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[Andlan]

Steve: There's a lot of material here so forgive me if I take one thing at a time.

If you look at what I've actually said previously, you will see that I agree with the statement "heliocentrism is better" for most uses of the word "better".

What you can perhaps say, without having to define purpose, is that both models are just as accurate a description of the empirical evidence. And in that case, you are right. There is no test simply involving the empirical evidence that can help you to decide between them. That, as I said in the previous post, is where Occam's razor comes in.

I think this decision is more of a rational process than you give it credit for. There might not be one test that can falsify the geocentric theory, but at some point, the weight of all the extra hypotheses that are added to the theory to account for all the hitherto unexplained observations (Teh has given some examples) becomes so great that it becomes unreasonable to support the theory and it is rejected. Except on a surface practical level, it is not utility that governs the decision. Utilitarian technology can be advanced through trial and error, and the ancient Chinese were masters at this, but they did not practise science in the modern sense because they had no general theories for what they were doing. Our real motivation for deciding is universality. We know we cannot take account of everything in the universe when developing our theories/models, but a deep-seated belief is somehow ingrained in us that we can extrapolate our present observations to create more general rules about the world. This is as fundamental as knowing that if I leave my car in row 3A in the car park, I expect to find it there in that precise spot when I finish my shopping. We seem to be able to infer what might happen in the future based on past events, and also what parts of the universe that we have not observed might be like based on those parts that we have. I don't see this as a psychological process like Hume. (Hume's view has merit in many eyes of chiming with modern cognitive science that holds the evolved brain responsible for all our normative judgements. It is a view entailing that empirical facts are divorced from any necessary prescriptive relationships concerning them).

[Teh]

Empiricism is no help, and Occam's razor is not necessarily much help. What you consider an over-complication is entirely dependent on your world view. You could argue that it is unnecessarily complicated to have the earth moving. Some people think real parallel universes an over-complication, some people regard them as a simplification.

Geocentrism is wrong because it does not explain planetary motion without unavoidably incorporating a rival theory.

Once you have a world-view - e.g. modern cosmology, you are more than welcome to choose your reference frame based on the guidance of Occam's razor.

-- Updated November 29th, 2012, 8:16 am to add the following --

[quote="Andlan" Our real motivation for deciding is universality. We know we cannot take account of everything in the universe when developing our theories/models, but a deep-seated belief is somehow ingrained in us that we can extrapolate our present observations to create more general rules about the world. .[/quote]

I am suspicious that we are beyond the stage of "belief" that we can achieve "universality". Has it not been proved in the Church-Turing-Deutsch Principle?

[Steve3007]

There might not be one test that can falsify the geocentric theory, but at some point, the weight of all the extra hypotheses that are added to the theory to account for all the hitherto unexplained observations (Teh has given some examples) becomes so great that it becomes unreasonable to support the theory and it is rejected.

Possibly we are talking across each other here, because I agree with this, but you seem to be under the impression that I don't. I think we're expressing the same principle in different language. Or maybe not. You decide!

For any given set of observations, there are an infinite number of possible theories that could accurately describe them. The criterea we use to decide which theories to support and which to reject is simplicity. To be a good theory, it has to be smaller than the set of things which it is describing and smaller than other theories. That is why the concept of symmetry is so key to physics. And that is the basis on which I say that the heliocentric model is "better".

Except on a surface practical level, it is not utility that governs the decision.

As I said, the use of Utility is something of a tautology: We use theories because they are useful. The sense in which I think Utility is useful, despite being a tautology, is simply in reminding us that what we do has a purpose to us. And that purpose to us shapes what we do and the way we do it. That purpose may be practical or it may be a quest to understand at a deeper level.

Our real motivation for deciding is universality.

Or, to put it another way: simplicity and smallness. Universality means: one description; multiple applicationsm, therefore a relatively small simple description. The ultimate non-universal descriptive law of the universe would be - the universe itself: a law that is as big as the thing it purports to describe; a model that is in fact the real thing.

