Friday, February 22, 2008

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:
    IDg: A lot of complex* things with an independently determinable origin were intelligently designed (by human beings)
and therefore we conclude the universal
    IDu: 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.


  1. It's a minor point, but when you say
    "we employ the technique out of desperation", I think you're way off base. It's a heuristic, an optimization, a threshold which allows us to devote resources to solving other problems of classification and discrimination. And the interesting thing is that we are wired (by evolution) to do this. It underpins all forms of learning, whether by humans, lab rats, chimps, or (OK, this is controversial) planaria.

    I'm not disagreeing that there may be some cases where universals are assigned out of desperation, but I suspect that these are driven by second-order factors, such as a poorly-grounded conviction that a particular category ought to be universalizable.

  2. I'm talking more about a sort of specifically philosophical desperation.

    For more than two millennia, philosophers have tried to construct a purely logical, deductive epistemology.

    From a purely logical, deductive perspective, we should never reason from a generalization to a universal. It doesn't matter, for instance, that we know that every even number less than 10^18 is the sum of two primes; that still doesn't prove Goldbach's Conjecture

    But every time, the problem of axiomatic foundationalism reared its ugly head: how do you justify your axioms? The latest failure is naive (or simple or axiomatic) empiricism: that we could deduce universal laws from the premises supplied by direct observation. However, naive empiricism still has the logical problem of logically justifying Humean Induction.

    See my earlier series on The Scientific Method for more information, especially the first article.


Please pick a handle or moniker for your comment. It's much easier to address someone by a name or pseudonym than simply "hey you". I have the option of requiring a "hard" identity, but I don't want to turn that on... yet.

With few exceptions, I will not respond or reply to anonymous comments, and I may delete them. I keep a copy of all comments; if you want the text of your comment to repost with something vaguely resembling an identity, email me.

No spam, pr0n, commercial advertising, insanity, lies, repetition or off-topic comments. Creationists, Global Warming deniers, anti-vaxers, Randians, and Libertarians are automatically presumed to be idiots; Christians and Muslims might get the benefit of the doubt, if I'm in a good mood.

See the Debate Flowchart for some basic rules.

Sourced factual corrections are always published and acknowledged.

I will respond or not respond to comments as the mood takes me. See my latest comment policy for details. I am not a pseudonomous-American: my real name is Larry.

Comments may be moderated from time to time. When I do moderate comments, anonymous comments are far more likely to be rejected.

I've already answered some typical comments.

I have jqMath enabled for the blog. If you have a dollar sign (\$) in your comment, put a \\ in front of it: \\\$, unless you want to include a formula in your comment.