Models versus sufficient reason

[wofsy]

While I know next to nothing about the philosophy of science, I would think about scientific models and explore whether there are features of these models that should be required in order to say they make a good theory or whether any model that predicts the data is as good as any other. From this question it would be interesting to explore the question of what it means to "understand" the world. What are the criteria of knowledge in Science?

I have learned from this forum that many believe that the only way to understand the world is through models and that all of our thoughts and areas of knowledge are merely ways of modeling sets of observations.

Some say that any model that describes accurately and predicts is as good as any other and that they differ not so much in whether they are right or wrong but in the domains of observation that they describe.

This viewpoint also tends not care about what is really going on and in fact may deny that "what is really going on" has any meaning.

I would like to explore whether this really true and ask whether there are valid criteria of knowledge that require more than modeling only.

Historically,this model-only view has existed since the Ancient Greeks but there has also been another point of view. This other view rejects the idea that any model is just as good as any other and imposes as a criterion of knowledge, a principal of design or sufficient reason. While I can not exactly define this, I can illustrate it with some examples that I have read about.

- In one of Plutarch's lives he addresses an empirical modeler who explains the behavior of a sundial. Paraphrasing Plutarch, his worlds were " Oh you empirical scientists! You tell me that you understand the sundial. You explain that you can predict the path of the sun's shadow as the day passes. You even tell me how the length and path of the shadow will change with the four seasons. But which one of you can tell me that it's purpose it to tell time?"

I interpret this to mean that without knowing the purpose we do not have knowledge even though we may have a good empirical model. It is sort of like in a murder trial we need motive as well as weapon and opportunity.

- The Ptolemaic system for the orbits of the planets was not only accurate but predicted the motions of the known solar system. Further, when after a long time it started to become noticeably off, it could be easily adjusted. The methodology, approximation by superposed circular motion, was not unlike modern Fourier analysis and could always be made arbitrarily accurate.

Despite its success, the Ptolemaic system was sometimes rejected because the modeling circles had centers with nothing in them, just empty space. These "quintessences" were viewed as arbitrary and some felt that no understanding of the world could be based on the construction of arbitrary points in space. It was felt that this did not represent a rational Universe and that God would not act arbitrarily. The model, though empirically successful, was thought to be wrong.

- Newton's physics did not work in every frame of reference as Newton was well aware and so he postulated an "absolute space" where his laws were true and which could be verified in any frame of reference moving uniformly with respect to it. Leibniz and others objected to his theory precisely because it required this absolute space. How was it that a rational Universe could only reveal its laws to special observers? Newton's absolute space was to Leibniz much the same as Ptolemy's quintessences. He said that Absolute space violated the principle of Sufficient Reason which I guess is what the demand for rationality became in modern times.

The objection on Absolute space was finally remedied with the Theory of Relativity. I find it remarkable that the General Theory was discovered on the demand for rationality rather than in an attempt to explain yet unexplained phenomena. Einstein it seems was asking for a rational theory of gravity - one without mystical and arbitrary forces - and was not trying to expand a model to new data.

In the end, the non purely empirical school of thought demands more than just a model from a scientific theory. Maybe it really requires a theory that explains the world as though there were a rational creator even if there isn't one. For without such a theory, as Plutarch argued, there can be no knowledge.

- It also seems that the belief in rationality has inspired much of Physics and wonder whether knowledge can really advance without it. If we question which thought processes lead to new science perhaps we find that the demand for rationality is required.

For instance, I believe the not-models-only objection to the Ptolemaic quintessences helped to inspire modern Physics. I think for Kepler and Copernicus, it was reassuring that the Sun was at the center of their models's orbits. In fact, I think it gave them confidence that their models were right.

I even think that Kepler believed that God resided on the Sun and guided the planets with a force analogous to magnetism. This again told him that his model was right and seems to be the first idea of gravity.

So maybe modern physics was brought forth through rejection of what was seen to be an arbitrary - though successful - modeling technique - and was inspired by a desire for a model that was consistent with rational design.

 

[apeiron]

You can think of it this way.

Yes, we can only model reality (even consciousness is a model of what is "out there").

And this in turn brings in the acceptance that modelling involves goals and purposes. You say your goal in modelling is to "know the truth". But there is plenty of evidence that the natural goal of modelling is "prediction and control".

