My comment above.
? Did you provide a citation in your comment above? I don’t see one.
My comment itself is the citation. I should have been more succinct in my reference.
Your own comment offers no analysis whatsoever, beyond the words “that’s because” followed by assertions that have no evidentiary support whatsoever. I am aware of no evidence that the cognition of a savant encompasses, to quote you, “direct manipulation of symbols or discrete movements or objects,” and not “mental analysis of existence.”
Point taken.
This is an online casual discussion forum. If you expect a full academic treatise on a claim regarding brain function then I’d advise you to look elsewhere.
My comment stands though, because it’s true.
If you are here to try to convince others of your point of view, some sort of support of your claim is generally appropriate. Just saying “because it’s true” isn’t going to convince anybody of the truth of your lazy, ill-researched supposition.
I’m not here trying to convince anyone for anything.
What I said stands. Savants do not respond to abstract mental constructs. They respond to immediate physical stimuli in a much different way that average people do.
You’re posting in the “Great Debates” forum. If you’re not trying to convince anyone of anything, you shouldn’t be posting here.
I’ll defer this statement to the moderators of this forum.
I’m not sure I’d call it anything, as I’m not sure that everything arrived at by this kind of procedure is the same kind of thing, and thus can be fittingly brought under the same umbrella of a common term – some of these things might be patterns, for instance. Some might not!
Well, I’m sympathetic to this point of view to a certain extent. But I think it’s important to emphasize that at the bit level, there holds no law, no rule, no pattern (do we agree on this?). Yet nevertheless, some sort of lawfulness (though only an approximate one – it’s entirely possible for the history of the bit string universe to consist of all 1s, just spectacularly unlikely) emerges; the point I want to make is just that you don’t need to start out with laws, that they can come about by themselves. That they’re something you may get out without putting them in beforehand. That because our macroscopic universe seems lawful, it doesn’t mean that there are fundamental, externally imposed laws of irreducible origin. We don’t need to assume there’s lawfulness at the base in order to observe a lawful world.
I don’t know, I think that if both ‘there is no pattern’ and ‘there is a pattern’ is true, that’s kind of contradictory…
I’m always slightly uncomfortable with making these things too anthropocentric. What if we manage to built an AI exceeding our pattern-grasping abilities – would the status of lawfulness of our world change relative to that AI?
Besides, I don’t think we need to assume an exceptionless pattern at all – in the bit string model, there is no underlying pattern at all, yet it supports the emerging exceptionful ‘pattern’ of equidistributed 1s and 0s.
That seems a Russellian kind of way out; maybe you can do something like this, but I don’t think it’s necessary. To me, it’s perfectly possible for law to emerge from non-law, through self-organizing processes; I’m not sure there’s a benefit to elaborate constructions like these…
Actually, it’s not.
Well, I think it’s a simplified version of what makes our world amenable to prediction.
Yes, I have not argued that there are irreducible externally imposed laws. Not at all.
A -> --A implies --A.
I’m not making lawfulness depend on human psychology–I’m making our ability to predict things require a presupposition that has in part to do with human psychology. I don’t think the latter is a surprise at all.
The world could be lawful while having no graspable patterns at all. But I think that would mean we couldn’t make predictions, even though the world was lawful. (Another life form or an AI with a mind different from ours might be able to, though.)
I guess “exceptionless” needs to be more clearly defined when we’re talking about statistics.
Well, but you assume there are laws, whatever their origin; yet a random bit string follows none.
But of course, we know that A holds.
Focus on the thing you said you agreed with me about. 
This reminds me of a question I asked before but that slipped past you:
You’ve said both “There are no laws” in the string and that “laws arise” in the string. I don’t think you can have this one both ways, though. So can you clarify your meaning?
Hm? If by that you mean we agree that A holds, then I’m not sure what just happened. A is “This has no pattern.” You and I disagree about whether there is a pattern extant in the bit-string universe. I say there’s a pattern to be found not among the bits but among the sequence of strings. You say that’s not a pattern.
I’m not saying “There is no pattern” is itself a pattern. I’m saying there’s a pattern.
What’s the point in discussing things one agrees about? What’re we gonna do, just pat each other on the back for being so darn clever? 
(However, are you honestly claiming that there are laws or patterns to random bit strings? But what, then, is randomness?)
Well, I’ve perhaps been a little clumsy in my phrasing, but essentially, I mean that there are no laws in the random bit string – otherwise, it wouldn’t be random – but nevertheless, collective, emergent properties can be described in an approximately lawful fashion. The key is that one ‘forgets’ some details of the microscopic description, or alternatively, that some details don’t matter, are mapped to identical macroscopic states – otherwise, of course, there would be no description shorter than the length of the bit string possible, since after all, random bit strings are lawless.
Well, you said that anything that holds true over many iterations of the system is a pattern; I offered up ‘there is no pattern’ as an example meeting this criterion, to which you then replied that at least ‘part of you’ then wants to say that then there’s no patternless thing. But this is contradictory, as your formalization shows, since starting from A, you arrive at --A, which can’t be, since we know A!
