Is syntactic simplicity (or elegance) more important than ontological simplicity?

Question

The SEP article here outlines different kinds of simplicity, otherwise known as parsimony. The two main ones outlined are elegance (related to the simplicity of a theory and how simply it can be formulated) vs. ontological parsimony (how many kinds of entities are posited in the theory).

Is there ever a case where the latter is preferred in practice by science? Or is there a rationalist case for preferring it over elegance? Examples tend to either include theories that are empirically equivalent but postulate more entities (such as Lorentz’s aether theory vs. special relativity) or theories that postulate more entities but make the theory more conceptually elegant (such as positing Neptune before it was discovered which “allowed the perturbations in the orbits of other observed planets to be explained without complicating the laws of celestial mechanics”).

Even in the aether case, the article notes

The problem with using this example as evidence for Occam’s Razor is that Special Relativity (SR) has several other theoretical advantages over the Lorentz-Poincaré (LP) theory in addition to being more ontologically parsimonious. Firstly, SR is a simpler and more unified theory than LP, since in order to ‘save the phenomena’ a number of ad hoc and physically unmotivated patches had been added to LP.

If SR is more simplified than LP, it also makes it more elegant. Thus, elegance, even here plays a role in preferring SR.

In other words, elegance seems to take precedence over ontological parsimony in history. Are there any justifications for taking ontological parsimony as more important, even at the cost of added complexity to a theory?

Answer 1

Treating the concept of parsimony as though it means 'simplicity' (whether syntactic or ontological) is a bit, well… oversimplified. Parsimony is closer to coherence or cohesion. Theory-people tend to get uncomfortable when a theory looks jerry-rigged (patchwork, piecemeal): giving an impression that things were slapped onto the theory in order to cover a weakness or hole. A theory (like a mathematical function) should cover its domain in a smooth and continuous manner, without sudden discontinuities or inclusions. When a theorist has to resort to such to gloss over some anomaly or lacuna, it's always a problem.

Syntactic simplicity implies domain coherence, since the breadth of the subject matter can be covered by simple statements, without add-ons. Ontological simplicity generally implies domain coherence, since unobserved phenomena can be interpolated via theory from observations without introducing new elements. Both serve the same goal in different ways, and we rarely find a case where we have to choose between them. The thing to remember is that a theory can become more complex without losing ontological or semantic simplicity, so long as it maintains coherence (e.g., Einstein's relativity is more complex than Newtons theory of gravitation, but is simpler in the sense that it resolves anomalies in Newton's theory without disrupting the continuity of Newton's theories).

Answer 2

In the pursuit of increasingly adequate scientific theory, neither enjoys a privledged status. Ultimately, both parsimony of theory and ontological simplicity, while good heuristics, must yield to being accountable to observation and experimental results. The best scientific theories are those that provide reliable explanatory inference, and that is determined on a case by case basis.