Secondly, we manage to routinely prove facts about the behavior of programs (this is the field of program analysis) despite the fact that in theory this should be "undecidable". This is because the undecidability issues don't really crop up in practice.
As someone with a reasonable acquaintance with program analysis, synthesis, and semantics... YIKES.
Rice's Theorem is, so to speak, the biggest, nastiest rock we semantics folks have to crawl around on a regular basis. The way we generally do it is by constructing algorithms, semantic frameworks, and even entire programming languages in which undecidability cannot happen in the first place, thus restricting ourselves to analyzing something less than the set of all possible programs.
Now, admittedly, in practice we've made a lot of progress this way, because in practice there are really four kinds of programs: ones that provably terminate by design, ones that provably don't terminate by design, provably undecidable programs (usually programs that rely on the halting behavior of some other program or logic for their own halting behavior), and just plain messed-up what-the-fuck programs.
The last kind are mostly created only by mistake. The third kind come up in program analysis and semantics, but we can usually construct a proof that we're dealing with a formally undecidable problem there and set reasonable hard bounds on length of iteration or depth of recursion (or even find decidable subclasses of these problems that are decently useful to real people). The second kind is handled by writing coterminating programs over codata. The first kind is handled by writing terminating programs over data.
Undecidability issues do come up in practice, and the current research frontier (MIRI's Lobian paper, Goedel Machines, AIXI) certainly indicates that these issues definitely come up in the study of Universal Artificial Intelligence. However, for most problems below the level of program analysis or universal induction, undecidability issues can be handled or contained productively by research effort.
Previously: Why Neglect Big Topics.
Why was there no serious philosophical discussion of normative uncertainty until 1989, given that all the necessary ideas and tools were present at the time of Jeremy Bentham?
Why did no professional philosopher analyze I.J. Good’s important “intelligence explosion” thesis (from 19591) until 2010?
Why was reflectively consistent probabilistic metamathematics not described until 2013, given that the ideas it builds on go back at least to the 1940s?
Why did it take until 2003 for professional philosophers to begin updating causal decision theory for the age of causal Bayes nets, and until 2013 to formulate a reliabilist metatheory of rationality?
By analogy to financial market efficiency, I like to say that “theoretical discovery is fairly inefficient.” That is: there are often large, unnecessary delays in theoretical discovery.
This shouldn’t surprise us. For one thing, there aren’t necessarily large personal rewards for making theoretical progress. But it does mean that those who do care about certain kinds of theoretical progress shouldn’t necessarily think that progress will be hard. There is often low-hanging fruit to be plucked by investigators who know where to look.
Where should we look for low-hanging fruit? I’d guess that theoretical progress may be relatively easy where:
These guesses make sense of the abundant low-hanging fruit in much of MIRI’s theoretical research, with the glaring exception of decision theory. Our September decision theory workshop revealed plenty of low-hanging fruit, but why should that be? Decision theory is widely applied in multi-agent systems, and in philosophy it’s clear that visible progress in decision theory is one way to “make a name” for oneself and advance one’s career. Tons of quality-adjusted researcher hours have been devoted to the problem. Yes, new theoretical advances (e.g. causal Bayes nets and program equilibrium) open up promising new angles of attack, but they don’t seem necessary to much of the low-hanging fruit discovered thus far. And progress in decision theory is definitely not valuable only to those with unusual views. What gives?
Anyway, three questions:
1 Good (1959) is the earliest statement of the intelligence explosion: “Once a machine is designed that is good enough… it can be put to work designing an even better machine. At this point an ”explosion“ will clearly occur; all the problems of science and technology will be handed over to machines and it will no longer be necessary for people to work. Whether this will lead to a Utopia or to the extermination of the human race will depend on how the problem is handled by the machines. The important thing will be to give them the aim of serving human beings.” The term itself, “intelligence explosion,” originates with Good (1965). Technically, artist and philosopher Stefan Themerson wrote a "philosophical analysis" of Good's intelligence explosion thesis called Special Branch, published in 1972, but by "philosophical analysis" I have in mind a more analytic, argumentative kind of philosophical analysis than is found in Themerson's literary Special Branch. ↩