[FOM] Quote from Russell

[Dean Buckner]

Gyula Klima reminded me of an excellent passage which shows up the puzzles
that occur when we ignore the real structure of the proposition.  Russell
writes (PoM)

"§ 54.  The twofold nature of the verb, as actual verb and as verbal noun,
may be expressed, if all verbs are held to be relations, as the difference
between a relation in itself and a relation actually relating.  Consider,
for example, the proposition "A differs from B."  The constituents of this
proposition, if we analyze it, appear to be only A, difference, B.  Yet
these constituents, thus placed side by side, do not reconstitute the
proposition.  The difference which occurs in the proposition actually
relates A and B, whereas the difference after analysis is a notion which has
no connection with A and B.  It may be said that we ought, in the analysis,
to mention the relations which difference has to A and B, relations which
are expressed by is and from when we say " A is different from B."  These
relations consist in the fact that A is referent and B relatum with respect
to difference.  But "A, referent, difference, relatum, B" is still merely a
list of terms, not a proposition.  A proposition, in fact, is essentially a
unity, and when analysis has destroyed the unity, no enumeration of
constituents will restore the proposition.  The verb, when used as a verb,
embodies the unity of the proposition, and is thus distinguishable from the
verb considerd as a term, though I do not know how to give a clear account
of the distinction."

This is one of many passages (cf § 38, § 52, § 54, § 478) where Russell
struiggles in his analysis of the proposition (which requires the Fregean
notion of propositional function).  He was taken to task for this by the
Oxford Harold Joachim, in the excellent book _The Nature of Truth_ (Oxford
1906), possibly the earliest work to discuss the then very new "mathematical
logic".  In Chapter II ("Truth as a Quality of Independent Entities")
Joachim takes on the ideas of _Principles of Mathematics_, from an Idealist
standpoint.  The difficulty Russell has got into is of course Bradley's
regress (see _Appearance and Reality_ Chapter II, beginning).

Bradley's regress is of course inherent in the Frege-Russell analysis of the
proposition.  ".  This splits "Shergar is a horse" into two parts, "Shergar"
and
"is a horse", each of which names an entity - Shergar and <is a horse>, say.
But of course the entities can exist even if the sentence is false.  So the
truth of the sentence must consist in some relation between the entities.
So we can assert the relation, as

    Shergar R <is a horse>

But, horror of horrors, that is also a sentence, so there must be a further
predicate <R <is a horse> >, and a further relation.  There are parts of The
Sophist and Theaetetus which touch on the same difficulty.

These points are all very much tied up with those made by Hartley Slater.

On a historical note, Harold's sister Gertrude Joachim was married to
Betrand's Uncle Rollo (see Ray Monk's biography).



Dean Buckner
London
ENGLAND

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