Again, this seems terminological, but nevertheless:
I’m looking at the bit strings. I notice they tend to have equinumerous ones and zeroes. On this basis, I predict that trend will continue. And it does. And I’m not just lucky–the reliability of my predictions is actually grounded in the nature of the string.
How can you say I haven’t stumbled onto a law governing the strings? I’ve discovered a characteristic of the strings which holds with some degree of necessity, and not just of the ones I’ve seen but of ones I haven’t seen as well. I can use this degree of necessity to make reliable predictions about future strings. This is just what it is to discover a law of bit-string-nature.
I may or may not be aware of the randomness of the bitstring. That’s irrelevant to the fact that I’ve glommed onto a law governing the strings.
And I may just be lucky–it may be (since the strings are in fact random) that there will be a wide swath of strings in my future which don’t exhibit behavior conforming to this law at all. In that case, my predictions will stop working. That’s too bad for me. But what I’ve been arguing is just this: In order to think I could make predictions in the first place, I had to assume that there is some law (any law at all) operant in the world I’m looking at. Right or wrong, I had to assume it. If I didn’t–if I genuinely thought it an open possibility that the world might with no measurable probability throw absolutely anything at me in the next instant–then I would be unable to make predictions at all (or anyway, I’d be crazy to think I could).
I don’t have to assume there’s a law governing the sequence of ones and zeroes, in the bitstring case. But, if I think I can make predictions, I do have to assume there’s some kind of law operant. In this bitstring case, laws turns out to actually exist, and at least one is very close to the surface–it’s just the law that ones and zeroes tend to be equinumerous in bitstrings.
“How is that a law?!” you’re asking. I don’t know how else to explain this, so I want to really get serious about asking you to tell me, as clearly as you can, how it’s not a law. I’m pretty sure this is going to turn out to be a terminological issue, but let’s be sure.
This is why I think it’s terminological. I could just rephrase myself as follows:
In order to make predictions without being insane for doing so, one must assume that there are properties of the world that can be described in what you’ve termed “an approximately lawful fashion.”
BTW because I have an extremely inflated idea of my philosophical capabilities, (and of my role in this conversation,) I keep suspecting during this conversation that we’re zeroing in on an outline of one holy grail of Philosophy–an actual solution (not just a dissolution or a making-peace-with) of the problem of induction.
I am almost certainly laughably wrong about this, but as a confessional matter, I hereby register that the thought passes through my mind.
I’ve read about randomness in passing, but I’ve never really thought of the implications of the possible randomness of the world for its predictability. What have you read that led you to the thoughts you’re describing here? (Is it a commonplace in physics or the philosophy thereof that I simply haven’t encountered? Is it from a particular writer or group of writers? Is it an idea original to you at least so far as you know?)
If you can detect patterns in randomness, you really ought to hit the casino…
See, my stance is simply the following: for any given bit, nothing will help you determine whether that bit is 1 or 0. There’s no law governing the value of this bit (or any other). No rule, no pattern. Do we agree at least on this?
This is the lawlessness I assume holds for random bit strings. And it does hold, for if it didn’t, it simply wouldn’t be a random bit string – it would be compressible by some amount. Yet, I can make (probabilistic) predictions about these bit strings, and I can precisely quantify the degree of reliability of these predictions. So how can my ability to have confidence in the predictions I make depend on an assumption of lawfulness?
What I think I don’t agree with is the logical priority the ‘assumption of lawfulness’ assigns to the existence of laws – the laws must exist prior to us being able to make predictions. But a certain degree of lawfulness arises, through spontaneous self-organization, from lawless fundamentals; this lawfulness has no logical priority, it is secondary to the fundamental lawlessness.
What the logical priority of lawfulness seems to imply to me is that in order to have laws, you must start out with laws, in which case the laws would be irreducible, and without further justification; but that’s not the case, you can start out without laws, and have them arise.
Most of it comes from the general area of Kolmogorov complexity*; in fact, I suspect it’s something like Solomonoff induction you’re after here: in any given series of symbols, one can predict the next symbol based on nothing but the assumption that there exists some unknown (but computable) probability distribution behind the series of symbols. The idea is that series of a lesser complexity are preferred to series of higher complexity, which is really nothing but a formulation of Occam’s razor in algorithmic terms. It can be formally proven that any agent acting according to this paradigm maximizes its predictive utility, i.e. has the best chance of being right, which is the basis for approaches to universal AI.
*About which I have written informally a little here…
An anecdote that’s often related in relation to these things is the one about Leibniz and the ink blots: on a page, a set of ink blots is distributed in some fashion; Leibniz mused that the distribution of these ink blots can be said to follow a law exactly if there exists a description able to reproduce this precise set of blots that is substantially shorter than just the description of the blots with, say, their co-ordinates or in some similar, merely descriptive fashion. This is, somewhat informally, the foundation of Kolmogorov- or description length complexity. One can indeed put this at the heart of scientific theorizing: the shortest description one has found can be viewed as a theory of the ink blot distribution; it will make a prediction in form of a possible spot for the next ink blot, which is then open to falsification.
Needless to say, according to this definition, a random bit string would be lawless…