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Causality, Randomness and Induction

 
 
ACB
 
Reply Sat 10 Jul, 2010 11:09 am
It is sometimes argued that causality is an illusion and that all events are actually random. It is further argued, however, that although there is no reason to suppose that past regularities will continue into the future, induction is still the best method of predicting the future and consequently deciding how to act. The reason given is that, if past regularities continue, induction will work; and if they do not continue, induction will be no worse than any other method of prediction and decision (e.g. random guessing, or asking a supposed deity).

I wish to raise some objections to this defence of induction in a random universe.

1. Pragmatic objection

In a random universe, induction is no worse than other methods of prediction and decision if all other factors are equal. But they may not be equal. For example, I may be watching my favourite TV programme when I suddenly notice that part of my house is on fire. If all events are random, I have no more reason for believing that the fire will spread than I have for believing it will spontaneously extinguish itself and leave no damage. What motive, therefore, do I have for getting out of my armchair and dealing with the fire? Why should I move if I am comfortable where I am? If inductive decision-making is no better and no worse than non-inductive decision-making, then the consideration of my immediate comfort and pleasure should clinch my decision in favour of continuing to watch TV.

2. Statistical objection

In a random universe, the assumption of a continued regularity is no worse than the assumption of any specified alternative sequence of events; but it is far worse than the assumption of an unspecified alternative. For example, if my watch (which is working) now shows 11.45, I might as well assume it will show 12.00 in 15 minutes' time; this is no less likely than that it will show e.g. 1.30 or 5.23. But what if I had to assess the probability that in 15 minutes' time the minute hand will completely cover the hour hand? Statistically, if the position of the hands at any time is completely random, the chance of one hand covering the other (anywhere on the dial) is only about 1 in 100. Rationally, therefore, I should think it highly probable that one hand will not cover the other in 15 minutes' time. If I use induction, however, I will conclude that it will cover the other, since (judging by past events) the watch will show 12.00 then. So induction would be irrational.

3. Psychological objection

Regardless of whether they think induction is a useful strategy, do those people who deny causality really believe that the (statistically improbable) amount of regularity in the universe will probably now cease? If not, why not? It is no use appealing to our 'habits of thinking' about the future; if causality-deniers are to be consistent, they should conclude that such habits are flawed, and abandon them.


My position is that (a) the universe is not random, (b) causality exists, (c) events have explanations, and (d) therefore, induction is rational. But I am open to any counter-arguments.

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kennethamy
 
  0  
Reply Sat 10 Jul, 2010 11:16 am
@ACB,
ACB wrote:

It is sometimes argued that causality is an illusion and that all events are actually random.






Perhaps it does not matter to the rest of what you say, but I would be interested if you could name someone who has ever argued such a thing.
ACB
 
  0  
Reply Sat 10 Jul, 2010 11:51 am
@kennethamy,
kennethamy wrote:
ACB wrote:
It is sometimes argued that causality is an illusion and that all events are actually random.
Perhaps it does not matter to the rest of what you say, but I would be interested if you could name someone who has ever argued such a thing.

Night Ripper, e.g. on 6 July in the "Defense of Freewill against Determinism" thread. Stones rolling downhill and all that.
kennethamy
 
  0  
Reply Sat 10 Jul, 2010 11:59 am
@ACB,
ACB wrote:

kennethamy wrote:
ACB wrote:
It is sometimes argued that causality is an illusion and that all events are actually random.
Perhaps it does not matter to the rest of what you say, but I would be interested if you could name someone who has ever argued such a thing.

Night Ripper, e.g. on 6 July in the "Defense of Freewill against Determinism" thread. Stones rolling downhill and all that.


That Night Ripper said that (and, of course, we would have to ask him whether that is what he meant, since you are interpreting him) is your support for the proposition that "it is sometimes argued that causality is an illusion etc."? But anyway, I was under the impression that he was advocating a Humean regularity view of causation, and that is certainly not a view that causality is an illusion.
0 Replies
 
Night Ripper
 
  1  
Reply Sun 11 Jul, 2010 09:07 am
@ACB,
1. You said "If inductive decision-making is no better and no worse than non-inductive decision-making..." but we don't know that is the case. It might actually be better if past regularities continue into the future, random universe or not.

