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336 Conversion

of any one belief, but it constrains which specific beliefs one can adopt and
remain coherent. The asymmetry of the subsumption relation – beliefs in one
belt subsume the beliefs in the next belt out from the core, but not vice versa –
imposes a structure, a partial ordering, on the belief system. I refer to such
structures as Rokeach structures; see Figure 9.2 for a graphical illustration.
Explicit theories in the empirical sciences are sometimes likened to axi-
omatic theories in logic and mathematics, but I suggest that they are better
thought of as Rokeach structures. Newton’s laws subsume their applications
to particular cases of mechanical motion but they do not logically imply those
applications, and Darwin’s theory of evolution through natural selection sub-
sumes but does not logically imply any particular Darwinian explanation.
If both informal belief systems and formal theories are structured by sub-
sumption, then it follows that logical reasoning from observational evidence
has little power to affect a core belief. If an observed case is subsumed under,
rather than logically implied by, a general belief, falsification cannot propagate
upstream, from periphery to core, through successive Modus Tollens infer-
ences; the latter are only valid with respect to implication. In the health exam-
ple, to falsify the general belief that diet influences health one would have to
prove that no foodstuff has any effect, a rather more extensive enterprise than
merely showing that, for example, dark chocolate has less of an effect than
previously thought. Likewise, to reject the notion that, for example, interna-
tional trade agreements lower the probability of war between nations, a his-
torian would have to show that every trade agreement throughout recorded
history left the probability of hostilities unchanged, an impossible task. In
short, changes in specific, peripheral beliefs have little impact on the core
beliefs that subsume them, because the subsumption relation is tolerant of var-
iability in the subsumed beliefs. Hence, contra Popper, falsification of periph-
eral beliefs through contradictory observations cannot be the main engine of
change in core principles. Subsumption, unlike deduction, does not support
the backward propagation of falsification.
If a belief system or informal theory is a cognitive unit in its own right,
a person can adopt (or reject, as the case might be) that system as a whole,
not only this or that single belief within it. A description of the state of mind
created by such an act cannot be reduced to a conjunction of assertions to the
effect that the person believes or disbelieves each individual proposition in
that system. This view is consistent with the fact that everyday discourse easily
accommodates statements like I believe (do not believe) in the theory of evolu-
tion or he now believes (no longer believes) in the Marxist theory of history or
geologists are now firmly convinced that ice ages are (are not) due to astronomic