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 zero ought to be a one if R is to hold)—but still, it seems clear that it is not an instance of the pattern. Still, does this mean that we have failed to identify any useful regularities in S$3$? I will argue that it most certainly does not mean that, but the point is by no means an obvious one. What's the difference between S$3$ and S$0$ such that we can say meaningfully that, in picking out R, we've identified something important about the former but not the latter? To say why, we'll have to be a bit more specific about what counts as a pattern, and what counts as successful identification of a pattern.

Following Dennett and Ladyman et. al., we might begin by thinking of patterns as being (at the very least) the kinds of things that are "candidates for pattern recognition. " But what does that mean? Surely we don't want to tie the notion of a pattern to particular observers—whether or not a pattern is in evidence in some dataset (say S$3$) shouldn't depend on how dull or clever the person looking at the dataset is. We want to say that there at least can be cases where there is in fact a pattern present in some set of data even if no one has yet (or perhaps even ever will) picked it out. As Dennett notes, though, there is a standard way of making these considerations more precise: we can appeal to information theoretic notions of compressibility. A pattern exists in some data if and only if there is some algorithm by which the data can be significantly compressed.

This is a bit better, but still somewhat imprecise. What counts as compression? More urgently, what counts as significant compression? Why should we tie our definition of a pattern to those notions? Let's think through these questions using the examples we've been looking at

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