If you look at complex adaptive systems - systems with life and mind - what makes them special is that they can predict their worlds and the consequences of their actions, and so gain control over things. Like metabolic pathways, repairing bodily structures, etc.

So modelling evolved as a way to control, not to know.

Humans can now choose to want to know. But you then have to do some work to define exactly what that means.

It really seems to mean to obtain objective invariance (http://en.wikipedia.org/wiki/Invariances), as opposed to subjective awareness (our highly refined modelling for prediction and control).

So the key notion - as you describe - is wanting to step outside of our highly adapted, but deeply embedded, subjective model of reality and imagine what it would be like to observe reality from the most generalised objective viewpoint.

The good news is that this seems achievable in some degree.

If we ask the question of what is the most general objective model, I would suggest it is whatever is our notion of logic, our model of causality. It is how things - anything, anywhen - must work.

Science is a mixed story because it is mostly shaped by the strong human desire for control over nature. We want the kind of models that can build machines. But generalisation or invariance is also a good thing and so there is trend towards "truth". Yet a weak one as the practical always trumps the philosophical.

As you say, there appears to be a strong rational hand - some objective invariance at work in nature. And when science gets too bogged down in the practical business of today's machines, theorists who step back towards the principle of invariance (eg: symmetries, self-organisation) can make the jump to a broader and higher level model. One that is more "global".

But caution. Modelling involves both a model and its measurements, the idea and the impressions that justify it. So pure reason fails. A higher level of modelling also has to bring with a matching higher level of measurement. In other words, the more generalised the model, the more particular the measurements must be.

Which would be in science why the measurements keep getting more difficult, the need for accuracy ever greater. Relativity dictated finer resolution measurements than classical physics. String theory's problem is that it is getting beyond measurement.

I would also say that because modelling is all we can actually do (and modelling is married to measurement) we should be prepared to do more reality testing of our ultimate model, our model of logic/causality/reason.

So standard logic is reductionist, mechanical, atomistic, monadic, local, materialistic. But a more delicate measurement of reality reveals a higher, more global, level of logic modelling which is systems-based, hierarchical, dynamic, dichotomistic, etc.

Like relativity incorporated classical physics, systems logic incorporates standard reductionist logic. It is just a step up to a more objective or invariant vantage point. Theoretically, there might be even broader views I guess.

 

[wofsy]

Interesting. Could you elaborate an example of objective invariance?
It does seem that the demand for invariance is a signature trend in physics but I would like to be clear on your point.

I also do not know anything about logic so more explanation would help.

BTW: It seems that Einsein disliked Quantum mechanics because it violated principles of rationality that he felt must govern any theory. The Bohm formulation seems to be an attempt at resolving this objection. But somehow it seems to fall short. Why do you think that is? Or do you think that is?

 

[Evo]

- In one of Plutarch's lives he addresses an empirical modeler who explains the behavior of a sundial. Paraphrasing Plutarch, his worlds were " Oh you empirical scientists! You tell me that you understand the sundial. You explain that you can predict the path of the sun's shadow as the day passes. You even tell me how the length and path of the shadow will change with the four seasons. But which one of you can tell me that it's purpose it to tell time?"

Well DUH. Men made the sundial to tell the time. Are you trying to imply that the sundial was not man made and could have come into existence on it's own for some other purpose?

Where on Earth did you get such a verse? Are you just making things up?

 

[wofsy]

Well DUH. Men made the sundial to tell the time. Are you trying to imply that the sundial was not man made and could have come into existense on it's own for some other purpose?

I think Plutarch's point was that one does not have full knowledge of a phenomenon without a theory that is consistent with a rational design. That it is man made is really a metaphor for a requirement for true knowledge.

While his point of view is maybe simplistic it was later abstracted into a principle of Sufficient Reason that Einstein and other Continental scientists, as Poincare calls them, such as Leibniz and Kepler, adhered to. Scientists such as Faraday and Newton for instance opposed the principle of Sufficient Reason or as they put it, their theories required "no hypotheses".

I think that the reformulation of Newtonian mechanics in terms of variational principles was an attempt at Sufficient Reason.

I also think that Gauss's astronomical theories were guided by Keplerian notions of harmony which are also part of the idea of Sufficient Reason in early Physics. The root of this line of thinking seems to be at least as old as the Pythagoreans. Kepler thought of himself as a neo-Pythagorean.

 

[apeiron]

Interesting. Could you elaborate an example of objective invariance?

