Handbook of the History of Logic: - Fordham University Faculty

Port Royal: The Stirrings of Modernity 677
to do this, since they seem to recognize some unity in complex ideas and this unity
would serve well as what Russell later called propositional concepts or “unasserted
propositions”. 16 By their own criteria, there is no assertion when I say simply “the
visible world,” since there is no act of affirming or denying anything. I could, for
example, be contemplating denying its existence. They could then have said that
the act of asserting was the act of judging that the parts of the complex idea go
together, and the act of negating involved judging they did not. The propositional
concepts would then have a unity, i.e. the unity of a complex term, though not one
created by the asserting will. Unfortunately, they did not address this difficulty
in this manner.
The Port-Royalists were taken by the fact that the sentence,
Invisible God created the visible world
was equivalent to the sentence,
God, who is invisible, created the world, which is visible.
This last sentence contains verbs occurring as verbs and it seems that someone
who states this is committed to the truth of the claims “God is invisible” and “the
world is visible”. With respect to the proposition “Invisible God created the visible
world,” these other propositions are probably better understood as presupposed
rather than asserted. There is a place in the Logic where Arnauld and Nicole
allow that a proposition can still be true even though the incidental propositions
are false:
...thefalsityoftheincidentalproposition does not ordinarily preclude
the truth of the main proposition. For example, “Alexander who was
the son of Philip defeated the Persian.” This proposition should be
considered true even if Alexander was not the son of Philip, because
the affirmation of the principal proposition affects only Alexander, and
what is joined to it incidentally, although false, does not prevent it from
being true that Alexander defeated the Persians. (125)
However, they hold that when the incidental proposition is related as in “Alexander
the son of Philip was the grandson of Amintas” the falsity of the incidental
proposition would make the principal proposition false. Unfortunately, they did
not elaborate this example, for it is not clear why, for example, if Amintas had
had two sons, Philip and Hector, and unbeknown to everyone Alexander was the
son of Hector, we would not gloss the example the same as the one above. In the
first section, Arnauld and Nicole point out what they call the ambiguity of such
expressions as “the true religion”. They say,
16 The example Russell uses is “The death of Caesar” as opposed to “Caesar died”. It is clear
from the Port-Royal discussion in Part II Chapter 2 that the first of these would simply be a
complex idea and not a proposition. See especially p.111.