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What kind of universe do we need to live in for induction to work?
Posted: 09 November 2011 08:38 AM   [ Ignore ]
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I’ve moved the following quote from a science thread in order to be able to discuss it further.

dougsmith - 07 November 2011 04:55 PM

Well, I think the answer—or at least part of the answer—is that we have to take certain things as given, as assumptions. Then all our knowledge is premised upon those assumptions being true. The assumptions are basically the framework of rational inquiry: that deduction, induction and abduction work.

These are reasonable assumptions to make, because without them there is nothing that counts as ‘reasonable’ at all. If you like, they are the ground sources of what is reasonable. One cannot have reasoning, reasonableness or rational inquiry without them.

I think I’m perfectly happy with this answer suprisingly. So if that’s the case what do I really want to know?

I want to know what kind of universe do we need to live in for induction to work?  And failing that, at least what can’t the universe be like.

Specifically would induction work in a universe in which laws of nature are just regularities as Norman Swartz describes?

http://www.iep.utm.edu/lawofnat/

I can’t see how.

Stephen

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Posted: 09 November 2011 09:05 AM   [ Ignore ]   [ # 1 ]
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Well, in the ‘regularities’ universe there would be no explanation for why induction works. It would work—if it did work—out of sheer chance. (Or so it would seem!) That is, in a ‘regularities’ universe nothing constrains the way things happen: there is nothing literally the same about this oxygen atom over here and that one over there, and nothing literally the same about this oxygen atom now and that one in the past or the future. So there’s no reason to believe that they will behave the same way.

This is one reason why I believe that an account of laws involving universals is better. In an account involving universals, these oxygen atoms share literally the identical universals (= properties), and it’s in virtue of their universals that they enter into law like relations. In a ‘universals’ universe there is at least the possibility that we’ve understood the right universal relationships and can make credible inductive inferences from them.

Of course, there’s no telling for sure which sort of universe we’re in. I’d like to think that the apparent structure we’ve seen around us is some reason for assuming the existence of universals, but it will always be unprovable in a logical sense.

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Posted: 09 November 2011 11:11 AM   [ Ignore ]   [ # 2 ]
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Thanks for the post Doug,

I’m thinking along similar lines. I’m sure a number of questions will follow. I’ll start with three.

dougsmith - 09 November 2011 09:05 AM

Well, in the ‘regularities’ universe there would be no explanation for why induction works. It would work—if it did work—out of sheer chance. (Or so it would seem!)

I would say this wasn’t really induction working because induction is not raising the epistemic probability at all, we are just thinking it is and luckily for us it doesn’t matter that we are wrong.

Would you agree?

Secondly, are there any universals for dummies type books you’d recommend?

And lastly, I think Bertrand Russell thought that we had knowledge of universals and that was our reason to believe in Induction.

You believe the opposite and start with it’s reasonable to assume induction works and then go on to give induction as reason to believe in universals.

Would you agree?

Stephen

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Posted: 09 November 2011 02:28 PM   [ Ignore ]   [ # 3 ]
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StephenLawrence - 09 November 2011 11:11 AM
dougsmith - 09 November 2011 09:05 AM

Well, in the ‘regularities’ universe there would be no explanation for why induction works. It would work—if it did work—out of sheer chance. (Or so it would seem!)

I would say this wasn’t really induction working because induction is not raising the epistemic probability at all, we are just thinking it is and luckily for us it doesn’t matter that we are wrong.

Well ... depends what one means by ‘epistemic probability’. If you mean how things seem to us, then I suppose at least so far it has done that. It might stop doing it tomorrow. If by ‘epistemic probability’ you mean something more like objective chance ... that’s a harder case to make. Again, it’s worked in the past, but there’s no reason to believe that such objective chances exist, not without universals. Or at least that’s how it looks to me.

StephenLawrence - 09 November 2011 11:11 AM

Secondly, are there any universals for dummies type books you’d recommend?

It’s been awhile, but I do remember very much enjoying reading books by David Armstrong, a top-notch metaphysician from Australia.

StephenLawrence - 09 November 2011 11:11 AM

And lastly, I think Bertrand Russell thought that we had knowledge of universals and that was our reason to believe in Induction.

You believe the opposite and start with it’s reasonable to assume induction works and then go on to give induction as reason to believe in universals.

