Sunday, July 26, 2009

Fundamental science

Bee has a post up on her blog, about what a fundamental theory means.
A theory is fundamental if it cannot be derived from another, more complete, theory. More complete means the theory is applicable to a larger range. Note that a fundamental theory can be derivable from another theory if both are equivalent to each other (though one could plausibly argue then one should consider both the same theory).

I believe this notion of fundamental misses a point. It is not that the definition is wrong or useless. I just don't think it is the most fruitful way to think about the world. I couldn't convey the point very well. So here is Samir Okasha, in his very slim volume "Philosophy of Science — A Very Short Introduction". This is from Chapter 3, Explanation in Science, from a section titled "Explanation and Reduction". After discussing the idea that everything is ultimately physical entities,
Does this mean that, in principle, physics can subsume all the higher-level sciences? Since everything is made up of physical particles, surely if we had a complete physics, which allowed us to predict perfectly the behaviour of every physical particle in the universe, all the other sciences would become superfluous?

Most philosophers resist this line of thought. After all, it seems crazy to suggest that physics might one day be able to explain the things that biology and economics explain. The prospect of deducing the laws of biology and economics straight from the laws of physics looks very remote. Whatever the physics of the future looks like, it is most unlikely to be capable of predicting economic downturns. From from being reducible to physics, sciences such as biology and economics seem largely autonomous of it.

This leads to a philosophical puzzle. How can a science that studies entities that are ultimately physical not be reducible to physics? {emphasis added}. Granted that the higher-level sciences are in fact autonomous of physics, how is this possible?

According to some philosophers, the answer lies in the fact that the objects studied by the higher-level sciences are 'multiply realized' at the physical level. To illustrate the ideas of multiple realization, imagine a collection of ashtrays. Each individual ashtray is obviously a physical entity, like everything else in the universe. But the physical composition of the ashtrays could be very different – some might be made of glass, others of aluminium, others of plastic, and so on. And they will probably differ in size, shape, and weight. There is virtually no limit on the range of different physical properties that an ashtray can have. So it is impossible to define the concept 'ashtray' in purely physical terms. We cannot find a true statement of the form 'x is an ashtray if and only if x is ....' where the blank is filled by an expression taken from the language of physics. This means ashtrays are multiply realized at the physical level.

Philosophers have often invoked multiple realization to explain why psychology cannot be reduced to physics or chemistry, but in principle, the explanation works for any higher-level science. Consider for example, the biological fact that nerve cells live longer than skin cells. Cells are physical entities, so one might think that this fact one day will be explained by physics. However, cells are almost certainly multiply realized at the microphysical level. Cells are ultimately made up of atoms, but the precise arrangement of atoms will be very different in different cells. So the concept 'cell' cannot be defined in terms drawn from fundamental physics. There is not true statement of the form 'x is a cell if and only if x is....' where the blank is filled in by an expression taken from the language of microphysics. If this is correct, it means that fundamental physics will never be able to explain why nerve cells live longer than skin cells, or indeed any other facts about cells. The vocabulary of cell biology and the vocabulary of physics do not map onto each other in the required way. Thus we have an explanation of why it is that cell biology cannot be reduced to physics, despite the fact that cells are physical entities.

Not all philosophers are happy with the doctrine of multiple realization, but it does promise to provide a neat explanation of the autonomy of the higher-level sciences, both from physics and from each other.

PS: In summary, if the idea of multiple realization is valid, cell biology cannot be derived from physics; cell biology is only constrained to be compatible with physics. Then cell biology is as fundamental a theory as physics using Bee's definition.


Bee said...

Dear Arun,

Thanks for the clarification. If I understand this correctly, you are saying there might be no way to satisfactorily define an "emergent feature," like for example a cell. But you could equally well take this as an argument that then the "cell" just isn't a useful thing to talk about in the emergent theory.

In any case, I don't understand why it should be impossible to define an ashtray, or a cell, or whatever else there is emergent as an equivalence class of objects that have certain properties. After all, that's why we are able to identify them. Such a definition might not coincide with everybody's understanding of a particular object, and it might turn out not to be useful, but a definition is just a definition. The alleged problem of "multiple realizations" lies simply in insufficient information (ie some arrangement of initial conditions or so).

It seems to me that in essence the writer of this piece is suggesting a theory on the emergent level might not be a function of the fundamental theory, in the sense that one object of the fundamental theory could be mapped to various objects in the emergent theory. Frankly, I think it's rather the other way 'round, there are many states in the fundamental theory that are being mapped to the same emergent object. If not, wouldn't the information on the emergent level actually have to be larger, meaning it would be the more 'fundamental theory,' from which the other one can be derived. Maybe I just don't understand this very.

Btw, Tegmark in his paper on the Mathematical Universe also talks about the difficulty of identifying structures within structures. Best,


Bee said...

Should have been: Maybe I just don't understand this very well.