A very natural objection to the way in which I have introduced
e.g. propositions of the form
xRy is
that by it propositions such as (∃x,y).xRy & similar
ones are not explained, which yet obviously have in common with
aRb
what
cRd has
in common with aRb.
But when we introduced propositions of the form xRy we mentioned no one particular
proposition of this form; & we only need to introduce
(∃x,y).φ(x,y) for all
φ's in any way which makes the
sense of these propositions dependent on the sense of all propositions of
the form φ(a,b), & thereby the
justification of our procedure is proved.
19