depth first search

Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusion drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white.

–Karl R. Popper, The Logic of Scientific Discovery

This passage caught my eye over coffee this morning. I had lunch the day before with Benjamin Kuipers and Satinder Singh Baveja along with associated graduate students. The lunch led to a lively discussion about the notion of “object” in artificial intelligence, and in particular, whether objects provide any durable power in artificially intelligent systems.

Part of the problem seems to be that the term object is difficult to define precisely. My own view (influenced heavily by Ben’s) is that an object is some heterogeneous collection of properties that explain part of the sensory state of a robot, and that a learning process that generates object concepts is some still not well understood collection of perceptual compression and bias. In any event, this somewhat more structured concept of object seemed to satisfy the critique brought up by Satinder, though its hypothetical nature certainly does not rule out alternative approaches.

So what does this have to do with the example above? The problem is with the word swan. What Popper treats as a separate concept from the observations of color is, in my view, actually a composite of the perceptions that we associate with the object. If we consider the example above as involving an assertion about a complex composition of perceptions that comprise a swan, we may find that one particular criteria for being a swan (or more accurately, being labeled as a swan) is that the object in question be white. With this view, we have no need for induction. What we have instead is some sort of set membership, where the observer is simply remarking that the object swan contains the property white. We are replacing induction with affirmation. Color is not a property to induct over, but a percept that summarizes.

Now consider a competing view that discards the notion of object and opts instead for explicit inductive predictions. With this view, observing that the swan is white merely verifies a prediction based on the perceptual history of swans. This view seems to co-opt induction by explicitly representing concepts as things which can be reliably predicted from histories of percepts. Under a possible interpretation of this approach, seeing a white swan and concluding that all swans are white is precisely identical to the way the concept of the swan is built. Under this view, the induction and the swan concept are actually the same, and the example above becomes a truism.

So we have two alternative notions of the object swan, as a set, where induction is instead a kind of (possibly fuzzy) set membership test, and as a prediction based on histories, where induction is the same as the object itself. Both alternatives to Popper are compelling in that they seem to bypass entirely the problem of induction.

I’ve been reading a lot of Searle recently. Searle bashing seems to be a popular pastime among young graduate students in AI, but I admit to a certain sympathy with his argument. I recently read about analogue computing in The New Turing Omnibus which reminded me of one of Searle’s central claims, that the locus of computation matters.

To Searle, a program doesn’t produce artificial intelligence, a program running somewhere produces artificial intelligence. Not only that, but a program running in the wrong place won’t actually produce intelligence, but maybe only the simulation of intelligence, or worse, a bunch of noise (image a computer constructed from beer cans).

To me the argument divides into two parts:

1. How universal is computation?
2. How universal is intelligence?

Searle claims that intelligence is less universal than computation. You can construct a Turing machine out of beer cans, but you can’t construct a thinking machine out of beer cans (but maybe you can construct a machine that simulates thinking out of beer cans). I believe the Church-Turing thesis, but I’m not yet convinced that intelligence is quite so universal.