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Notes to Pages 20–25 399

of climate on our evolutionary history is a minor academic cottage industry; see
Burroughs (2005), Calvin (1991), Fagan (2005), Potts (1996) and Stanley (1998),
among others.
51. Periods of sudden population growth in pre-history are well documented (Bar-
Yosef, 1992; Steiner et al., 1999). Warfare has been with us since the beginning of
the archeological record (Keely, 1997).
52. The mathematical term “monotonic” applies to a function f, y = f (x), if f is such
that every increase (decrease) in the value of x yields an increase (decrease) in
the value of y. For example, y = f (x) = 2x + 3 is a monotonic function. In con-
trast, if f is non-monotonic, an increase in the value of x might yield a decrease
2
in the value of y, or vice versa. For example, y = x is non-monotonic, because
an increase from x = 2 to x = 4 yields an increase in y from 4 to 16, while an
increase from x = – 4 to x = – 2 yields a decrease in the value of y, from 16 to 4.
In logic, the term “monotonic” is applied metaphorically to a formal logical sys-
tem in which the inference rules can only add further consequences of already
proven propositions. A non-monotonic logical system, in contrast, includes rules
for inferring that some previously accepted proposition needs to be rejected in
the light of new information. The logical systems developed in the 19th century
and first half of the 20th by George Boole, Augustus De Morgan, Gottlob Frege,
Bertrand Russell, Alfred North Whitehead and others were monotonic (Kneale &
Kneale, 1962/1984). Non-monotonic logics were developed by Artificial Intelli-
gence researchers in the late 1970s and early 1980s (McCarthy, 1980; McDermott &
Doyle, 1980; Reiter, 1980). The application of non-monotonic logics to the analy-
sis of human reasoning is recent; see Ford (2005). Applying the term to learning,
I refer to learning that augments or extends a person’s knowledge base without
revision of prior knowledge as monotonic and learning that forces revisions in
prior knowledge as non-monotonic.
53. Kuhn (1977).
54. A. I. Miller (2001), Chapter 4, offers an analysis of how Picasso painted Les
Demoiselles d’Avignon that highlights the roots of this painting in the intellec-
tual movements within science at the time. Hence, the painting was, in a sense,
an adaptation to changes in Picasso’s conceptual environment. Once it became
widely known, other painters had to adapt to it in some way or another.

Chapter 2. The Nature of the Enterprise
1. Cummins (2000, p. 120).
2. Newell, Shaw and Simon (1958, p. 151).
3. For a history of chemistry, see, e.g., Brock (1993). Regarding the discovery of the
structure of DNA, see Oldby (1974/1994). The volume of essays edited by Oreskes
(2003) describes the emergence of plate tectonic theory; it should be read in the
context of the facts that threaten to falsify that theory (Pratt, 2000).
4. The best summary and overview of the behaviorist approach to learning is Hilgard
and Bower’s (1966) textbook. The best summary and overview of Piaget’s theory of
cognitive change is Flavell (1963); see Furth (1968, 1969) for an analysis of Piaget’s
theory of knowledge.