The ultimate at the other end of the scale would be the Grand Unified Theory that many physicists regard themselves as searching for. The current reality is somewhere in between. The Standard Model of Particle Physics, for example, contains a lot of symmetries and is therefore a lot smaller than the thing it describes/models. But it is certainly not generally regarded as being small, and non "ad-hoc", enough yet. Hence it is not thought to be perfectly elegant. Also, of course, it is not a complete description of all observations either. The search continues.

We know we cannot take account of everything in the universe when developing our theories/models, but a deep-seated belief is somehow ingrained in us that we can extrapolate our present observations to create more general rules about the world.

Absolutely. Induction. Based, somewhat self-referentially, on the observation that this has worked up until now.

If I were arguing from the point of view of Evolutionary Biology, I might say that this belief is ingrained in us because creatures that do not have it would tend not to be able to predict what is going to happen next and would be less capable of surviving. From the quote below, it seems you're not keen on this viewpoint?

Or I might take another view and say that this belief is ingrained in us because we are part of a Universe which is not utterly chaotic. The belief in the predictable order of the Universe is a product of that order. And creatures with that ability, or any ability, or any creatures, or any ordered structures, could only exist in such a Universe. So self-referential again. The anthropic principle. The same as the reason why my legs are exactly long enough to reach from my body to the ground.

I don't see this as a psychological process like Hume. (Hume's view has merit in many eyes of chiming with modern cognitive science that holds the evolved brain responsible for all our normative judgements. It is a view entailing that empirical facts are divorced from any necessary prescriptive relationships concerning them).

You'll probably be glad to hear that I think I'm going to have to think about this quote and get back to you! I'm trying to tease out precisely what it means. Perhaps my limited knowledge of Hume is letting me down a bit!

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Teh:

What you consider an over-complication is entirely dependent on your world view. You could argue that it is unnecessarily complicated to have the earth moving.

You could, yes. That's what I meant by utility, in this context. The question of what you believe depends on what you want to use it for. You could indeed argue that the "moving Earth" hypothesis or, for that matter, the "spherical Earth" hypothesis is too complicated for a particular small subset of all possible observations - i.e. for your purposes. I suspect that the ancients, long before the Earth had been circumnavigated or there was any conception that the Earth was spherical, would have argued just that. The complication (as they would see it) of explaining why people don't fall off would be too much to bother with. Maybe?

Geocentrism is wrong because it does not explain planetary motion without unavoidably incorporating a rival theory.

General Relativity is not a rival theory to Newton's Law of Universal Gravitation. It contains it as a special case.

[Teh]

Absolutely. Induction. Based, somewhat self-referentially, on the observation that this has worked up until now.

There's your problem. You believe something false: that there is a process of induction that works.

[Andlan]

Possibly we are talking across each other here, because I agree with this, but you seem to be under the impression that I don't. I think we're expressing the same principle in different language. Or maybe not. You decide!

For any given set of observations, there are an infinite number of possible theories that could accurately describe them. The criterea we use to decide which theories to support and which to reject is simplicity. To be a good theory, it has to be smaller than the set of things which it is describing and smaller than other theories. That is why the concept of symmetry is so key to physics. And that is the basis on which I say that the heliocentric model is "better".

I don't think there is much disagreement between us over scientific method because, after all, scientists generally proceed quite happily without such concerns. Unlike Popper, for instance, I don't think philosophy can prescribe how scientists should work.

I don't know about 'infinite number of possible theories' for a given set of observations. Scientists are generally lucky enough to find one theory that works. I think the world 'resists' too much for this logical thesis of yours to be possible. I agree with you that there is not one perfect fit, and that our models 'correct' the observations in some way - like fitting different curves through a set of points. I also accept that external factors, such as the experimental aparatus, social factors, networks, funding etc. controls what curve/model we find most useful (the 'purpose' you talk about cannot be discounted). I guess what I'm saying is that in the end, it is not just which model is simplest, but how the world is (in a non definite sense) that controls things. Perhaps you can say that the form of the model is controlled by external factors, but the content is pretty much internal to the 'stuff' we are trying to explain.

