We have now got everything which is required for expressing, in a short
symbolic form, the proposition, with regard to a given thing A and
a given relational property P, which A in fact possesses, that P is
_internal_ to A. The required expression is
_xP_ entails (°_x_ = A°)
which is to mean the same as "Every proposition which asserts of any
given thing that it has not got P _entails_ the proposition, with
regard to the thing in question, that it is other than A." And this
proposition is, of course, logically equivalent to
(_x_ = A) entails _x_ P
where we are using "logically equivalent," in such a sense that to
say of any proposition _p_ that it is logically equivalent to another
proposition _q_ is to say that both _p_ entails _q_ and _q_ entails
_p._ This last proposition again, is, so far as I can see, either
identical with or logically equivalent to the propositions expressed
by "anything which were identical with A would, in any conceivable
universe, necessarily have P" or by "A could not have existed in any
possible world without having P"; just as the proposition expressed by
"In any possible world a right angle must be an angle" is, I take it,
either identical with or logically equivalent to the proposition "(_x_
is a right angle) entails (r is an angle)."
We have now, therefore, got a short means of symbolising, with
regard to any particular thing A and any particular property P, the
proposition that P is _internal_ to A in the second of the two senses
distinguished on p. 286. But we still require a means of symbolising
the general proposition that _every_ relational property is internal
to any term which possesses it--the proposition, namely, which was
referred to on p. 287, as the most important consequence of the dogma
of internal relations, and which was called (2) on p. 289.
Public-domain text, read in full here on John Shaqi.
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