Would you agree?

Dunno. The epistemology here is difficult. I think also there’s a tendency to want to foundationalize everything, find out where all the roots go, and that may be impossible, particularly around the edges. Not to say that’s the case here, but at least it would take a lot of work to figure out how the reasoning might go. Prima facie it looks as though our knowledge of universals—at least the ones responsible for the phenomena we see about us—is a posteriori, coming from our experience of environmental regularities.

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Posted: 10 November 2011 01:01 AM   [ Ignore ]   [ # 4 ]
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dougsmith - 09 November 2011 02:28 PM
StephenLawrence - 09 November 2011 11:11 AM
dougsmith - 09 November 2011 09:05 AM

Well, in the ‘regularities’ universe there would be no explanation for why induction works. It would work—if it did work—out of sheer chance. (Or so it would seem!)

I would say this wasn’t really induction working because induction is not raising the epistemic probability at all, we are just thinking it is and luckily for us it doesn’t matter that we are wrong.

Well ... depends what one means by ‘epistemic probability’. If you mean how things seem to us, then I suppose at least so far it has done that. It might stop doing it tomorrow.

What I mean is probability as grading of what the certainty of an observer should be. So if an observer is fairly certain a die will land on six, the observer should not be, for instance. (unless it’s weighted or something)

If by ‘epistemic probability’ you mean something more like objective chance ... that’s a harder case to make. Again, it’s worked in the past, but there’s no reason to believe that such objective chances exist, not without universals. Or at least that’s how it looks to me.

What there is reason to believe is that there is something that does raise the probability as I’ve defined, because it doesn’t make sense to A) Believe induction works and B) Believe we live in a universe in which it can’t work.

What that something is I don’t know for sure, the problem is we only seem to have chance and necessity to play with. So I think I’m talking about either objective probability, or epistemic probability of something being objectively necessary.

You favour belief in a universe in which something “constrains”, I can only imagine that to mean reduced objective probability or total constraint being objective necessity.

So I think we are in broad agreement?

It’s been awhile, but I do remember very much enjoying reading books by David Armstrong, a top-notch metaphysician from Australia.

Thanks. I’ll give one a go.

Stephen

[ Edited: 10 November 2011 01:11 AM by StephenLawrence ]
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Posted: 10 November 2011 01:27 AM   [ Ignore ]   [ # 5 ]
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I am not sure if this relates to induction, or even philosophy, but I cannot understand the concept of regularity when speaking of elementals.  I can understand regularity in weather patterns, in the orbit of the moon, i.e. complex systems.
But is it not the function of chemistry and physics to identify those elementals which are the same and those which are not the same, not if they act with regularity? 
The table of elements describes the physical differences not the similarities of elements.  The identification of subatomic particles describes the physical differences, not their similarties. We do not identify and describe them individually as behaving a certain way with regularity. A proton is a proton, a neutron is a neutron, they do not act with regularity, they act as protons and neutrons must. That is why we named them differently.

[ Edited: 10 November 2011 01:29 AM by Write4U ]
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Posted: 10 November 2011 08:03 AM   [ Ignore ]   [ # 6 ]
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StephenLawrence - 10 November 2011 01:01 AM

What I mean is probability as grading of what the certainty of an observer should be. So if an observer is fairly certain a die will land on six, the observer should not be, for instance. (unless it’s weighted or something)

This stuff gets very hairy quickly. It’s all dependent on what you consider the correct background conditions: if you knew everything about the way the person would toss the die, you might be able to be quite certain that a six would come up. The question is whether or not there are ‘objective chances’ or not, associated with causation, or whether all chance is subjective. This is a big topic in metaphysics and not one that I feel very comfortable discussing. It certainly seems as though quantum physics tells us there are objective chances.

In the ‘regularities’ universe OTOH it looks as though the next instant literally anything could happen, and with no one way privileged over any other. But that seems so silly as to be a straw man of the position: there are many people who reject universals and they will have some sort of a response here. So I’m a bit reluctant to push them to a reductio just yet.

StephenLawrence - 10 November 2011 01:01 AM

You favour belief in a universe in which something “constrains”, I can only imagine that to mean reduced objective probability or total constraint being objective necessity.