Absolutely. Induction. Based, somewhat self-referentially, on the observation that this has worked up until now.

Whooa - hold on. As you know, what I'm getting at is where does this belief that we can extrapolate come from, and how is it that we can know about completely unexpected things, such as dinosaurs, that we have never experienced. You make some good points here about the non chaotic nature of things..

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You could, yes. That's what I meant by utility, in this context. The question of what you believe depends on what you want to use it for. You could indeed argue that the "moving Earth" hypothesis or, for that matter, the "spherical Earth" hypothesis is too complicated for a particular small subset of all possible observations - i.e. for your purposes. I suspect that the ancients, long before the Earth had been circumnavigated or there was any conception that the Earth was spherical, would have argued just that. The complication (as they would see it) of explaining why people don't fall off would be too much to bother with. Maybe?



General Relativity is not a rival theory to Newton's Law of Universal Gravitation. It contains it as a special case.

This is right of course - our newer and greater theories have to incorporate the older theories. So GR permits us to use the less accurate theory when we are working at the scale appropriate to that theory. OK - utility describes this process, but GR could also be used to get the same result, so you could also say we are just lazy not to use it.

[Steve3007]

Just to clarify:

Steve3007:

Absolutely. Induction. Based, somewhat self-referentially, on the observation that this has worked up until now.

Andlan:

Whooa - hold on. As you know, what I'm getting at is where does this belief that we can extrapolate come from, and how is it that we can know about completely unexpected things, such as dinosaurs, that we have never experienced.

Yes, I realised that was the question you were rhetorically asking. But my statement, above, was perhaps jumping ahead a little and needs to be "unpacked", as they say.

I was thinking: "Yes, quite, why do we have a belief in the use of induction?". And I gave two possible perspectives on that. Then I was wondering how small a set of absolutely axiomatic assumptions the scientific method could be reduced to. The validity of using induction appears, on the face of it, to be one such. But, it seems to me, we don't just rely on the principle that the world is repetative out of faith. We rely on it because it seems, so far, to be working. In other words, there is an established pattern that says this: the method of assuming the world to follow patterns and using those patterns to make predictions has worked before. So I'll keep using it. Extrapolation has always worked before, so I'll keep doing it.

But this uses the method of induction to validate the method of induction! That was what I meant by "self-referential". And that is perhaps why induction is axiomatic. Just a thought.

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Probably too much info here, but I feel the need for a couple more clarifications/comments:

I think the world 'resists' too much for this logical thesis of yours to be possible

I think that's a good way of putting it.

I agree with you that there is not one perfect fit, and that our models 'correct' the observations in some way - like fitting different curves through a set of points.

I'm not so keen on this way of putting it! I don't think fitting the theoretical curve to the empirical dots means "correcting" them. It doesn't change the position of the empirical dots (bearing in mind the fact that all empirical dots have error bars). It means postulating the existence of a continuous (AKA infinitely large) set of other dots in between. There are, in principle, an infinite number of variations in the possible shape of this line, while still fitting the empirical dots. But some variations are clearly wrong and ugly. This is perhaps one aspect of your "world resisting".

GR could also be used to get the same result, so you could also say we are just lazy not to use it.

Or, to put a more positive spin on it, we are sensible not to expend unnecessary effort. This principle is my understanding of Occam's razor.

[Teh]

I don't think there is much disagreement between us over scientific method because, after all, scientists generally proceed quite happily without such concerns. Unlike Popper, for instance, I don't think philosophy can prescribe how scientists should work.

You appear to be contradicting yourself. You claim to agree there is a scientific method, (which Popper would disagree with), and then claim Popper would "prescribe how scientists should work", which is also false. Perhaps I'm wrong, perhaps you aren't contradicting yourself, you are just making 2 false claims.

[Andlan]

Is there not a difference between prescribing and describing? Maybe I expressed this a bit clumsily.

[Teh]

Is there not a difference between prescribing and describing? Maybe I expressed this a bit clumsily.

