So, is your complaint just that they use the same formalism to talk about logical relations and causal relations? Or even just that they don't use the same two specific formalisms that you use?
That seems to me like a red herring. Pearl's causal networks can be encoded in ZFC. Conversely, ZFC can be talked about using various kinds of decorated networks --- that's what category theory is. Using the same formalism for the two different kinds of relations should only be a problem if it leads one to ignore the differences between them. As I tried to show above, philosophers of mathematics aren't making this mistake in general. They are keenly aware of differences between logical relations and causal relations. In fact, many would point to differences that don't, in my view, actually exist.
And besides, I don't get the impression that philosophers these days consider nth- order logic to be the formalism for physical explanations. As mentioned on the Wikipedia page for the deductive-nomological model, it doesn't hold the dominant position that it once had.
Pearl's causal networks can be encoded in ZFC
That's what I would expect most mathematical-existence types to think. It's true, but it's also the wrong thought.
Wei, do you see it now that I've pointed it out? Or does anyone else see it? As problems in philosophy go, it seems like a reasonable practice exercise to see it once I've pointed to it but before I've explained it.
Last summer, 15 Less Wrongers, under the auspices of SIAI, gathered in a big house in Santa Clara (in the SF bay area), with whiteboards, existential risk-reducing projects, and the ambition to learn and do.
Now, the new and better version has arrived. We’re taking folks on a rolling basis to come join in our projects, learn and strategize with us, and consider long term life paths. Working with this crowd transformed my world; it felt like I was learning to think. I wouldn’t be surprised if it can transform yours.
A representative sample of current projects:
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ETA (as of 3/25/10): We are still accepting applications, for summer and in general. Also, you may wish to check out http://www.singinst.org/grants/challenge#grantproposals for a list of some current projects.