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falls short of providing an adequate explanation for the first two questions and
thereby not being able to appreciate the full significance of SP.
In response to the first question, Pearl draws attention to the distinction
between what he calls “Simpson's reversal”, which is merely an “arithmetic
phenomenon in the calculus of proportions” and “Simpson's paradox” which is
“a psychological phenomenon that evokes surprise and disbelief” [10, p. 9]. He
thinks that the latter is the result of intuitions guided by causal considerations
and the fallacy of equating correlation with causation. While agreeing with him
about the fallacy, we pointed out, with the help of the marble counter-example,
that fundamentally, SP is devoid of any causal intuitions, although most day-to-
day examples of SP can be interpreted causally. We think that human puzzlement
about SP stems from the unexpected failure of CP which closely resembles valid
inference rules (section 2.2). With respect to the second question, Pearl identifies
“scenarios” in which one can expect a reversal. A scenario, according to him,
is “a process by which data is generated” [10, p. 10]. The causal calculus/models
which represent these causal scenarios are different from our formal conditions
which have been derived from the structure of the paradox (section 2.1). So our
conditions capture
all
cases of SP regardless of the causal process involved and
provide a more general account than either of the causal accounts.
7 Re-evaluating the Place of SP in Paradox Literature
Logicians tend to hold different views concerning what paradoxes are. Whether
SP is a paradox depends on how one defines and slices paradoxes. Priest [11],
for example, may not consider SP to be a paradox as it is neither a set-theoretic
paradox such as Russell's nor a semantic one like the Liar Paradox. But, under
Sainsbury's construal, SP could be regarded as a paradox since he understands
a paradox as “an apparently unacceptable conclusion derived by apparently ac-
ceptable reasoning from apparently acceptable premises.” [14, p. 1]. However,
this might not furnish a genuine rationale for what makes paradoxes paradoxical
since one might worry what an “apparently acceptable reasoning” is. In this re-
gard, we find a better explanation in W.V.Quine, who both defines and provides
a general rationale for the apparently paradoxical nature of paradoxes. A para-
dox, according to him, is “just any conclusion that at first sounds absurd but
that has an argument to sustain it” [12, p. 1]. SP can be treated as a paradox
in this Quinean sense.
Two points are to be noted here. First, Quine's use of the word “absurd”
could be ambiguous since it lends itself to two interpretations: a) psychological
confusion and b) logical contradiction. Our analysis of SP suggests that SP
“sounds absurd” under both interpretations. Given the logical reconstruction of
SP (section 2.2), we see how it leads to a self-contradictory conclusion. And,
given our response to question (i), we find that people tend to apply CP across
the board and their psychological confusion results when they find out that
CP, in fact, cannot be so applied. Second, our research shows that the sharp
distinction Quine draws between “veridical paradox” and “falsidical paradox”
