Handbook of the History of Logic: - Fordham University Faculty

Port Royal: The Stirrings of Modernity 695
of the twenty-first century the concern with ordering ideas and judgments so as
to obtain systematic knowledge will appear to be a subject better suited to epistemology
than logic. But if we remember that for Arnauld and Nicole logic is to
give rules for all the operations of the mind with the goal of discerning the true
from the false, the inclusion of this material makes sense. The part on method
includes a criticism of skepticism, a discussion of the Cartesian methods of analysis
and synthesis, and toward the end a discussion of reasoning from less than perfect
information, which includes one of the very early discussions of probability.
With respect to the method of analysis, or resolution, Arnauld and Nicole borrow
heavily from Descartes, importing directly Rule 13 from Descartes’ Rules for
the Direction of the Mind, which gave examples of the method such as solving the
problem of how a clever statue of Tantalus could have been constructed so that
the water from the cup spilt as soon as it reached the lips of the figure. Analysis
is best seen as a method of discovery, starting from a problem and proceeding
from the particular problem to the more general principles. This is the method
Descartes himself advocated and used in the Meditations. 30 The four rules given in
the Port-Royal Logic for proper conduct of this method are taken from Descartes’
Discourse on Method (306). The method of synthesis or composition Descartes
thought was ill suited to metaphysics, since he thought the first principles were the
hardest things to come by epistemologically. Synthesis does not yield first principles,
but demonstrates conclusions from them. Descartes saw analysis, though,
as a method of discovery of these principles. He did state that synthesis may be
“suitable to deploy in geometry as a follow-up to analysis”, [Adam and Tannery,
1964-76, VII, 156; Cottingham et al., 1985-1991, II, 111] but in his own Geometry,
he did not give axioms and definitions and then proceed to prove theorems, but
approached particular problems using the method of analysis.
In the Port-Royal Logic, though, synthesis is considered the “most important
method” as it is used “to explain all the sciences” (306). The rules given for proper
reasoning and ordering apply to this method, rather than analysis. There is also a
discussion of the dangers of synthesis, a discussion which mirrors earlier discussions
of problems occurring with respect to the activities of clarifying ideas, forming
judgements, and reasoning. Arnauld and Nicole begin by giving five rules, two for
clarifying terms, involving definitions, one for axioms, and two for demonstrations
(308). These three groups correspond to the three first parts of the Logic. After
a further discussion of the rules and of the dangers of the method, they conclude
with a list of eight rules, 2 for ideas, two for axioms, two for arguments, and two
for method. Here is the list:
For definitions:
1. Leave no term even slightly obscure or equivocal undefined.
2. In definition use only those terms perfectly known or already explained.
30 Analysis is praised by Descartes as being “the best and truest method of instruction” [Cottingham
et al., 1985-1991, II, 111; Adam and Tannery, 1964-76, VII, 156].