- Elliot Temple wrote:

> In the genuine absence of prior ideas, you would not guess one way > or the other. Nor would you see those as the only two

I've held off replying while I try to assimilate these ideas better. I read part of Unended Quest which helped clarify one of your points. Then I wrote out what I think your point is, in my own words:

> possibilities: your focus on those two possibilities, instead of

> others, is itself a product of your background knowledge.

"Suppose that you're asked to guess what the square root of 72,361 is (it's 269). You wouldn't guess that it is a single- or double-digit number, nor would you expect it to be a number with four or more digits; definitely not a sixteen-digit number, or a ten-billion-digit-number! Why? Because 72,361 has five digits, and you know that multiplying even the largest double-digit number by itself would not result in a five-digit number, and that multiplying the smallest four-digit number would not give you a five-digit number either. So, the answer must be in the three-digit range.

Any guess you come up with will be an educated guess -- not random. It'll be 'educated' in the sense of being unrefuted in the light of those preexisting theories pertaining to multiplication, which play a critical role by eliminating from consideration any guesses that fall outside the three-digit range. They have significant critical reach, too. They ruled out an infinitely broad swath of guesses that you could have made without their guidance. This makes them invaluable tools.

These 'guiding theories' (a.k.a. background knowledge) allow us to perform targeted *conscious* criticism by preconsciously screening the set of solutions, or preventing such guesses from even forming in our minds in the first place.

Without them, we could not guess anything, because among the set of guiding theories we have are theories about what problem we're attempting to solve, and theories about how particular classes of guesses are relevant to the problem context. If we don't have any of these, all guesses will seem like equally good solutions, and any selection will be completely and utterly arbitrary. So you might guess "Hippopotamus!" or "For the lulz" or "4zh$8673*f94e" instead of "269.""

Elliot Temple wrote:

> Maybe, besides the above, it has to do with an Occam's Razor type

When would it be appropriate for you to think that something is infinitely extended (such as a line), or that it applies in ALL cases? Is it simply when you can think of no reason why it should end, or what would cause it to apply to only *some* cases?

> intuition. End points could seem like a complicating factor, that

> could only be found at arbitrary positions.

That's what I'm really driving at.

As DD pointed out in BoI, it's easy to slip into parochialistic thinking, and mistake something local for being global/finite for infinite/restricted for unrestricted/etc. He gives examples of that happening (e.g. people thinking the seasons are the same all across the earth).

That's all well and good. But under what circumstances is it a mistake *not* to think some idea has universal reach? When would it be foolish to think something *isn't* global? And further....what guiding theories yield judgements of universal reach/infiniteness/unrestrictedness? I don't recall that being answered in BoI, but I could've easily missed it. - On Feb 29, 2012, at 5:19 PM, Destructivist wrote:

> Elliot Temple wrote:

Also the square root of 90,000 is 300, so it's going to be a bit less than that. And the square root of 40,000 is 200, so more than that. And if you know what 25*25 is (or it's not very hard to figure that out quickly), you can easily narrow it down more.

>

>> In the genuine absence of prior ideas, you would not guess one way > or the other. Nor would you see those as the only two

>> possibilities: your focus on those two possibilities, instead of

>> others, is itself a product of your background knowledge.

>

>

> I've held off replying while I try to assimilate these ideas better. I read part of Unended Quest which helped clarify one of your points. Then I wrote out what I think your point is, in my own words:

>

> "Suppose that you're asked to guess what the square root of 72,361 is (it's 269). You wouldn't guess that it is a single- or double-digit number, nor would you expect it to be a number with four or more digits; definitely not a sixteen-digit number, or a ten-billion-digit-number! Why? Because 72,361 has five digits, and you know that multiplying even the largest double-digit number by itself would not result in a five-digit number, and that multiplying the smallest four-digit number would not give you a five-digit number either. So, the answer must be in the three-digit range.

