cannot form a predicate with a name as we need it.
Therefore the relations must be predicative.
>Predicativeness, >Impredicativeness.
Relational propositions make predications about the related things A and B. - Then it makes sense to say that there is something in A which answers the predication, but if we apply the same sentence to B, there is nothing that answers the relation.
It is unnatural to regard the state of "being envied" as a property of Herbert.
- - -
Russell I 48
Relation/Russell: D"R: class of all terms that have the relation R to this or that thing. - R"y": "the R of y": "the father of y".


1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press.