Friday, 11 July 2014

Against Rationalism

By “Rationalism” in this article I mean the philosophical position, opposed to Empiricism and Skepticism, that knowledge can be acquired by reason alone, rather than from observation and experience (Empiricism) or not at all (Skepticism). To distinguish “Rationalism” from other terms (such as “rational”), I'll stick to capitalizing it.

Hume's Fork

If we take in our hand any volume—of divinity or school metaphysics, for instance—let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames, for it can contain nothing but sophistry and illusion.

Thus Hume stated what is probably the best known declaration of the position restricting Rationalism to abstract topics only, and demanding empiricism about factual matters. Naturally, philosophers since Hume have explored the divide in various ways, such as the “analytic/synthetic distinction”, or the a priori versus a posteriori distinction. I don't propose to explore these philosophical details here.

For the purposes of this article we will initially note that, in agreement with Hume, the Rationalist position applied to mathematics and abstract logic is not particularly controversial. (Though philosophy of mathematics appears to be a field singularly lacking in consensus, this seems to have remarkably little impact on actual mathematicians or the process of mathematics as a discipline.)

The more interesting question is what to do about the fact/existence side of the fork. As we've been seeing a lot lately, there's a strong thread of Rationalism about metaphysics running through what passes for religious philosophy and apologetics; we'll get into the whys and wherefores of that later.

Square circles

I'm going to start off with an analogy from mathematics. Are square circles logically possible? They've been referred to in comments as examples of logical impossibility... let's see what we can come up with:

  • C1. Definition: a circle is a plane figure with all points at an equal distance from a designated internal point (its center).
  • S1. Definition: a square is a plane figure with four equal straight sides meeting at four identical vertices.

These are valid definitions, yes? In fact we could go all Aristotelian and say that these are the essences of circles and squares.

It turns out that there are (at least) two simple examples where we can satisfy conditions C1 and S1 simultaneously: simply choose the definition of “distance” to be either the Chebyshev norm or the Manhattan norm.

“Woah! Stop right there!” says the apologist. “You equivocated on the meaning of distance!” To which I respond, by what right do you privilege one meaning of “distance” over another? Our use of the Euclidean distance as the common meaning of the word is not based in logic but experience; Euclidean distances model the physical world exceptionally well at human scales, so we naturally assume that's the intended meaning; but this is an a posteriori fact, not available to the Rationalist.

Fortunately, this being a mathematical problem, the disagreement is easy to highlight and the problem can be removed by simply specifying everything in mathematical notation rather than words, or otherwise unambiguously indicating what fundamental axioms we are relying on. This works because we can define mathematical concepts in sufficient precision to be able to agree on them perfectly, and because we can define them independently of anything that exists in the real world.

Ambiguous concepts

  • C2. Definition: a circle is a plane figure with constant non-zero curvature at all points.

Definition C2 is clearly not equivalent to C1 in all cases (though it is equivalent in Euclidean space). Which is the “correct” definition? Does it even make sense to label one definition as “correct”? Is one an essential property and one an accident?

This problem gets much worse when looking at concepts from the real world. The space of possible concepts is unimaginably huge; not just bigger than the universe, but at least doubly exponentially so. Each possible concept is one choice from a vast set of related concepts from which it differs only in counter-factual cases. One consequence of this is that we have to be careful about picking out concepts; why highlight one rather than another? It also means we have to be careful about assuming that everyone is agreeing on the same concepts. But possibly most importantly, it means that the specific concepts that we pick out from experience, or collective experience in the form of language and culture, are subject to our cognitive biases.

Physics and Metaphysics

The fact that concepts are derived from experience, rather than springing from some logical realm, is a major reason for the failure of Aristotelian physics. Over time, more and better experience allowed for the creation of a successful physics, correcting the old mistakes.

But a Rationalist approach to metaphysics has the same problem with concepts, but lacks any corrective mechanisms. Even concepts as apparently simple as “exists” prove to be quite slippery; the idea that a concept like, say, “per se series of efficient causes” is sufficiently well-founded in reality to serve as the basis for an argument about anything important is quite implausible.

The Elephant In The Room

Given all the above, a rational Rationalist—assuming they did not abandon Rationalism altogether—would at least consider the possibility that their “logical” arguments might be subject to errors more subtle than simple mistakes of logic, and look at the evidence to see whether their conclusions might be incorrect.

After all, there is no rational reason, having concluded that something necessarily exists and therefore actually exists, why there should not also be evidence for its existence.

But the religious apologist cannot do this, because the evidence is unfavorable to the desired conclusion. Rationalism as a religious apologetic has one and only one purpose: to put discussion of the real world and its evidence out of bounds. Whether the aim is to convert the infidel or merely to reassure the already faithful, Rationalist arguments are a valuable rhetorical weapon—but used this way they are not truth-seeking or intellectually honest.

The Dragon In The Garage

When the one claims to have a dragon in their garage, but also has a ready-made explanation for why it is not detected by specific experimental tests, we can conclude that—at some level—they really do not believe it; they have a sufficiently accurate model of a dragon-free universe in their head to be able to predict the outcome of tests—and to bet on those outcomes.

Denial of the value of evidence can be regarded as an example of this—a defense-in-advance against having to acknowledge the discrepancy between the “belief” model and the model that works in the real world. Similarly with other forms of anti-empiricism and anti-epistemology.

Evidence as Common Ground

The Rationalist has literally nothing to say to the person who rejects one or more of their premises or methods; if an appeal to common intuition (never a valid guide to truth!) or common concepts (see above) fails, there is nothing left but to agree to disagree.

Evidence, on the other hand, can in principle be accepted by anyone. Even empiricists with differing priors will not find their degree of disagreement to be increased by further evidence.

What then to make of someone who denies the possibility of evidence?