> Any guess you come up with will be an educated guess -- not random. It'll be 'educated' in the sense of being unrefuted in the light of those preexisting theories pertaining to multiplication, which play a critical role by eliminating from consideration any guesses that fall outside the three-digit range. They have significant critical reach, too. They ruled out an infinitely broad swath of guesses that you could have made without their guidance. This makes them invaluable tools.

I agree with this.

>

> These 'guiding theories' (a.k.a. background knowledge) allow us to perform targeted *conscious* criticism by preconsciously screening the set of solutions, or preventing such guesses from even forming in our minds in the first place.

>

> Without them, we could not guess anything, because among the set of guiding theories we have are theories about what problem we're attempting to solve, and theories about how particular classes of guesses are relevant to the problem context. If we don't have any of these, all guesses will seem like equally good solutions, and any selection will be completely and utterly arbitrary. So you might guess "Hippopotamus!" or "For the lulz" or "4zh$8673*f94e" instead of "269.""

> Elliot Temple wrote:

No, I don't think so.

>

>> Maybe, besides the above, it has to do with an Occam's Razor type

>> intuition. End points could seem like a complicating factor, that

>> could only be found at arbitrary positions.

>

> When would it be appropriate for you to think that something is infinitely extended (such as a line), or that it applies in ALL cases? Is it simply when you can think of no reason why it should end, or what would cause it to apply to only *some* cases?

What if you can't think of a reason it should end, or a reason it shouldn't end? That'd be symmetrical.

You have to come up with criticisms relevant to the problem situation. And if you can't figure it out (now), accept you don't know.

>

Explanations about conjectures and refutations apply to all conjectures and all refutations. This is because the logic of the explanations apply to those cases. E.g. the explanations make use of aspects of conjectures (e.g. they are a type of idea), but not aspects of potatoes. So they apply to conjectures but not potatoes. They have an amount of reach that makes sense.

> That's what I'm really driving at.

>

> As DD pointed out in BoI, it's easy to slip into parochialistic thinking, and mistake something local for being global/finite for infinite/restricted for unrestricted/etc. He gives examples of that happening (e.g. people thinking the seasons are the same all across the earth).

>

> That's all well and good. But under what circumstances is it a mistake *not* to think some idea has universal reach? When would it be foolish to think something *isn't* global? And further....what guiding theories yield judgements of universal reach/infiniteness/unrestrictedness? I don't recall that being answered in BoI, but I could've easily missed it.

Or ideas that apply to replicators apply to all replicators, inherently, but not to towels. (Well actually anything will replicate in the right environment, but never mind that complication.)

It's a mistake to deny reach arbitrarily. Ideas always have a right amount of reach.

Ideas about electrons can/should apply to all electrons in the whole multiverse.

Or consider axis tilting and seasons. Does that apply on other planets orbiting other suns? Yes. If they have axis tilting then we're going to see some of the same heat distribution effects. Saying it wouldn't work, because that's a different solar system, would be an unexplained denial of the explanations of how axis tilting and seasons work. The explanations never make use of which solar system they are in, so they don't just apply to one solar system.

The case with the line is different. There's no particular reason to go either way. Out of context, there's nothing about seeing a line, here, that implies it will or won't be elsewhere.

-- Elliot Temple

http://curi.us/ - On 1 Mar 2012, at 1:19am, Destructivist wrote:

> under what circumstances is it a mistake *not* to think some idea has universal reach? When would it be foolish to think something *isn't* global? And further....what guiding theories yield judgements of universal reach/infiniteness/unrestrictedness? I don't recall that being answered in BoI, but I could've easily missed it.

Judging what the reach of an explanation is does not involve conjecturing a second theory. The reach of an explanation is an inherent property of it. It is determined by the fact that the explanation would become a bad explanation if its domain of applicability were restricted or extended outside a certain range. Moreover, the better the explanation, the narrower that range is. This is discussed in BoI, especially on pp26-29.

So, we judge that a good explanation is universal when assuming any smaller domain of applicability would make it a bad explanation.

-- David Deutsch