Well, the point is that it’s in virtue of a physical thing’s properties that it has the causal interactions it does. The properties dictate that given these initial conditions at T1, one can assure (or assure with probability P) those later conditions at T2. And since this thing over here and that thing over there (or this thing at T1 and that thing at T2) share the same property, they will interact in the same way under the same conditions.

StephenLawrence - 10 November 2011 01:01 AM

So I think we are in broad agreement?

Dunno. You tell me.

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Posted: 10 November 2011 10:52 AM   [ Ignore ]   [ # 7 ]
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dougsmith - 10 November 2011 08:03 AM

In the ‘regularities’ universe OTOH it looks as though the next instant literally anything could happen, and with no one way privileged over any other.

Right.

But that seems so silly as to be a straw man of the position:

Yes, I feel that, which is why I press for an answer from them. I’m very much open to persuasion, really, in this case. But with no such answer we are left with just that.

there are many people who reject universals and they will have some sort of a response here. So I’m a bit reluctant to push them to a reductio just yet.

I have no idea what the response is, that’s the problem. That’s why I’ve pressed, to try and bring that response out, but I have not suceeded.

Dunno. You tell me.

I dunno either Doug I thought I did. grin

I’ve been around a while, I hope I don’t have to tell you I have best intentions.

something aside from the debate I know but something that matters in all human interactions.

Best,

Stephen

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Posted: 12 November 2011 01:19 AM   [ Ignore ]   [ # 8 ]
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I do not want to be Swartz’ advocate, so Stephen, do not identify my standpoint with Swartz.

I must make two steps:

1. Laws of nature are descriptions, not prescriptions. In this sense, laws of nature do not force anything, so they do not constrain anything in a literary way. It is just a matter of speaking. Electrons just behave the way they do, otherwise it would not be an electron.

2. Regularities are discovered, it turns out that these exist, otherwise science would not even exist. But it is something else to say laws of nature are mere regularities.

But of course these regularities do suppose something like ‘natural kinds’: things that are recognised as being of exactly the same kind as others. But I think this is circular with the fact that laws of nature can be discovered. ‘Being of the same kind’ and ‘regularities’ presuppose each other. How can I find out that the same behaviour is found in this electron, and that over there, when I do not identify both as electrons, i.e. objects of the same kind? But the other way round: how do I discover that 2 objects are of the same kind? Because they behave the same way in my experiments.

So in what kind of universe we live? Obviously in a universe where ‘natural kinds’ exist.

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Posted: 12 November 2011 02:24 AM   [ Ignore ]   [ # 9 ]
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GdB - 12 November 2011 01:19 AM

So in what kind of universe we live? Obviously in a universe where ‘natural kinds’ exist.

Ok, a step forward.

I’m very hazy about natural kinds at the mo, hoping to improve on that. The thing about natural kinds is they are constrained in a sense aren’t they? They are constrained by virtue of being what they are.

Or not?

Stephen

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Posted: 12 November 2011 02:46 AM   [ Ignore ]   [ # 10 ]
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StephenLawrence - 12 November 2011 02:24 AM

They are constrained by virtue of being what they are.

How couldn’t they?  smile
You are not a cheetah, Stephen, you will never run 120 km/h. Your freedom is seriously constrained…

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Posted: 12 November 2011 03:19 AM   [ Ignore ]   [ # 11 ]
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GdB - 12 November 2011 02:46 AM
StephenLawrence - 12 November 2011 02:24 AM

They are constrained by virtue of being what they are.

How couldn’t they?  smile
You are not a cheetah, Stephen, you will never run 120 km/h. Your freedom is seriously constrained…

It’s not enough that I never will GdB, it needs to be the case that either I can’t or it’s highly objectively improbable. That’s because otherwise natural kinds do not help with the problem of induction.

I’m not convinced I’m a natural kind b.t.w I think perhaps natural kinds need to be immutable.

http://plato.stanford.edu/entries/natural-kinds/

Natural kinds should permit inductive inferences.
This is a point emphasized by Whewell (1860) and Mill (1884), and is central to Quine’s (1969) discussion of natural kinds (see Section 1.2.1).

Stephen

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Posted: 12 November 2011 06:31 AM   [ Ignore ]   [ # 12 ]
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I’m not exactly clear on how the theory of natural kinds differs from that of universals. A “kind” after all, is something that is wholly present in each of its instances, like a property.