2. If I flip a coin 1,000 times, the string of flips that is HHHHHHHH.... and so on, all heads, is equally as likely as HHHHTTHTTHHHTTHHTHHHTTH... and so on. Both particular strings have equal probability of happening. Therefore, in a random universe, the universe where your watch hand continues on as expected is as equally probable as any other PARTICULAR sequence.

3. I don't think regularities will cease because I don't think I'm special. For regularities to cease to exist would mean that billions of years of regularities would have occurred up until now when they suddenly cease to exist. Obviously, since the universe is random, it could happen but why now instead of during the other eons of years?
kennethamy
 
  0  
Reply Sun 11 Jul, 2010 09:52 am
@Night Ripper,
Night Ripper wrote:

1. You said "If inductive decision-making is no better and no worse than non-inductive decision-making..." but we don't know that is the case. It might actually be better if past regularities continue into the future, random universe or not.

2. If I flip a coin 1,000 times, the string of flips that is HHHHHHHH.... and so on, all heads, is equally as likely as HHHHTTHTTHHHTTHHTHHHTTH... and so on. Both particular strings have equal probability of happening. Therefore, in a random universe, the universe where your watch hand continues on as expected is as equally probable as any other PARTICULAR sequence.

3. I don't think regularities will cease because I don't think I'm special. For regularities to cease to exist would mean that billions of years of regularities would have occurred up until now when they suddenly cease to exist. Obviously, since the universe is random, it could happen but why now instead of during the other eons of years?


Quote:
Obviously, since the universe is random,


What does that mean? Does it mean that it is only by chance that we have the universe we have, or does it mean that all events that occur are by chance? I don't know what the first means (except perhaps that this universe exists is a contingent truth) and the second is clearly false since there are laws of nature.
0 Replies
 
ACB
 
  1  
Reply Sun 11 Jul, 2010 06:13 pm
@Night Ripper,
Night Ripper wrote:
1. You said "If inductive decision-making is no better and no worse than non-inductive decision-making..." but we don't know that is the case. It might actually be better if past regularities continue into the future, random universe or not.

But statistically, the chance of past regularities continuing into the future is vanishingly small, when you consider the unimaginably vast number of possible permutations of non-regularity.

Night Ripper wrote:
2. If I flip a coin 1,000 times, the string of flips that is HHHHHHHH.... and so on, all heads, is equally as likely as HHHHTTHTTHHHTTHHTHHHTTH... and so on. Both particular strings have equal probability of happening. Therefore, in a random universe, the universe where your watch hand continues on as expected is as equally probable as any other PARTICULAR sequence.

Agreed. I made exactly this point in my OP. But suppose you had to choose not between "all heads" and a particular alternative sequence, but between "all heads" and any (unspecified) alternative sequence. That is to say, between "all heads" and "not all heads". Clearly, "not all heads" is vastly more likely.

Well, the choice between "regularities continue" and "regularities do not continue" is analogous to the choice between "all heads" and "not all heads". It is not analogous to the choice between "all heads" and a particular alternative sequence. Therefore, if all events are random, we should rationally believe that past regularities will almost certainly not continue.

Night Ripper wrote:
3. I don't think regularities will cease because I don't think I'm special. For regularities to cease to exist would mean that billions of years of regularities would have occurred up until now when they suddenly cease to exist. Obviously, since the universe is random, it could happen but why now instead of during the other eons of years?

But if you believe that events are random, you must conclude that all past regularities have occurred by pure chance - a coincidence of mind-boggling size. Well, you may say, it's possible. And so it is. But here's the point: the continuation of such regularities well into the future would be an even greater coincidence, so how can it be rational to believe that will happen?

It might at first sight seem strange that ages-old regularities should come to an end today, but my point is that it would be even stranger if they were to continue. The past regularities, if random, are an exceedingly strange phenomenon in any case!

