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There were many historical instances where phenomena could be explained by seemingly incompatible theories, Copernican and Ptolemaic systems, corpuscular and wave theories of light, interpretations of special relativity with and without ether (Lorenz vs. Einstein), Copenhagen, Bohmian and many worlds interpretations of quantum mechanics. There are several interesting features. First, these alternative theories weren't comprehensive, they only covered a limited range of phenomena, even quantum mechanics excludes relativity and quantum field theory. Second, with the exception of the theories of light they are mathematically equivalent, in other words, it's not that different mathematics describes the same physics, but rather that the same mathematics admits vastly different interpretations.

One could say therefore that the theories are "isomorphic", and the interpretational differences are "unphysical" and irrelevant. So the answer also depends on the meaning of "determine". However, for something "unphysical" physicists spent a great deal of energy arguing about these interpretational differences (and still do in the case of quantum mechanics). One of the reasons may be that such theories are expected to produce different predictions when extended to a wider range of phenomena, at which point the difference will become physical.

Is it possible to have different ontologies that account for all phenomena? They could postulate existence of different objects, give different explanations for the same events, have different moral and religious implications, etc. What is the value of interpretational parts in theories if they have no effect on predictions? Multiple ontologies would seem to turn them into comforting illusions used for didactic purposes. How do different philosophical traditions address this issue? Plato's and Aristotle's views were recently discussed here.

EDIT: I realized belatedly that I didn't say enough to make the question non-trivial. There are uninteresting ways to multiply ontologies by adding decorations to them, objects that have no effect on phenomena like ether was, or by ontologizing different representations of the same mathematics, like choosing different "centers of the world" in astronomy. Fortunately, the answers offered more substantive sources of multiplicity and I enjoyed reading all of them. The one I accepted was the one more educational for me personally.

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It is generally assumed that scientific theories are underdetermined by experience (there can be alternative theories with the exact same empirical content), and that in turn the metaphysical interpretation of the theory is underdetermined by the theory. One argument that supports this assumption is the Quine/Duhem thesis: no hypothesis is tested in isolation (there are always many auxillary hypothesis, for example concerning measuring apparatus), and when a test fails, there are always different ways to fix the theory, which means different theories equally well supported by experiment.

The examples you provide are good historical examples and generally, although there are other more philosophical ones, such as Descartes' evil demon (the theory that everything I sense is produced by an evil demon) and toy examples constructed by philosophers themselves (Newton's theory, plus the assumption that the whole universe moves at a certain speed). Philosophers discuss the criteria that allow one to choose between competing theories, such as simplicity, non-adhocness, explanatory power, and whether these criteria have anything to do with truth. Some argue that they are strategic criteria for directing inquiry toward the truth, or that they are pragmatically justified by their success in past scientific inquiry.

It can be also argued that apart from trivial cases (such as Descartes' demon or Newton's theory plus universal movement), there will always be a way to discriminate empirically between competing theories in the future. What counts as empirical data evolves with time and somehow depends on the theories. New theories can provide new kinds of experiments. Furthermore, the process of unifying distinct theories which apply to distinct areas of inquiry could eventually solve the underdetermination. Differences in interpretation could play a role in entailing different ways of unifying distinct theories, and could then be indirectly discriminated empirically.

In this debate, you seem to be advocating some form of structural realism: we should only be commited to the mathematical structure of theories, not their metaphysical interpretation. This is a rather fashionable position. However there are also objections to it (which in turn might be answered): for example, how do you make sense of the distinction between mathematical and physical structure if not through a metaphysical interpretation? Or do you endorse mathematical platonism? Don't you need some common-sense interpretative content to apply your theory in specific experimental contexts?

There are also arguments to the effect that claiming that a mathematical structure exists or is instantiated in reality is some trivial statement, from a logical point of view (you can always arbitrary arrange anything in order to "view" it like any structure you like, if only the number of objects to realise that structure are sufficient). So structural realism would boil down to another, anti-realist position: the claim that our theories are empirically adequate. This amounts to accept the underdetermination of theories, and therefore refuse to assume that we are in a position to know whether our theories are "true" in a strong sense.

Having said that structural realism is still defensible and could be a good answer to underdetermination.

  • Thanks, I wasn't aware of structural realism. I certainly agree that new intuitions should be developed based on mathematical structure instead of imposing old ones on it (as in the wave/particle debacle in QM), and invariant aspects of it rather than representational (as in Bohmian theory that hypostatizes artefacts of the position basis). But I'd still be curious how this abstracted structure makes its way into the mess of phenomena and reaches us through them only. So I'd want an ontological model for the tower below the phenomena in addition to epistemological one for the tower above. – Conifold Sep 27 '14 at 21:24
  • So you are advocating at least some minimal metaphysical interpretation beyond the structure of the theory? I think it's a sensible position. – Quentin Ruyant Sep 30 '14 at 11:48
  • To put it shortly I am for ontology without committments, "as if" ontology, and a model of interaction with it consistent with predictive mathematics. I can even imagine mutually exclusive ontologies being useful to clarify different aspects of the theory. For instance, Bohmian mechanics helped me understand how entanglement functions in mathematics of QM. – Conifold Dec 12 '14 at 7:00
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Is it possible to have different ontologies that account for all phenomena?

