Sunday, July 1, 2012

two kinds of inference errors


We’re in the midst of a searing heat wave in Minneapolis. It about 91 degrees, and I’m sitting in my backyard enjoying a tasty Hefeweizen while thinking about cognitive errors.

Here are two different kinds of breakdowns in inference (among the multitude of types).

The first one is really simple to understand, but an example is better than an explanation.

type one

In a game of chess, the bishop can only move diagonally. This rule governing its movement is built into the chess universe. This rule has no exceptions.

A player has two bishops, one on a red-square and one on a black-square.

If one of the given bishops starts on a red-square, then one might be tempted to conclude that the bishop must always be on a red square and never can be on a black square. It can seem like this corollary is every bit without exception as the diagonal movement rule.

In many cases, a bishop that starts on a red square will stay on red squares for as long as the game is live.

But there are exceptions. Suppose the bishop is captured. The player who lost her bishop may promote a pawn that manages to cross to the other shore. Suppose that the pawn is promoted on a black-square. That reincarnated bishop is a black-square bishop, contrary to the ersatz-rule that it can only be on a red-square.

This illustrates in a stupendously nerdy way the threat of too hasty inferences in a game context in which there are more complex but accessible rules that would otherwise block or temper the mistaken inference.

Again, this seems to be the most common and straightforward kind of inference breakdown.

type two

There is, however, another kind of breakdown in inference that has less to do with failing to account for accessible rules. It’s subtler and more interesting in that the complete rules themselves are not quite available, yet the person who makes inferences cognitively acts under the fiction that they are. But how does this occur? It seems that it has to do with a blindness to the changing conditions of observation, where the conditions change because of either a technological or cultural innovation.

Again, an example is better than an explanation.

For a long time in physics (immediate qualifier: limiting the discussion to scientific realism), it was thought that the mass of an object does not change even under conditions of motion. From the point of view of the crude observations of macro-sized objects, this appears true. Even at the micro-level of most observations that any of us would make, this is sufficient. Even objects that are moving extremely fast relative to how most animals move retain the same mass in said motion.

Generate a rule of physics: The mass of an object is independent of speed.

This rule about mass and motion is mostly correct modulo the context of ordinary conditions of observation. In fact, for a long time (not too long ago, in terms of the scale of the history of science), it was sufficient for physicists!

This changed when our technology changed. This changed when we became able to inspect a bit deeper into the nature of material substance.

Contrary to the former rule, mass does appreciably increase with velocity, but only at velocities near c (speed of light).

It’s not that Nature changed; rather, our conditions of observational access to Nature have evolved in a good way. As our evolution moves us forward in our observational powers, we reform old rules, replace them, and find new mysteries of material substance that suggest that even our reformed rules may be overturned in time. Orthodoxy in physics is (or should be) always hypothetical – meaning, that allegiance is a complex negotiation between Nature’s presentation of herself, our observational technologies, our theoretical models of explanation and prediction (prediction is explanation with time’s arrow imaginatively reversed), and a judgment about acceptable alienation between the theory’s predictions and current anomalies that have yet to become recalcitrant.

The nice thing about some scientists (and some philosophers) is that this complex relationship involving both observation sentences and value sentences (the epistemic and aesthetic values of simplicity, parsimony, elegance, etc., that inextricably are entangled with theory assessment) is front and center of their theorizing. There is no need to hide what is obvious under even minimal analysis.

This more subtle epistemic orientation is a nice contact point for science and philosophy, whose interrelationships have been written about voluminously. While not immune to breakdowns in these more subtle epistemic orientations, I see more numerous breakdowns occurring elsewhere.

The possible breakdown in inference in these sorts of contexts is when an agent makes a mistake about the quality of his observational placement. He is not properly taking into account the likelihood – much less, the possibility – that further evolutions in observational conditions may provide further insight into the very nature of the subject matter about which he exhibits dogma.

I’m sad to report that this happens noticeably in reasoning about religion and God/god/G-d/g-d/gods/The-Real.

Over the years, I’ve come to see the affinities between on the one hand the Kuhnian (but not the more baroque readings) and Lakatos-ian interpretations of the history of science and on the other hand the notion that Christian theology should operate with some formal family resemblances to the earlier aforementioned complex negotiation of rationality that exists in science. (I focus on Christian theology only because (i) I’m more familiar with it, and (ii) I self-identify as some form of Christian 4 out of 7 days a week.†)

But this dynamic isn’t even acknowledged – much less fretted about – by a huge contingent of religious folk.

I think I’m beginning to understand Christian Fundamentalists* a bit more, in that they tend to make both types of inference errors: (a) mistakenly believing that they have the right rules (as opposed to the hypothetical “right now” rules) and (b) not taking into account the probability that the conditions for observation evolve and in fact alter (and should alter) our allegiance to hypothetical “right now” rules (or propositions or creedal statements or…). They forget the motto Ecclesia semper reformanda est (“The church is to be always reforming.”).

Please allow me to head off a red herring at the pass. The bogeyman of “relativism” does not apply at all, precisely because the whole enterprise is premised on progress. In science (well, in scientific realism, to which I subscribe), the march towards better and more accurate representations of The Real is prosecuted hand-in-hand with – for lack of a better phrase – epistemic humility on the part of the scientists and philosophers of science I resonate with most. In the philosophy of science, we even invented a term to describe this orientation: verisimilitude.

In religion, I don’t see why it can’t be the same. (Actually, I see why, but it has nothing to do with rationality.) One specific analog for religious programs and religious ethics of the new observational possibilities and technologies in science should be the complex cluster of new social, political, and economic possibilities that exist for women, racial/ethnic minorities, and other types of under-represented or historically-repressed groups in the West and increasingly other global places. These new “encyclopedias of reference” allow for deeper insight into religiously important phenomena such as scripture, hermeneutics, nature/function of religious communities, etc., while simultaneously correcting a gross distortion – namely, the distortion that religious/doctrinal history floats somehow free of other social and historical realities such as the political economies that largely determined the modern consciousness, to name just one. (This is not a reductively Marxist claim! Adam Smith could say the same!)

The character of these new insights cannot be controlled, and hence they may and perhaps should be expected to subvert older “rules.” None of this can be legitimately controlled in advance, unless “legitimacy” is narrowly defined as “not contradicting orthodox understandings of Scripture.” That narrow definition wears on its sleeve the logical fallacy of begging the question, since the very conversation that is of most interest to religious believers whose brains are turned on revolves around questions such as “In what ways might Scripture gesture beyond the confines of its historically situated representations?” and “What new discoveries and semantic horizons – possibly in tandem with evolving conditions of observation/reading/interpretation – does Scripture have for us who sincerely seek to live from a religious point of view?"

Well, it’s getting hot out here, and this simple blog post has inflated beyond my intention. I’m headed back indoors to retreat to air-conditioned bliss.

Signing off on this really hot Sunday afternoon…

Peace be with you.

* Any form of Fundamentalism (religious or otherwise, left or right, etc.) will do, since various forms of Fundamentalism share the same tendencies towards inference errors.

† Gospel of Mark 9:24.

1 comment:

Craig said...

Should we say that type two mistakes are just one of the reasons why we make type one mistakes?