Is it possible for two different theories to describe nature correctly without one being reductible into the other?

Question

I suppose the whole thing is already in the title but if I shed some light on the centre of my doubt...

In the macroscopic world we tend to have our objects of study "right at hand" but when we start moving into the microscopic realm everything, from entities to interactions, become more abstract (at least abstract to our macroscopic-accustomed minds). Is it possible to create different sets of entities and interactions that are equally satisfactorily successful in describing a phenomenon without being possible to arrive at one set from the other through some kind of transformation? There is examples of that in history of science? Could you help me with some literature on the matter?

I think the closest I can get to an example of what I mean was the 17th century discussion on the nature of light. I know the history of light had a magnificent turn in 20th century, but from the eyes of Newton and Descartes I think my question would not be so strange.

Thank you very much.

Answer 1

Aristotle begins his Physics, which his philosophy on the first principles of scientific discourse in the following way:

In any subject which has principles, causes and elements, scientific knowledge and understanding stems from a grasp of these.

Because

For we think we know a thing only when we have grasped its first causes and principles and have traced it back to its elements.

And

It follows obviously that if we are to gain a scientific knowledge of nature as well, we should begin by trying to decide on its principles.

This doesn't entail reductionism, say in the sense that everything is related directly to a single axiomatic foundation.

What it does entail is:

The natural way to go about this is to start with what is more intelligible and clear to us and move from there to what is clearer and more intelligible in itself. For the fact that something is more intelligible to us does not mean that it is intelligible tout court.

So it's a clarification, and a discovery of principles; and one that is constituted naturally in relation to the subject matter at hand.

The question then is, say we have several subjects to hand: say biology and physics, what is their relation? That there must be a relation is obvious; but should this relation entail that one is reduced to the other?

Not neccessarily, for opposites are related and neither, obviously can be reduced to the other (but it can be enlargened, for black and white are opposites, but the species colour contains them).

But this does not deny that an aspect of one can be reduced to another; Aristotle elaborates that the Ionian Monists as supposing that:

it may be possible for everything to be made of the same stuff; this ... is the sense in which natural scientists say that everything is one.

Not that all is alike in species; alike in kind - the subject matter of zoology is different from physics, say; they are different species of knowledge; and the same goes for poets and physicists - as one might find if one set a physicist to write a poem and find they write doggerel, or set a poet to think through a physical concept, like relativity but his wilful will, will not; his soul subtending an angle and aching and arcing through sensual music - the music of sense - to the firmament of some absolute.

More could be written from this angle, emergentism as a kind of becoming - say ...

Answer 2

Here are a few examples:

• Light can be describes as either a particle or wave. Neither description is reducible to the other. Also, neither describes all phenomena fully (the particle model doesn't explain the famous double-slit experiment, the wave model doesn't explain the photon quanta experiment).
• Relativity and Quantum Mechanics describe different aspects of reality, but neither describes the other. Similarly to the light example, both models explain some thing well and don't explain other things particularly well.
• As another example not from physics, there are models in the study of population dynamics of animals that explain over the course of generations how many of a given species there might be, but you could not use those to predict how many animal births there will be tomorrow.
• As still another example, climate and weather are clearly linked somehow, but models of what the weather will be like tomorrow have little to do with models for longer term climate trends.

As the above examples show, models explain some aspect of reality within some error bounds. In practice then, one does not often speak of a model being "correct," but rather a model is able to make good predictions or not within some specific set of cases.

Answer 3

What you are after is what is call underdetermination by experience. Here is a useful resource on the subject: http://plato.stanford.edu/entries/scientific-underdetermination/

There are undoubtedly metaphysical cases of underdetermination: for example you can be dreaming, which would explain your experience just as well as if reality existed. There are also trivial cases: imagine a newtonian universe which is identical to our own except it has a certain uniform speed relatively to absolute space. Both are indiscernible but different.

Here is another example: newtonian physics can be formulated by replacing gravitational forces with deformation of the geometry of space (as in relativity except that the geometry is not relativistic).

There is also the issue of the metaphysical interpretation of theories (is space a substance or a structure of relations?). Different interpretations do not change the predictions but they can be considered distinct explanations. In quantum mechanics, Bohm's theory makes the same predictions as standard quantum mechanics.

There is no consensus on whether there are genuine cases of underdetermination apart from metaphysical and trivial cases. You will find more information on the debate on the link I provided.

Answer 4

There are two positions with different answers to your question:

• Reductionism: All scientific theories about the world should eventually be reduced to one basic central theory (presumably of fundamental physics). Those theories that we can't reduce to another right now are so because they are incomplete and we lack the knowledge to do so. Sometime in the future however, as we make progress, we will eventually be able to do so. To take James Kingsbury's example of Realtivity and QM: Current physicists hope that at some point they will be able to perfect String theory to the point where G.R and Q.M can both be reduced to it. A reductionist will have the following answer to your question: Yes it is possible, but only because those two different theories are incomplete, in the long term, we should progress beyond that and all theories should be reducible to one central theory of everything.

• Emergentism: This is the principle that some large scale properties and patterns of a systems can never fully be described in terms of their lower level components. This theory has mostly be significant in the philosophy of mind and in biology, where it has been held that higher level theories about living systems (consciousness, psychology, population dynamics, etc...) can never be reduced to lower theories about, neuroscience, genetics and biochemistry, etc... There are people who believe this about physics theories as well. An Emergentist will answer your question: Yes it is possible, and in fact it is true.

P.S: some people seem to think that emergentism necessarily implies some form of dualism or vitalism -- it doesn't, one can be a materialist physicalist and still subscribe to emergentism

Answer 5

There are, I believe, a number of cases of distinct scientific theories that are equally good at explaining phenomena...until experimental evidence favors one over the other.

Proponents of the steady state universe versus the expanding universe were about equally divided, with the discovery of background radiation tipping the balance. The Ptolemaic system and the Copernican system existed alongside one another for a time, both equally coherent and consistent with phenomena. I believe the "holographic model" of the universe recalculates general relativity with a dimension subtracted, but I may have that bolloxed up. In both cosmology and quantum theory three are a number of mathematically developed, competing theories awaiting some experimental framework. And in many cases, Occam's razor may become the sole distinction between equally plausible theories.

The problem lies in "describe nature correctly." Correlation with phenomena is often complex and usually based on forthcoming predictive capacity. I think that if two distinct theories both correlate to the same phenomena they would logically be "reducible to on a another."