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?
I take this to be your point:
Suppose that you want to understand causation better. Your first problem is that your concept of causation is still vague, so you try to develop a formalism to talk about causation more precisely. However, despite the vagueness, your topic is sufficiently well-specified that it's possible to say false things about it.
In this case, choosing the wrong language (e.g., ZFC) in which to express your formalism can be fatal. This is because a language such as ZFC makes it easy to construct some formalisms but difficult to construct others. It happens to be the case that ZFC makes it much easier to construct wrong formalisms for causation than does, say, the language of networks.
Making matters worse, humans have a tendency to be attracted to impressive-looking formalisms that easily generate unambiguous answers. ZFC-based formalisms can look impressive and generate unambiguous answers. But the answers are likely to be wrong because the formalisms that are natural to construct in ZFC don't capture the way that causation actually works.
Since you started out with a vague understanding of causation, you'll be unable to recognize that your formalism has led you astray. And so you wind up worse than you started, convinced of false beliefs rather than merely ignorant. Since understanding causation is so important, this can be a fatal mistake.
--- So, that's all well and good, but it isn't relevant to this discussion. Philosophers of mathematics might make a lot of mistakes. And maybe some have made the mistake of trying to use ZFC to talk about physical causation. But few, if any, haven't "noticed the difference in style between the relation between logical axioms and logical models versus causal laws and causal processes." That just isn't among the vast catalogue of their errors.
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:
Interested, but not sure whether to apply?
Past experience indicates that more than one brilliant, capable person refrained from contacting SIAI, because they weren’t sure they were “good enough”. That kind of timidity destroys the world, by failing to save it. So if that’s your situation, send us an email. Let us be the one to say “no”. Glancing at an extra application is cheap, and losing out on a capable applicant is expensive.
And if you’re seriously interested in risk reduction but at a later time, or in another capacity -- send us an email anyway. Coordinated groups accomplish more than uncoordinated groups; and if you care about risk reduction, we want to know.
What we’re looking for
At bottom, we’re looking for anyone who:
Bonus points for any (you don’t need them all) of the following traits:
If you think this might be you, send a quick email to jasen@intelligence.org. Include:
Our application process is fairly informal, so send us a quick email as initial inquiry and we can decide whether or not to follow up with more application components.
As to logistics: we cover room, board, and, if you need it, airfare, but no other stipend.
Looking forward to hearing from you,
Anna
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.