Let's go back to the coin-flip example. If you have thrown 100 consecutive heads with a fair coin, what is the probability that the next 10 flips will all be heads? About one in a thousand. And for 20 consecutive heads, about one in a million. Why would the coin's past behaviour be any guide to its future behaviour if it falls randomly? From the fact that its past behaviour gave the illusion of being ordered, it does not follow that its future behaviour will likewise give the illusion of being ordered. Statistically, it will almost certainly not.

So if you think that events are truly random, you ought to believe that past regularities will almost certainly cease right now! But, of course, nobody really believes that they will. Everyone (yourself included) believes that there is good reason to think the regularities will continue into the foreseeable future. Therefore, they must believe that there is some factor that has overcome, and will continue to overcome, the unfavourable statistics. Whatever that factor may be (call it "the laws of nature" or something else) it follows that events in the universe are not random. QED.
Night Ripper
 
  1  
Reply Sun 11 Jul, 2010 06:22 pm
@ACB,
ACB wrote:
But statistically, the chance of past regularities continuing into the future is vanishingly small, when you consider the unimaginably vast number of possible permutations of non-regularity.


Oh really, you've done the math? Let's see it. I think you are letting your intuition lead you astray.

ACB wrote:

Agreed. I made exactly this point in my OP. But suppose you had to choose not between "all heads" and a particular alternative sequence, but between "all heads" and any (unspecified) alternative sequence. That is to say, between "all heads" and "not all heads". Clearly, "not all heads" is vastly more likely.


You've made the same mistake others have made so you are in good company. The fact that you are picking out a string, say X and then comparing it to not-X ignores the fact that you can do the same for EVERY possible string, Y, Z. If you add them all up you will see that any particular string is extremely rare when you are looking for it. If you pick HTTTHTHHTHT... vs. not-HTTTHTHHTHT... the same argument holds.

ACB wrote:
But if you believe that events are random, you must conclude that all past regularities have occurred by pure chance - a coincidence of mind-boggling size. Well, you may say, it's possible. And so it is. But here's the point: the continuation of such regularities well into the future would be an even greater coincidence, so how can it be rational to believe that will happen?


Wrong. Put all possible universes into a hat and pick one at random. You have the same probability of picking the universe that has regularities that continue forever vs. the universe that has regularities that continue until next Thursday.

ACB wrote:
Let's go back to the coin-flip example. If you have thrown 100 consecutive heads with a fair coin, what is the probability that the next 10 flips will all be heads? About one in a thousand. And for 20 consecutive heads, about one in a million. Why would the coin's past behaviour be any guide to its future behaviour if it falls randomly? From the fact that its past behaviour gave the illusion of being ordered, it does not follow that its future behaviour will likewise give the illusion of being ordered. Statistically, it will almost certainly not.

So if you think that events are truly random, you ought to believe that past regularities will almost certainly cease right now! But, of course, nobody really believes that they will. Everyone (yourself included) believes that there is good reason to think the regularities will continue into the foreseeable future. Therefore, they must believe that there is some factor that has overcome, and will continue to overcome, the unfavourable statistics. Whatever that factor may be (call it "the laws of nature" or something else) it follows that events in the universe are not random. QED.


Wrong again. See the above explanation. Write down every possible string of 100 coin flips and toss them into a hat. Pick one at random. They all have the same odds. There's nothing special about the string of all heads or all tails or alternating heads or tails.

You shouldn't say QED when you haven't demonstrated anything. It's kind of obnoxious.
ACB
 
  1  
Reply Sun 11 Jul, 2010 09:57 pm
@Night Ripper,
Night Ripper wrote:
The fact that you are picking out a string, say X and then comparing it to not-X ignores the fact that you can do the same for EVERY possible string, Y, Z. If you add them all up you will see that any particular string is extremely rare when you are looking for it. If you pick HTTTHTHHTHT... vs. not-HTTTHTHHTHT... the same argument holds.

I agree entirely. But remember, we are concerned here with whether regularities will continue or whether they will not. "They will continue" corresponds to HHHHHHHHHHH... "They will not continue" corresponds to not-HHHHHHHHHHH... It does not correspond to HTTTHTHHTHT... or to any other particular string. We are not looking for any particular alternative string; any one will do.

