Generalizations and universals

Evidentiary arguments rely on the elevation of generalizations (a lot of X are A) to universals (all X are A). This technique, though, is analytically fallible, and we employ the technique out of desperation.

If there are any universals at all, then the elevation of a generalization to universal can sometimes be true even if it is not logically valid (and thus always true). Since all universals are generalizations, if there are some universals, then some generalizations are universals.

First, We can't be certain that any particular generalization really is a universal, but we can be certain that some generalizations are not universals by discovering a counterexample; a generalization that really is a universal will have no counterexamples. Hence Popper's criterion of falsifiability. If it is logically impossible to observe a counterexample for some generalization, then the generalization is not a generalization; it's an analytical statement.

We can observe counterexamples by the same means that we observe examples that do fit the generalization: Just making the generalization in the first place means that we can directly determine that some thing is X, and we can directly and indepentently determine that an X is in fact A.

For example, if a "crow" is defined to be "a black bird", then by definition we cannot find a crow that is not black; by virtue of being non-black, the being, whatever it is, is by definition not a crow. Since we cannot determine whether a crow is black independently of determining that some thing is a crow, it's not a generalization to state that "all crows are black". If it's not a generalization in the first place, we can't reason from a generalization to a universal.

A subtler way of defeating a generalization is to hold it true "come what may" and always adjust other statements around any observations. This technique is not entirely illegitimate, but it's more honest and clear to explicitly phrase such a statement as a definition. All the statements that one has adjusted around the statement held true "come what may" contribute to the analytical definitions of the terms used in the statement.

To come around to our original point, the evidentiary argument for Intelligent Design relies on the generalization that:

ID_g: A lot of complex* things with an independently determinable origin were intelligently designed (by human beings)

and therefore we conclude the universal

ID_u: All complex things — even those with an origin that we cannot independently determine — were intelligently designed

*With "complex" standing in for a lot of specific features that human artifacts uncontroversially share with terrestrial life forms.

(Intelligent Design looks moderately acceptable, but only so far; it won't be until the next post that I'll start exploring more features of reasoning from generalizations to universals that ID starts to fail catastrophically.)

We do want to avoid specious analyticity. If we define "intelligent design" as "any process that produces complexity" then we aren't saying anything other than "complex things are the result of some process." This trivial generalization is not at all a matter of controversy. Worse yet, by defining "intelligent design" in such a manner, we practically beg the reader to import connotations (intention, memory, desire, will) that have been explicitly excluded from the definition. (Only a lawyer, theologian or philosopher could love the fine line between actually lying and intentionally leading the reader to a false conclusion.)

We also want to avoid holding the generalization true "come what may"; we want to avoid defining all our other terms around holding as true the statement "All complex things are the result of intelligent design," or, worse yet, accepting new statements willy-nilly for the only reason that they support the truth of the statement.