If I recall correctly, Popper does "describe" how knowledge in general is gained (i.e. he developed an epistemology) and he demarcates between science and philosophy. Scientific conjectures can be refuted experimentally, while philosophical ones can be criticised by reason alone.

Also, I get the impression that he has no "prescription" on how conjectures should be made, nor a "description" of how they are made.

[Andlan]

You might be right - I've only read commentaries on Popper. His deep distrust of inductive reasoning probably just gives the impression that he is telling scientists how to work. On a common sense level, what usually works is a good guide to what will work in future, even though the logic of the method is refuted by the black swan case. My own view is that there is more going on than meets the eye when we say we are reasoning inductively, and I think intuition plays a key role.

[Steve3007]

His deep distrust of inductive reasoning probably just gives the impression that he is telling scientists how to work.

My view is that Popper rightly places emphasis on falsifiabilty but fails to adequately explain how the thing being falsified is arrived at by any process that does not involve induction. Falsification subtracts. You still need something to add first. But that is based on a small red book called "Popper" that has sat on my bookshelf and not been touched these 20 years.

I think intuition plays a key role.

I think you are right. But I think intuition is essentially an amalgam of past inductions, both in our own experiences and in the experiences of our forbears and passed down through inheritence.

[Teh]

You might be right - I've only read commentaries on Popper. His deep distrust of inductive reasoning probably just gives the impression that he is telling scientists how to work. On a common sense level, what usually works is a good guide to what will work in future, even though the logic of the method is refuted by the black swan case. My own view is that there is more going on than meets the eye when we say we are reasoning inductively, and I think intuition plays a key role.

Popper, and other, have provided several definitive proofs that induction is false.

[Andlan]

Steve. You have put your finger on the main problem with falsification - it doesn't explain how theories are derived at in the first place. It says you dream up any number of theories and then discard them one by one.

Your intuition sounds like a happy combination of memory and common sense. One thing I'm sure of though is that scientific theories are not derived from common sense notions, since they regularly defy them. That white light is a combination of coloured lights is not at all obvious. In coming up with hypotheses, there is obviously deep learning involved, plus we need to have a hunch what things in nature we should focus our attention on, so theory precedes observation in this sense.

[Steve3007]

One thing I'm sure of though is that scientific theories are not derived from common sense notions, since they regularly defy them.

I disagree. I think that common sense is essentially an informal precursor to formal science. Common sense is, at least partly, "rules of thumb" created by induction from common, everyday experiences and observations. The point when scientific theories cease to agree with common sense is invariably the point when the things being observed cease to be ordinary everyday objects.

The reason that quantum mechanics and general relativity (for example) defy common sense is that common sense was not derived from the objects on which they are based. We can intuit the behaviour a a baseball because we have a great deal of direct experience of such objects. Not so with electrons or black holes.

That white light is a combination of coloured lights is not at all obvious.

I think that's because we don't naturally constantly observe an event that is clearly and unambiguously a beam of white light shining through a refractor and turning into different colours. We've always had rainbows. But the act of sunlight refracting through tiny water drops high in the atmosphere is not directly observable.

In coming up with hypotheses, there is obviously deep learning involved, plus we need to have a hunch what things in nature we should focus our attention on, so theory precedes observation in this sense.

True, they often preceed the observations to which they directly apply, but they always follow previous not entirely dissimilar observations. Science is an iterative process of observation and conjecture.

[Andlan]

The reason that quantum mechanics and general relativity (for example) defy common sense is that common sense was not derived from the objects on which they are based. We can intuit the behaviour a a baseball because we have a great deal of direct experience of such objects. Not so with electrons or black holes.

Is not the reason why QM and GR defy common sense because they are heavily based on mathematics; not because we don't ordinarily encounter the objects that they refer to?

Let's take an example from geology (my field as it happens) since we are in danger of getting biased by physics (which is not all of science, despite what Rutherford thought): Common sense would dictate that finding fossils of marine creatures on top of a mountain means that there was a global flood.