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Posted: 12 November 2011 06:42 AM   [ Ignore ]   [ # 13 ]
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StephenLawrence - 12 November 2011 03:19 AM

It’s not enough that I never will GdB, it needs to be the case that either I can’t or it’s highly objectively improbable. That’s because otherwise natural kinds do not help with the problem of induction.

I think I answered your original question.
From other threads you already know that for me ‘probability’ is a concept that does not apply to deterministic laws of nature. (I assume you noticed with how much care Doug reacted on your idea of ‘epistemic probability’.)

Let’s try to flesh out the concept of ‘probability’ a little. Probability is normally used as an expression for the fact that I do not have detailed knowledge about the events under consideration, or about the laws of nature involved. What exactly will happen is determined by initial conditions (the weight of the die, how the person throwing the die is moving, the kind of surface of the die and the table etc etc.) and the laws of nature involved (gravity, friction, mechanics etc). As only a tiny difference in the initial conditions can make a difference there is no practical way I can predict what the throw will be: a one or six.

A different case is QM. In QM we principally cannot know the exact initial conditions, and even if we could know, the laws of nature in QM are not deterministic exactly when we want to translate back to observables. The surprising fact is that obviously in our interaction with quantum nature there is a principal limit we cannot dive under. So the probability element cannot be reduced to a necessary level of detail for exact predictions.

Now, given this meaning of probability, can we say that the laws of nature themselves are probable or not? In my view this makes no sense, it is a category mistake. Laws of nature are no causes themselves, they are descriptions of how events are causally related to others. They describe how a die behaves when thrown. But the cause of the ‘six-above’ is the throwing, there is no question about that.

Saying that a ‘natural law is probable’ makes only sense when spoken by a scientist, who has still not found out how the causal relationship between certain events is. If a scientist has erred, and called something a law of nature, but tomorrow it turns out that gravity has changed, then the law of gravity obviously was not correct. But it does not say that a law of nature has changed. It only says that a scientist (or science as a whole) has erred in identifying (or formulating) a law of nature.

When we already could know in advance what exact natural kinds are in reality (e.g. electrons), science would be nothing more then derive laws of nature from the attributes of the natural kinds. Experiments would not be needed anymore.

StephenLawrence - 12 November 2011 03:19 AM

I’m not convinced I’m a natural kind b.t.w I think perhaps natural kinds need to be immutable.

Well, you, as Stephen Lawrence, are at most just an instantiation of a natural kind, namely a human. And humans cannot run 120 km/h.

Natural kinds should permit inductive inferences.
This is a point emphasized by Whewell (1860) and Mill (1884), and is central to Quine’s (1969) discussion of natural kinds (see Section 1.2.1).

If there were no natural kinds at all, science would be impossible. But as said, having pre-knowledge of all instantiations of natural kinds, science would be purely deductive.

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Posted: 12 November 2011 06:46 AM   [ Ignore ]   [ # 14 ]
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dougsmith - 12 November 2011 06:31 AM

I’m not exactly clear on how the theory of natural kinds differs from that of universals. A “kind” after all, is something that is wholly present in each of its instances, like a property.

No difference, I assume. I just find it a bit clearer than universals. ‘Universals’ remind me too much of Plato… I still get shivers about the question if the universal ‘horse’ exists, even if there is no single instantiation of a horse.

BTW, I ordered ‘Sketch for a Systematic Metaphysics’ of D. M. Armstrong. Thanks for the hint.

Stephen, if you buy it too we can discuss it here!

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Posted: 12 November 2011 07:10 AM   [ Ignore ]   [ # 15 ]
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GdB - 12 November 2011 06:46 AM
dougsmith - 12 November 2011 06:31 AM

I’m not exactly clear on how the theory of natural kinds differs from that of universals. A “kind” after all, is something that is wholly present in each of its instances, like a property.

No difference, I assume. I just find it a bit clearer than universals. ‘Universals’ remind me too much of Plato… I still get shivers about the question if the universal ‘horse’ exists, even if there is no single instantiation of a horse.

BTW, I ordered ‘Sketch for a Systematic Metaphysics’ of D. M. Armstrong. Thanks for the hint.

Stephen, if you buy it too we can discuss it here!

Good idea GdB.


Stephen

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