Shape

64 I What Makes It Visual?
Whenever I read William James, I always find something new about shapes and
rules. What’s more, there’s an account of reasoning in The Principles of Psychology that
works flawlessly for what I want to do. For James, reasoning is a compound process
with interlocking parts. He divides the ‘‘art of the reasoner’’ into moieties:
First, sagacity, or the ability to discover what part, M, lies embedded in the whole S which is before
him;
Second, learning, or the ability to recall promptly M’s consequences, concomitants, or implications.
This is precisely what happens whenever rules are used to calculate. A rule M fi P
shows the part M to be embedded in the whole S, and specifies the consequences,
etc.—call them P—of finding M in S. Remember how the rule
that I described in the introduction used embedding to rotate triangles. Any part I can
see and trace I can change. In just the same way, the rule M fi P applies to S to produce
something new. Of course, this is only a sketch. It leaves out most of the important
details. I have to say a lot more about how the rule M fi P works when it’s used.
The trick is first to find a suitable embedding relation, and then to show how M can be
embedded in S, and how together with P, this changes S.
James takes the syllogism (predicate calculus) as his example—this only confirms
the link to calculating—with almost no attention to the underlying details that make
rules work. James isn’t an engineer. Sagacity and learning are taken for granted. He
has something else far more interesting and weighty in mind. He wants to plumb creative
thinking and describe the source of originality. In fact, James’s overarching definition
of reasoning is the ability to deal with novelty. This is why reasoning makes a
difference.
If we glance at the ordinary syllogism—
MisP;
SisM;
8 SisP
—we see that the second or minor premise, the ‘‘subsumption’’ as it is sometimes called, is the
one requiring the sagacity; the first or major the one requiring the fertility, or fulness of learning.
Usually, the learning is more apt to be ready than the sagacity, the ability to seize fresh aspects in
concrete things being rarer than the ability to learn old rules; so that, in most actual cases of reasoning,
the minor premise, or the way of conceiving the subject, is the one that makes the novel
step in thought. This is, to be sure, not always the case; for the fact that M carries P with it may
also be unfamiliar and now formulated for the first time.
For James, there are twin ways to be creative—using rules (‘‘the way of conceiving
the subject’’) and also defining them (connecting M and P in the first place). And