Night Ripper wrote:
ACB wrote:
But if you believe that events are random, you must conclude that all past regularities have occurred by pure chance - a coincidence of mind-boggling size. Well, you may say, it's possible. And so it is. But here's the point: the continuation of such regularities well into the future would be an even greater coincidence, so how can it be rational to believe that will happen?

Wrong. Put all possible universes into a hat and pick one at random. You have the same probability of picking the universe that has regularities that continue forever vs. the universe that has regularities that continue until next Thursday.

That cannot be right. There is only one possible sequence in which the regularities continue forever, but there are countless possible sequences in which events become chaotic after next Thursday. I may pick the universe corresponding to the sequence HHHHHHHHHHH... (where the bold letter corresponds to next Thursday), or I may pick HHHHHTTHTHT... or HHHHTTHHTTT... or HHHHTHHTTTH... or HHHHHHTHTHH... etc. All those sequences, except the first, correspond to the description "regularities continue (only) until next Thursday", so I have a far higher probability of picking a universe that fits that description. (Incidentally, why do you refer to "the universe that has regularities that continue until next Thursday" in the singular?)
Night Ripper
 
  1  
Reply Sun 11 Jul, 2010 10:00 pm
@ACB,
Do we really care that they will continue forever or just that they will continue for the next few years? I personally don't care about forever.
0 Replies
 
ACB
 
  1  
Reply Mon 12 Jul, 2010 07:09 am
@Night Ripper,
Night Ripper wrote:
Put all possible universes into a hat and pick one at random. You have the same probability of picking the universe that has regularities that continue forever vs. the universe that has regularities that continue until next Thursday.

OK, let's make 2050 the cut-off point. The permutations of possible universes that stay regular only until next Thursday, and then become chaotic, are still far greater in number than the permutations that stay regular until 2050. The former set can have the values HTHHTTHTHH..., HTTTTHTHHH..., THHTHTHTTT..., TTHTTHTHTH... etc between next Thursday and 2050, but the latter set is restricted to all-H between those two dates. So I have a much greater chance of picking a universe in which the regularities stop next Thursday.
Night Ripper
 
  1  
Reply Mon 12 Jul, 2010 08:27 am
@ACB,
ACB wrote:

Night Ripper wrote:
Put all possible universes into a hat and pick one at random. You have the same probability of picking the universe that has regularities that continue forever vs. the universe that has regularities that continue until next Thursday.

OK, let's make 2050 the cut-off point. The permutations of possible universes that stay regular only until next Thursday, and then become chaotic, are still far greater in number than the permutations that stay regular until 2050. The former set can have the values HTHHTTHTHH..., HTTTTHTHHH..., THHTHTHTTT..., TTHTTHTHTH... etc between next Thursday and 2050, but the latter set is restricted to all-H between those two dates. So I have a much greater chance of picking a universe in which the regularities stop next Thursday.


All heads is not the only regularity. There are alternating heads and tails. All tails. Alternating double heads and tails, etc.

Also, I need to see some math before I can commit to even saying you have a good point because right now it's not very well formed.
ACB
 
  1  
Reply Mon 12 Jul, 2010 11:23 am
@Night Ripper,
Night Ripper wrote:
All heads is not the only regularity. There are alternating heads and tails. All tails. Alternating double heads and tails, etc.

True. Some possible strings have a simple regularity, some a more complex regularity, and others (the vast majority) none. "All heads" and "all tails" are the simplest regularities of all; they can be described most briefly. In that sense, they are special.

Night Ripper wrote:
Also, I need to see some math before I can commit to even saying you have a good point because right now it's not very well formed.

OK, I did touch on the math aspect in an earlier post. I will elaborate.