Yes, if by "all" we mean practically (what humans can now do), instead of theoretically (see, for example, John Barrow's New Theories of Everything). See the following, from Massimo Pigliucci's Essays on emergence, part I:

Batterman takes on an alleged (as it turns out) case of reduction of a phenomenological to a more “fundamental” theory: the relationship between classical thermodynamics (phenomenological) and statistical mechanics (fundamental). The fact is, “the quantities and properties of state in orthodox thermodynamic equations appear largely to be independent of any specific claims about the ultimate constitution of the systems described,” which would seem to cast some doubts on the simple version of the reduction story. As Batterman puts it, “Reduction in this context typically is taken to mean that the laws of thermodynamics (the reduced theory) are derivable from and hence explained by the laws of statistical mechanics (the reducing theory) ... [but] there are very good reasons to deny that all thermodynamic (and hydrodynamic) phenomena are reducible to “fundamental” theory,” and these reasons have to do with phase transitions (solid and liquid, liquid and gas, etc.).
[...]
Batterman continues: “The renormalization group explanation provides principled physical reasons (reasons grounded in the physics and mathematics of systems in the thermodynamic limit) for ignoring details about the microstructure of the constituents of the fluids. It is, in effect, an argument for why those details are irrelevant for the behavior of interest.” [Italics in the original]

Pigliucci is clearly concerned with talking about emergence, but two bits come out of the discussion above which bear on the cardinality of the phenomenology–ontology relationship:

  1. "the quantities and properties of state in orthodox thermodynamic equations appear largely to be independent of any specific claims about the ultimate constitution of the systems described"
  2. "ignoring details about the microstructure of the constituents of the fluids"

Now, there is some wiggle-room, here. A scientific theory can be fantastically successful even if it is not precise. So, perhaps the microstructure—the ontology—is only relevant when one goes down to a high enough precision. To use another example, in physics, there are open questions at energy levels well past what can currently be tested in the laboratory and perhaps even what is generally observed from cosmic rays (see the Greisen–Zatsepin–Kuzmin limit). So, it seems that multiple different ontologies are viable options.

Switching to philosophy of mind, you may find Putnam and Fodor's multiple realizability of interest:

Multiple realizability, in the philosophy of mind, is the thesis that the same mental property, state, or event can be implemented by different physical properties, states or events.

P.S. My answer to What is the difference between Fact and Truth? may also be relevant.


What is the value of interpretational parts in theories if they have no effect on predictions?

From reading a decent amount of the history of the philosophy of science, I suspect these matter when forming new hypotheses. Karl Popper, in The Logic of Scientific Discovery, famously stated:

I said above that the work of the scientist consist is in putting forward and testing theories.
    The initial stage, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor to be susceptible of it. The question how it happens that a new idea occurs to a man—whether it is a musical theme, a dramatic conflict, or a scientific theory—may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge. The latter is concerned not with questions of fact (Kant's quid facti?), but only with questions of justification or validity (Kant's quid juris?). (7)

I do not know of any good, systematic treatment of how hypotheses are formed. I do know that this is a deep desire of machine learning folks; much ML is currently pattern matching; making the transition to hypothesis formation would likely mark a major leap forward. The following, from What emotions really are, may be of interest:

Children do not create concepts simply by grouping particulars on the basis of overall similarity. Instead, they create causal explanatory theories of particular domains and cluster instances according to their possession of theoretically significant properties in the these schemes of explanation (Keil 1989). (6)

I do not recall whether there was any particular connection to emotions here; what I do know is that Griffiths is concerned to group emotions into natural kinds. That being said, studying early development of humans may shed light on the use of non-mathematical parts of hypotheses.


How do different philosophical traditions address this issue?

I don't have the time to get into detail, but Michael Friedman's Dynamics of Reason may help point the way, especially his use of "constitutive principle" and "correlative principle". A bit on those terms:

Michael Friedman in his Dynamics of Reason is intrigued by the physical theory of a time being composed of a mathematical language, coordinating principles, and empirical laws and regularities, and how their status changes through a revolution.

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Does phenomenology determine ontology?

Sure; if one interprets phenomenology as experiment, and recalling that physics is an experimental/empirical science; for example phenomenology in particle physics is the art :

of theoretical particle physics that deals with the application of theoretical physics to high-energy particle physics experiments...[it] is the calculating of detailed predictions for experiments, usually at high precision (e.g., including radiative corrections).

and

Beyond the Standard Model, phenomenology addresses the experimental consequences of new models: how their new particles could be searched for, how the model parameters could be measured, and how the model could be distinguished from other, competing models.

hence

Phenomenology forms a bridge between the mathematical models of theoretical physics (such as quantum field theories and theories of the structure of space-time) and experimental particle physics.

Of course the full picture is much more complex; for example Milesian physics and Cosmology was almost all speculative.

There are several interesting features. First, these alternative theories weren't comprehensive, they only covered a limited range of phenomena, even quantum mechanics excludes relativity and quantum field theory.

As a general rule the art of the solvable is in part understanding limitations; for example Newton gave up on locality to get a usable theory of gravity, even though he clearly understood its necessity.

Second, with the exception of the theories of light they are mathematically equivalent

Why the exception for light?

in other words, it's not that different mathematics describes the same physics, but rather that the same mathematics admits vastly different interpretations.

Agreed.

One could say therefore that the theories are "isomorphic", and the interpretational differences are "unphysical" and irrelevant.

'Isomorphic' has a technical definition which I don't think is wholly appropriate here; for example just because any two books are written in the same languge oesn't mean that they're equivalent.

However, for something "unphysical" physicists spent a great deal of energy arguing about these interpretational differences (and still do in the case of quantum mechanics).

Well it took 2500 years to verify atoms; 350 years to incorporate locality in Gravity. They're arguing over these 'interpretations' because thy very much matter; but one expects the answer may take a couple of lifetmes to solve.

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