Nozick's last book was called Invariances. It's his term.

His basic points are "truth" is borne out by success in acting upon beliefs. The modelling point. And then "an objective fact is one that is invariant under all admissible transformations."

So if you see one bouncing ball, that is a single subjective experience. But if you generalise from such observations well enough to create laws of motion, then you have a fact about reality.

It is really another way of explaining why symmetries are fundamental to reality modelling. Symmetries are invariances. But symmetries sound platonic. Invariance shows that there is a modelling process by which we generalise to arrive somewhere - to move from located subjectivity to the global view of objectivity.

BTW: It seems that Einsein disliked Quantum mechanics because it violated principles of rationality that he felt must govern any theory. The Bohm formulation seems to be an attempt at resolving this objection. But somehow it seems to fall short. Why do you think that is? Or do you think that is?

QM violates locality, a cardinal tenet of mechanics. If you are employing standard materialist logic and ideas of causality, QM is upsetting because it works as a model and violates your logic.

Happily QM fits very nicely with a logic based on ideas of development, potential, vagueness, hierarchy and systems.

Bohm is an attempt to keep QM local and mechanical. It is an attempt to keep the new scientific model while preserving the old causal framework.

Why are people so attached to their models of causality? I guess it is because it is the fundamental machinery of how they think. And thinking about your thinking so that you could think about how it might be like to think in a different way is not a simple feat.

 

[Evo]

I think Plutarch's point was that one does not have full knowledge of a phenomenon without a theory that is consistent with a rational design. That it is man made is really a metaphor for a requirement for true knowledge.

- In one of Plutarch's lives he addresses an empirical modeler who explains the behavior of a sundial. Paraphrasing Plutarch, his worlds were " Oh you empirical scientists! You tell me that you understand the sundial. You explain that you can predict the path of the sun's shadow as the day passes. You even tell me how the length and path of the shadow will change with the four seasons. But which one of you can tell me that it's purpose it to tell time?"

Post the link to this work. I don't find any such reference.

 

[apeiron]

Cicero (c. 106–c. 43 B.C.) an early teleological argument in De Natura Deorum (On the Nature of the Gods). He stated, "The divine power is to be found in a principle of reason that pervades the whole of nature".

"When you see a sundial or a water-clock, you see that it tells the time by design and not by chance. How then can you imagine that the universe as a whole is devoid of purpose and intelligence, when it embraces everything, including these artifacts themselves and their artificers?" (Cicero, De Natura Deorum, ii. 34)

http://en.wikipedia.org/wiki/Teleological_argument

 

[Evo]

Cicero (c. 106–c. 43 B.C.) an early teleological argument in De Natura Deorum (On the Nature of the Gods). He stated, "The divine power is to be found in a principle of reason that pervades the whole of nature".

"When you see a sundial or a water-clock, you see that it tells the time by design and not by chance. How then can you imagine that the universe as a whole is devoid of purpose and intelligence, when it embraces everything, including these artifacts themselves and their artificers?" (Cicero, De Natura Deorum, ii. 34)

http://en.wikipedia.org/wiki/Teleological_argument

Bolding mine. That backs me up, and has nothing to do with the nonsense posted by wofsy.

 

[wofsy]

Bolding mine. That backs me up, and has nothing to do with the nonsense posted by wofsy.

I think it has exactly to do with what I was saying. Cicero says the same thing. I may have forgotten the author. It is an old memory. Why do you say it is nonsense?

In any case, the idea that knowledge requires a purpose is the essential point and is certainly entertained in ancient times as a counter to purely empirical explanation.

 

[Evo]

I think it has exactly to do with what I was saying. Cicero says the same thing. I may have forgotten the author. It is an old memory. Why do you say it is nonsense?

In any case, the idea that knowledge requires a purpose is the essential point and is certainly entertained in ancient times as a counter to purely empirical explanation.

We don't allow members to make things up. Don't do it again.

 

[wofsy]

http://books.google.com/books?id=os...num=10&ved=0CBwQ6AEwCTgK#v=onepage&q=&f=false

here is a partial reference that i just found though admittedly not what I remember it refers to the shadow of the sundial and its cause as insufficient to explain it.

 

[wofsy]

We don't allow members to make things up. Don't do it again.

Thanks evo - I guess this thread is closed.

 

[wofsy]

Nozick's last book was called Invariances. It's his term.