If I have thrown all heads so far, I can throw either H or T next time, so my chance of throwing H is 1/2. My next two throws from now can be HH, HT, TH, or TT, so my chance of HH is 1/4. For HHH it will be 1/8, for HHHH 1/16, and so on. For 10 straight H's it will be 1/1024, and for 20 straight H's it will be 1/1,048,576. Out of 1,048,576 possible permutations of 20 flips, one has the simplest kind of regularity, some have more complex regularities, but most have no regularity at all.
Night Ripper
 
  1  
Reply Mon 12 Jul, 2010 11:27 am
@ACB,
ACB wrote:
If I have thrown all heads so far, I can throw either H or T next time, so my chance of throwing H is 1/2. My next two throws from now can be HH, HT, TH, or TT, so my chance of HH is 1/4. For HHH it will be 1/8, for HHHH 1/16, and so on. For 10 straight H's it will be 1/1024, and for 20 straight H's it will be 1/1,048,576. Out of 1,048,576 possible permutations of 20 flips, one has the simplest kind of regularity, some have more complex regularities, but most have no regularity at all.


Each coin toss is independent from the others. You're invoking the gambler's fallacy. The odds of getting H on the very next toss is always 1/2. It doesn't matter how many H's you've gotten beforehand.
ACB
 
  1  
Reply Mon 12 Jul, 2010 01:52 pm
@Night Ripper,
Night Ripper wrote:
The odds of getting H on the very next toss is always 1/2.

Yes, that's right. And the odds of getting H on the toss after that is also 1/2. So the odds of getting H on both of those tosses is 1/2 x 1/2 = 1/4.

As you say, each toss is independent from the others. No toss has any influence on any other toss.
Night Ripper
 
  1  
Reply Mon 12 Jul, 2010 02:55 pm
@ACB,
You also didn't answer my objection satisfactorily about patterns. I don't agree that all H vs. not-all-H represents regularities continue vs. regularities don't continue. There are many other patterns as well such as HHHTTTHHHTTT... forever and so on.
ACB
 
  1  
Reply Mon 12 Jul, 2010 04:45 pm
@Night Ripper,
If past regularities corresponded to the regular sequence HHHTTTHHHTTT..., then the continuation of that sequence (and no other) would correspond to "(past) regularities continue". An example would be three consecutive dry months always alternating with three consecutive wet months. In this case any other regular sequence, such as HHHHHHHHHHHH... or HTHTHTHTHT... or HHTHHTHHTHHT..., or any irregular sequence, would represent "(past) regularities do not continue".

The possibility of picking a universe with one of the many possible other future regularities is much higher than that of picking a universe with a continuation of the unique past regularity. The possibility of picking a universe with no future regularity is vastly higher still.
Night Ripper
 
  1  
Reply Mon 12 Jul, 2010 04:49 pm
@ACB,
ACB wrote:

If past regularities corresponded to the regular sequence HHHTTTHHHTTT..., then the continuation of that sequence (and no other) would correspond to "(past) regularities continue". An example would be three consecutive dry months always alternating with three consecutive wet months. In this case any other regular sequence, such as HHHHHHHHHHHH... or HTHTHTHTHT... or HHTHHTHHTHHT..., or any irregular sequence, would represent "(past) regularities do not continue".

The possibility of picking a universe with one of the many possible other future regularities is much higher than that of picking a universe with a continuation of the unique past regularity. The possibility of picking a universe with no future regularity is vastly higher still.


I'm still not convinced that's an accurate representation. I'll give it some more thought and back to you. In the end we might have to drop the talk of coins altogether.
0 Replies
 
Night Ripper
 
  1  
Reply Thu 15 Jul, 2010 06:56 pm
I've given it more thought and I think that a 3x3 grid of boolean values can paint the picture better. The grid evolves over time randomly. Since there is no connection between one configuration to the next, every configuration is just as likely. It makes no sense to say that since all the prior configurations have been all true that somehow the grid owes you a false. That's the gambler's fallacy.
ughaibu
 
  1  
Reply Thu 15 Jul, 2010 07:35 pm
@Night Ripper,
Night Ripper wrote:
It makes no sense to say that since all the prior configurations have been all true that somehow the grid owes you a false. That's the gambler's fallacy.
If a gambler watches the roulette table and, observing a string of reds, backs the black in the belief that it's overdue, that gambler commits a gamblers fallacy. But, backing the red, in the belief that it's having come up so far is inductive justification for the belief that it'll continue coming up, commits the same fallacy.
 

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