Page 415 - Deep Learning

398 Notes to Pages 16–20

issue is how multiple instances support a generalization. Intuition suggests that
more instances provide more support, but this notion has also turned out to be
intractable. There are many attempts to use probability theory to produce a cal-
culus of corroboration (Hàjek & Hall, 2002), but no such calculus is perceived as
successful. In psychology, the idea that people extract commonalities from sets of
exemplars is implicitly presupposed by most researchers. One explicit formula-
tion, the prototype theory of concept formation, claims that people compute the
mean (or some other statistic) of each relevant dimension across the set of exem-
plars seen so far. These are assembled into a representation of a typical member
of the relevant category; the category is then defined in terms of that prototypical
(but possibly fictional) member. Experiments in which people are asked to rate
the familiarity of members of a category that they have not, in fact, seen before,
shows a strong tendency to rate such members as familiar if they are close to the
mean of the set of seen exemplars on the relevant dimensions (Posner & Keele,
1968; Solso & McCarthy, 1981). However, such results are obtained with artificial
stimuli that only vary in a small number of dimensions. It is not clear how proto-
type formation would operate in real life. (What is the average of a sofa and a rug,
two instances of the category “furniture”?) The importance attached to proto-
type theory among experimental psychologists testifies to the enduring appeal of
induction. However, the difficulties in understanding how any inductive process
could possibly work makes it unlikely that a process of this type plays a central
role in human cognition.
45. “… the problem of prediction from past to future cases is but a narrower ver-
sion of the problem of projecting from any set of cases to others” (Goodman,
1954/1983, p. 83).
46. See Note 43, this chapter.
47. The reader is referred to journals like Cognition, Memory & Cognition, Cognitive
Psychology, Cognitive Science, Journal of Experimental Psychology: Learning,
Memory, and Cognition, and dozens of others.
48. Butterworth and Laurence (2005).
49. I have been unable to locate any in-depth treatment or hard data on the role
of predator-prey cycles on the evolution of hunter-gatherers during pre-history;
research has focused on the impact in the opposite direction.
50. Potts (1996), p. 168. The best theory of human origins says that Homo sapiens
evolved in Africa, close to the tropics, and later migrated. Hence, there must
have been a moment in the history of the human species when humans saw
snow for the very first time. The image of them standing on a hilltop and watch-
ing in amazement as a snowstorm unfolds is of course grounded in nothing but
dramatic license; walking across isolated patches of snow might be more likely,
albeit less picturesque. The factual point is that our hunter-gatherer ancestors
lived outdoors, so the weather was obviously a factor in their lives. Climate
changes typically appear over a long enough time period that they might not be
experienced in their entirety by any one person. However, some authors have
argued that at least some climate changes might have occurred so abruptly that
they might have constituted learning experiences, events to be tracked by cogni-
tion rather than by evolution. The attempt to trace the importance and influence