His basic points are "truth" is borne out by success in acting upon beliefs. The modelling point. And then "an objective fact is one that is invariant under all admissible transformations."

So if you see one bouncing ball, that is a single subjective experience. But if you generalise from such observations well enough to create laws of motion, then you have a fact about reality.

It is really another way of explaining why symmetries are fundamental to reality modelling. Symmetries are invariances. But symmetries sound platonic. Invariance shows that there is a modelling process by which we generalise to arrive somewhere - to move from located subjectivity to the global view of objectivity.

QM violates locality, a cardinal tenet of mechanics. If you are employing standard materialist logic and ideas of causality, QM is upsetting because it works as a model and violates your logic.

Happily QM fits very nicely with a logic based on ideas of development, potential, vagueness, hierarchy and systems.

Bohm is an attempt to keep QM local and mechanical. It is an attempt to keep the new scientific model while preserving the old causal framework.

Why are people so attached to their models of causality? I guess it is because it is the fundamental machinery of how they think. And thinking about your thinking so that you could think about how it might be like to think in a different way is not a simple feat.

Could you list some links. I am interested in reading more about what you said.

The thread is closed so conversation ended. My apologies.

 

[disregardthat]

Don't close this thread.

 

[apeiron]

here is a partial reference that i just found though admittedly not what I remember it refers to the shadow of the sundial and its cause as insufficient to explain it.

Plutarch's shadow of a sundial example here is in fact an ancient comment on what today would fall within the realm of semiotics. Or the issue of symbol grounding in complex adaptive systems. How do signs (like genes and words) gain their meaning?

Cicero's sundial example is a forerunner of today's blind watchmaker arguments - dawkins vs intelligent design.

The two are in fact somewhat aligned debates as they do argue for the acceptance of purpose and meaning as part of causality. And here we would normally turn in ancient times to Aristotle and his four causes which included telos, or final cause.

http://en.wikipedia.org/wiki/Four_causes

The modern scientific approach to final cause would be the idea of an attractor - an emergent constraint (as we find in self-organising systems) rather than an intelligent fabricator (as posited in various religions).

 

[dx]

This viewpoint also tends not care about what is really going on and in fact may deny that "what is really going on" has any meaning.

"Reality" is also a theoretical notion, and therefore part of a model. In fact, our everyday thinking about the world is also based on a model, except that this model is so ingrained in our minds that we don't think of it as a model. The notion of 'reality', for example, and the notion of 'space' are parts of this model. So I think it is important to understand that without a model, we cannot ascribe a form to experience. The content of experience must always be interpreted using theoretical notions. I think this is one of the most important lessons of 20th centry physics (i.e. relativity and quantum mechanics): that the purpose of science is not to find out what is 'really going on' (science cannot be tied down to any particular physical idea like reality or space or time), but to find relationships between aspects of our experience using a conceptual language. The pictures of Nature that we make using these concepts must be given the same logical status as the 3D spatial image we make in our heads from of visual experience. Both are conceptual pictures, but these pictures reflect structure in Nature.

 

[apeiron]

Could you list some links. I am interested in reading more about what you said.

Invariances is a good book, one of the few modern philosophy books I could recommend.

On modelling theory, Rosen is great - see Essays on Life Itself - but it is somewhat technical.

Or a really quite simple introduction to symmetry (the static face of invariance) is Why Beauty Is Truth: The History of Symmetry by Ian Stewart.

Symmetries are "rational" because they seem all that is left when everything else has been erased.

So when you suggest that modern physics may be secretly inspired by a desire for a model that is consistent with rational design, what is actually true is that physics is consciously climbing the hierarchy of generalisation to ascend to the highest possible heights of symmetry (or invariance).

 

[wofsy]

Invariances is a good book, one of the few modern philosophy books I could recommend.

On modelling theory, Rosen is great - see Essays on Life Itself - but it is somewhat technical.

Or a really quite simple introduction to symmetry (the static face of invariance) is Why Beauty Is Truth: The History of Symmetry by Ian Stewart.

Symmetries are "rational" because they seem all that is left when everything else has been erased.

So when you suggest that modern physics may be secretly inspired by a desire for a model that is consistent with rational design, what is actually true is that physics is consciously climbing the hierarchy of generalisation to ascend to the highest possible heights of symmetry (or invariance).

This really interests me. Thanks for the references.