What distinction are you trying to draw between "arbitrarily large" and "indefinitely large" that turns the concept into one which is applicable to the real world?
Arbitrarily large means just that in the mathematical sense. Indefinitely large is a term that would be used in other contexts. In the contexts that I've seen "indefinitely" used and the way I would mean it, it means so large as to not matter as the exact value for the purpose under discussion (as in "our troops can hold the fort indefinitely").
Lots of factors indicate that "FOOM" is poorly defined - including the disagreement surrounding it,
Disagreement about something is not always a definitional issue. Indeed, when dealing with people on LW where people try to be rational as possible and have whole sequences about tabooing words and the like, one shouldn't assign a very high probability to disagreements being due to definitions. Moreover, as one of the people who assigns a low probability to foom and have talked to people here about those issues, I'm pretty sure that we aren't disagreeing on definitions. Our estimates for what the world will probably look like in 50 years disagree. That's not simply a definitional issue.
Usually, step 1 in those kinds of discussions is to make sure that people are using the terms in the same way - and have a real disagreement - and not just a semantic one.
Ok. So why are you now doing step 1 years later? And moreover, how long should this step take as you've phrased it, given that we know that there's substantial disagreement in terms of predicted observations about reality in the next few years? That can't come from definitions. This is not a tree in a forest.
Recently I participated in this exchange - where a poster here gave p(FOOM) = 0.001 - and when pressed they agreed that they did not have a clear idea of what class of events they were referring to.
Yes! Empirical evidence. Unfortunately, it isn't very strong evidence. I don't know if he meant in that context that he didn't have a precise definition or just that he didn't feel that he understood things well enough to assign a probability estimate. Note that those aren't the same thing.
I don't see how the proposed word substitution is supposed to help. If FOOM means: "to quickly, recursively self-improve so as to influence our world with indefinitely large strength and subtlety", we still face the same issues - of how fast is "quickly" and how big is "indefinitely large". Those terms are uncalibrated. For the idea to be meaningful or useful, some kind of quantification is needed. Otherwise, we are into "how long is a piece of string?" territory.
So why are you now doing step 1 years later?
I ...
Michael Anissimov posted the following on the SIAI blog:
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We are pleased to receive donation matching support this year from Edwin Evans of the United States, a long-time Singularity Institute donor, and Jaan Tallinn of Estonia, a more recent donor and supporter. Jaan recently gave a talk on the Singularity and his life at a entrepreneurial group in Finland. Here’s what Jaan has to say about us:
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Make a lasting impact on the long-term future of humanity today — make a donation to the Singularity Institute and help us reach our $125,000 goal. For more detailed information on our projects and work, contact us at institute@intelligence.org or read our new organizational overview.
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Kaj's commentary: if you haven't done so recently, do check out the SIAI publications page. There are several new papers and presentations, out of which I thought that Carl Shulman's Whole Brain Emulations and the Evolution of Superorganisms made for particularly fascinating (and scary) reading. SIAI's finally starting to get its paper-writing machinery into gear, so let's give them money to make that possible. There's also a static page about this challenge; if you're on Facebook, please take the time to "like" it there.
(Full disclosure: I was an SIAI Visiting Fellow in April-July 2010.)