And if you’re allowed to end in something assumed-without-justification, then why aren’t you allowed to assume anything without justification?
I address this question in Incremental Doubt. Briefly, the answer is that we use a background of assumptions in order to inspect a foreground belief that is the current focus of our attention. The foreground is justified (if possible) by referring to the background (and doing some experiments, using background tools to design and execute the experiments). There is a risk that incorrect background beliefs will “lock in” an incorrect foreground belief, but this process of “incremental doubt” will make progress if we can chop our beliefs up into relatively independent chunks and continuously expose various beliefs to focused doubt (one (or a few) belief(s) at a time).
This is exactly like biological evolution, which mutates a few genes at a time. There is a risk that genes will get “locked in” to a local optimum, and indeed this happens occasionally, but evolution usually finds a way to get over the hump.
Should I trust Occam’s Razor? Well, how well does (any particular version of) Occam’s Razor seem to work in practice?
This is the right question. A problem is that there is the informal concept of Occam’s Razor and there are also several formalizations of Occam’s Razor. The informal and formal versions should be carefully distinguished. Some researchers use the apparent success of the informal concept in daily life as an argument to support a particular formal concept in some computational task. This assumes that the particular formalization captures the essence of the informal concept, and it assumes that we can trust what introspection tells us about the success of the informal concept. I doubt both of these assumptions. The proper way to validate a particular formalization of Occam’s Razor is to apply it to some computational task and evaluate its performance. Appeal to intuition is not a substitute for experiment.
At present, I start going around in a loop at the point where I explain, “I predict the future as though it will resemble the past on the simplest and most stable level of organization I can identify, because previously, this rule has usually worked to generate good results; and using the simple assumption of a simple universe, I can see why it generates good results; and I can even see how my brain might have evolved to be able to observe the universe with some degree of accuracy, if my observations are correct.”
It seems to me that this quote, where it mentions “simple”, must be talking about the informal concept of Occam’s Razor. If so, then it seems reasonable to me. But formalizations of Occam’s Razor still require experimental evidence.
The question is, what is the scope of the claims in this quote? Is the scope limited to how I should personally decide what to believe, or does it extend to what algorithms I should employ in my AI research? I am willing to apply my informal concept of Occam’s Razor to my own thinking without further evidence (in fact, it seems that it isn’t entirely under my control), but I require experimental evidence when, as a scientist, I use a particular formalization of Occam’s Razor in an AI algorithm (if it seems important, given the focus of the research; is simplicity in the foreground or the background?).
By examining our cognitive pieces (techniques, beliefs, etc.) one at a time in light of the others, we check not for adherence of our map to the territory but rather for the map’s self-consistency.
This would appear to be the best an algorithm can do from the inside. Self-consistent may not mean true, but it does mean it can’t find anything wrong with itself. (Of course, if your algorithm relies on observational inputs, there should be a theoretical set of observations which would break its self-consistency and thus force further reflection.)
And if you’re allowed to end in something assumed-without-justification, then why aren’t you allowed to assume anything without justification?
I address this question in Incremental Doubt. Briefly, the answer is that we use a background of assumptions in order to inspect a foreground belief that is the current focus of our attention. The foreground is justified (if possible) by referring to the background (and doing some experiments, using background tools to design and execute the experiments). There is a risk that incorrect background beliefs will “lock in” an incorrect foreground belief, but this process of “incremental doubt” will make progress if we can chop our beliefs up into relatively independent chunks and continuously expose various beliefs to focused doubt (one (or a few) belief(s) at a time).
This is exactly like biological evolution, which mutates a few genes at a time. There is a risk that genes will get “locked in” to a local optimum, and indeed this happens occasionally, but evolution usually finds a way to get over the hump.
Should I trust Occam’s Razor? Well, how well does (any particular version of) Occam’s Razor seem to work in practice?
This is the right question. A problem is that there is the informal concept of Occam’s Razor and there are also several formalizations of Occam’s Razor. The informal and formal versions should be carefully distinguished. Some researchers use the apparent success of the informal concept in daily life as an argument to support a particular formal concept in some computational task. This assumes that the particular formalization captures the essence of the informal concept, and it assumes that we can trust what introspection tells us about the success of the informal concept. I doubt both of these assumptions. The proper way to validate a particular formalization of Occam’s Razor is to apply it to some computational task and evaluate its performance. Appeal to intuition is not a substitute for experiment.
At present, I start going around in a loop at the point where I explain, “I predict the future as though it will resemble the past on the simplest and most stable level of organization I can identify, because previously, this rule has usually worked to generate good results; and using the simple assumption of a simple universe, I can see why it generates good results; and I can even see how my brain might have evolved to be able to observe the universe with some degree of accuracy, if my observations are correct.”
It seems to me that this quote, where it mentions “simple”, must be talking about the informal concept of Occam’s Razor. If so, then it seems reasonable to me. But formalizations of Occam’s Razor still require experimental evidence.
The question is, what is the scope of the claims in this quote? Is the scope limited to how I should personally decide what to believe, or does it extend to what algorithms I should employ in my AI research? I am willing to apply my informal concept of Occam’s Razor to my own thinking without further evidence (in fact, it seems that it isn’t entirely under my control), but I require experimental evidence when, as a scientist, I use a particular formalization of Occam’s Razor in an AI algorithm (if it seems important, given the focus of the research; is simplicity in the foreground or the background?).
By examining our cognitive pieces (techniques, beliefs, etc.) one at a time in light of the others, we check not for adherence of our map to the territory but rather for the map’s self-consistency.
This would appear to be the best an algorithm can do from the inside. Self-consistent may not mean true, but it does mean it can’t find anything wrong with itself. (Of course, if your algorithm relies on observational inputs, there should be a theoretical set of observations which would break its self-consistency and thus force further reflection.)