Apparently these days he’s working on something called “two-dimensional modal logic”, which according to this book description that Chalmers links to, is part of a movement that

[wishes to] revive descriptivism in the philosophy of language, internalism in the philosophy of mind, and conceptualism in the foundations of modality. … In the last twenty-five years, this attack on the anti-descriptivist revolution has coalesced around a technical development called two-dimensional modal logic that seeks to reinterpret the Kripkean categories of the necessary aposteriori and the contingent apriori in ways that drain them of their far-reaching philosophical significance.

Well. Glad that’s clear. Perhaps when chapter two is finished our philosopher friend can explain?

The goal of science (it can be argued) is the accurate prediction of future or novel events. Since the days of Aristotle, and especially since Bacon, the essential means of scientific inference is induction. Bearing Hume’s warnings in mind, we generally follow this familiar process:

*Make a number of observations *Induce a general law (or mathematical function) that we think is generating the phenomenon. *Use the law to make predictions about future phenomena.

To simplify the discussion, let’s restrict ourselves to a problem of classification. You are encountering a steady stream of objects — say, liver cells. First you get a batch (the “training set”) which are labelled in two groups, say “normal” vs “cancerous”. Your goal (especially in applied science) is simply to devise a rule by which you can accurately classify future cells (the “test set”) as normal or cancerous.

To make your classification, you measure various characteristics of the liver cells; for example, size, color, mitotic activity, expression level of various proteins, etc. For simplicity, let’s suppose you measure just two characteristics, size and the level of “protein A”. You could draw a graph plotting all of the cells on these two characteristics, coloring the normal cells blue, and the cancerous red:

Now, if you’re doing normal scientific induction, you’ll look at this training data and try to posit a simple rule that will explain the data, and help you understand nature’s “hidden rule” that makes some cells cancerous and others not. In classical statistics, this means you come up with a function that will “paint” part of the surface red, and part blue. This paint forms your prediction about any cell that lands in each region:

Vapnik helped found the field of computational learning theory, in which one takes a slightly different approach. Rather than trying to guess nature’s “hidden rule”, you worry solely about minimizing the error your function will have when you test it against more liver cells. The surface-painting you come up with might not be parsimonious or a sensible guess about what nature is doing, but if it is a successful predictor, that’s fine.

Now comes the upheaval that is transductive reasoning. Vapnik has established mathematically that you pay a certain price in the accuracy of your predictions by generalizing to pain the entire surface either red or blue. So his idea is this: rather than first doing induction to posit a general rule, then making predictions about new liver cells as you see them, you simply transduce to make a prediction about each new cell as you see it, based on everything you’ve seen before. You don’t get a simple rule that you can explain or write down — all you get is a prediction each time. Vapnik has demonstrated that transduction will always perform better than induction on a given problem.

So this leaves us with this abbreviated scientific method, in which we:

*Make a number of observations * Use transduction to make predictions about new phenomena as we encounter them.

At least in particular problems in applied science, this really could be an upheaval. Who cares about having tidy theories and approximations of nature’s mysterious inner ways if we can always have the better predictor? As a general approach to natural science, however, it’s problematic. We induce models that measure the importance of Protein A not just so that we can make great predictions of whether a cell is cancerous. We also want to know whether we should investigate Protein A more deeply, learn about its structure and function, or invent drugs to mimic or inhibit it. Transduction doesn’t help us make these decisions, and so we will always need some inductive reasoning along with our transductive predicting.

Thus far, the potential impact of transduction has only begun to make an impression on the philosophical community. I haven’t found any discussion of it in the philosophy of science, but that could be because I don’t understand the current problems and arguments in that field. Gilbert Harman, a former professor of mine, is making an intriguing application of transduction to moral reasoning in a paper to be published later in 2005 (RTF, HTML). Essentially, Harman asks whether, if transduction can offer superior classification, we shouldn’t attempt to use transduction to “classify” moral actions into “should do” and “shouldn’t do.” We would sacrifice the formation of inducing general moral principles which we could elaborate and trasmit, but we would (presumably) gain “better” moral decisions.

Is it worth giving up comprehensible theories for better predictions? Will we see transductive inference gain a foothold in economics, finance, the social sciences? It’s one to watch.

For a brief introduction to the idea, wander over to the Maltheism blog, which I stumbled onto today. Start at the bottom and scroll up. There’s a sad sweet story embedded there, and I offer my condolences to Craig.

To frame the issue from the top, we begin with whether there is a divine presence. Supposing one decides that there is (whether from miracle, first cause, design, etc.), one next faces the questions of whether God is one or many, and the ethical alignment of those god(s).

In a class on the problem of evil that I took from Mark Larrimore, I remember we discussed dualist beliefs such as Manichaeism and Zoroastrianism, i.e. that there are opposed good and evil supernatural influences in the world. Polytheist religions often have gods of a mixed character; one need only inspire the wrath of Juno once to understand that the divinities are fickle. And of course, some versions of Christianity place more emphasis on the existence of Satan, a divine but not omnipotent figure who works for evil. All of these systems capture a feeling of dynamic struggle that resonates with me, and apparently with many others throughout history.

Against the “struggle” view are the twin possibilities of a single beneficent God, and a single malevolent God. The former seems to me to compel a Panglossian hypothesis that we live in the best of all possible worlds. To maintain that this the best of all possible worlds, one must undertake a series of contortions to explain how just this much suffering is required, lest we live in a still worse world. Such lines of argument strain my imagination to its limit, and don’t particularly resolve the emotional problem of evil. Instead, they feel like a theological neat trick that seems more designed to defend God than to help the human.

Or, we consider the (historically rare) maltheist position: there is a malevolent God. An omnipotent, malevolent God immediately poses a complementary “problem of good”: how does any good exist in the world? As we discussed in Larrimore’s class, most definitions of evil take the form of evil as a privation of good, i.e. a deficit of a good. So the existence of at least some good seems to be required. Now, is this really the worst of all possible worlds? Do we have a malevolent, omnipotent God coaxing things along to be just good enough to keep the wheels of life turning around, so as to permit the next generation’s catastrophe?

I admit this strains credulity. Surely there could be worse possible worlds, ones of unmitigated suffering (perhaps punctuated by 30 minute stretch breaks to remind us how bad we have it). But framing this problem against its converse suggests the outline of an antinomy to weigh with the others.

This leaves me with the possibility of a malevolent God that is not omnipotent. Rather, there simply exists some dark being out there, throwing us curveballs and tidal waves. What I like about this proposition is that it that restores the focus on human action. Rather than wondering whether we’re pleasing God, and how best to avoid his wrath, we simply assume he’s out to get us, and so must strive in every way possible to ward Him off. We may just be ant underfoot, but we’ve got a bit of maneuvering room, and so must get busy to keep our fragile way of life together.

• Thou shalt not cause pain and suffering to sentient beings <-- my rationale
• Thou shalt eat healthily
• Thou shalt avoid meats and produce made with nasty synthetic hormones, pesticides, and fertilizer
• Thou shalt protect thy Earth; i.e. prevent destruction of Western grazelands or Amazon rainforest for cattle <-- my rationale in high school
• Thou shalt indirectly feed the hungry, by minimizing thy impact on world resources (i.e. eat vegetables because of the extraordinary inefficiency of meat production, as measured by raw materials per calorie afforded)
• Thou shalt hold wacky deep-green beliefs

• Thou shalt eat only the foods freely given by a living being, without taking its life