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Notes to Pages 335–341 449

12. Ausubel (1963, p. 26).
13. The axiomatic format for theories was invented in antiquity. Euclid of Alexandria’s
axiomatic presentation of geometry, The Elements, dates from the third century
b.c.; see, e.g., the summary and discussion by Boyer (1985, Chapter 7). An axiom-
atic theory is specified through two main components: a set of axioms, assertions
that are accepted as true at the outset, and a set of truth-preserving inference
rules by which new assertions, theorems, can be derived. Euclid’s paradigmatic
example was clear with respect to the axioms but less so with respect to the infer-
ence rules. Developments in formal logic in the 19th century enabled Bertrand
Russell and Alfred N. Whitehead to produce a formally specified axiomatic the-
ory of logic in their Principia Mathematica, published in three volumes between
1910 and 1913, but available in abbreviated form in Whitehead and Russell (1962).
The latter, in turn, was the basis for the first fully functional Artificial Intelligence
program, the Logic Theorist, by A. Newell, J. C. Shaw and H. A. Simon (Newell,
Shaw & Simon, 1958). Although some logicians, mathematicians and philoso-
phers nurture a fascination with axiomatic theories, no serious theory in the
empirical sciences was ever initially proposed in this form, nor are working sci-
entists disposed to put their theories on this form.
14. See Chapter 4, Note 34, and Chapter 6, Note 18, for references about the role of
hierarchical organization.
15. The concept of tangled hierarchies was introduced into cognitive science by
Hofstadter (1999) but is used here in the slightly different sense of Chi and Ohlsson
(2005). Two hierarchies are tangled if some node in one is identical to a node in the
other. For example, hierarchical classifications of “tools” and “kitchen implements”
are tangled by the fact that a “bottle opener” belongs in both, and a person’s intui-
tive theories of health and biological evolution might be tangled because the belief
that “random background radiation can cause mutations” appears in both.
16. Leon Festinger tried to separate cognitive conflict from logical contradiction, but
did not quite succeed: “I will replace the word ‘inconsistency’ with a term which
has less of a logical connotation, namely, dissonance. … The terms ‘dissonance’
and ‘consonance’ refer to relations which exist between pairs of ‘elements’ …
[which refer to] the things a person knows about himself, about his behavior, and
about his surroundings. … two elements are in a dissonant relation, if considering
these two alone, the obverse of one element would follow from the other. To state
it a bit more formally, x and y are dissonant if not-x follows from y” (Festinger,
1957/1962, pp. 2–13, italics in original). These terminological twists do not suffice
to insert any significant wedge between cognitive dissonance and logical contra-
diction (i.e., “x and not-x”).
17. For a discussion of medieval views of change, see Bynum (2001).
18. The weird aspects of quantum physics – entanglement, the quantized nature of
energy, quantum non-locality, wave-particle duality and the uncertainty principle –
continue to exercise philosophers (Camilleri, 2006; Cushing, 1991; Putnam, 2005) as
well as physicists (Afshar, Flores, McDonald & Knoesel, 2007; Baggott, 2004).
19. The text says: “In the beginning God created the heavens and the earth. … And
God said, ‘Let there be light,’ and there was light. … And God said, ‘Let there be