Handbook of the History of Logic: - Fordham University Faculty

676 Russell Wahl
asserting verb in propositions. All propositions are either affirmations or denials.
Subordinate clauses which are not affirmed are not propositions on this view, and
so it does not appear to be possible to consider a proposition without affirming it,
since it appears that it is the ingredient of affirmation or denial which creates the
proposition.
It should be noted, though, that despite this view, Arnauld and Nicole do appear
to include in ideas what we would call propositional content. For them, as much as
for Descartes, having angles which add up to two right angles is contained within
the idea triangle. Descartes’ view was that the clear and distinct perception of
this containment would determine the will to make a judgement. The same is
the case for Arnauld and Nicole, although they would deny that prior to assertion
we are considering a proposition. Instead they would say we are contemplating
a complex idea. With respect to relative clauses, Arnauld and Nicole actually
get into a difficulty. In Part I, chapter 8 they hold that “a transparent body”
and “a body which is transparent” are the same thing, and are complex terms,
not propositions (65). But in Part II, Chapter 6 they refer to relative clauses as
incidental propositions, but none the less propositions, and thus want to include
an assertion in them (122). They come to the somewhat unsatisfactory position
that in the case of explicative relative clauses the clause as well is asserted, but
in the case of determinative clauses there is a “tacit or virtual” assertion that
combination is possible. Thus if I say that “Alexander, who was the son of Philip,
defeated the Persians” I am asserting that Alexander was the son of Philip (125),
and if I say “A transparent body has weight” on this view I am not asserting that
there are transparent bodies, but that it is possible that there be.
In the Grammaire, the focus is on explicative clauses in the discussion of relative
pronouns. There, Arnauld and Lancelot held that when someone says,
Invisible God created the visible world,
there are “three judgments in my mind contained in this proposition, for I judge
first that God is invisible, second that he created the world, third that the world
is visible” [Arnauld and Lancelot, 1660, II, 9, 68]. So while there is only one verb
occurring here, what seem to be complex ideas, invisible God and visible world,
contain judgments.
Probably the best way to understand the Port-Royal view is to see that in
one sense they were more sensitive than Descartes to the difference between a
proposition and a complex idea. They emphasized the occurrence of what Bertrand
Russell would later call the verb as a verb, as opposed to the verb as term as the
crux of this difference. 15 However, since they thought of assertion and negation
as acts of judging, they ended up with a view which makes the very unity of the
proposition dependent on the act of the judging mind. In fact, they did not have
15 See [Russell, 1903, Chapter IV, especially sections 48 to 53]. There are actually many
similarities between the analyses given in the Port-Royal Logic and the Principles of Mathematics
on this point, although Russell is very clear, as was Frege, that the propositions are not formed
by the act of judging.