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There is an SEP article on the proposed incommensurability of at least some conflicting pairs of scientific theories, which goes over Kuhnian and Feyerabendian proposals regarding this incommensurability. Perhaps ironically, the article concludes by comparing two theories of incommensurability that might themselves be meta-incommensurable! (Note that the article does briefly emphasize the commensuration/comparison distinction, however, in that same concluding section.)

Now, is it possible that a manifestation of scientific incommensurability might be explanatory incommensurability with regards to degrees of theoretical simplicity/complexity? Must we always assume that elements of pairs of theories can be ratioed one to another along this line? I wonder, for example, if an elaborate conglomerate of multiversal set theory, pluralistic modal logic, and a mechanism for a unified field would be neither more nor less nor equally complex (much less simple!) in comparison with a divine nature having exotic meta-properties such as divine simplicity (plus, somehow, tri-unity and the capacity for incarnation, say). As I've noted before, in Cantor's set world, there seemingly (as far as I can tell, anyway) would have been no nontrivial elementary embeddings of his divine counterpart to V, into that counterpart itself or models of V (or sets that model fragments of V), for such would conflict with his depiction of the divine transet (as an ens simplicissimum). But the presence or absence of order-indiscernibles/sharps (including class-many of them) is the kind of thing that might make commensurability hard to attain to even on a purely mathematical level, so if we tried to move from that level to a physically explanatory one, would we be able to commensurate a physical theory involving e.g. Cantor's God with a physical theory coupled to a set theory with endless amounts of order-indiscernibles/sharps/w/e along those lines?

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  • This question is piling up quite a lot of speculations and builds a tower of hypothetical constructions, which often lack sufficent clarity of the concepts. E,g, what does mean the term "Cantor's God?" - Of course it can be difficult to find criteria to compare two different theories. But it would be helpful to study some real and concrete examples first.
    – Jo Wehler
    Nov 13, 2023 at 17:36
  • @JoWehler if a theistic hypothesis is not even mathematically commensurable with a non-theistic one, whence would they be explanatorily commensurable modulo Occam's razor? Are they neither more nor less complex than each other, but merely different, on this count, in some otherwise ineffable manner? That is, I suppose, the gist of the question... Nov 13, 2023 at 17:53
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    It is obvious that by scaling up (particle-QM, atom-physics, molecule-chemistry, cell-biology, human, society etc) explanatory complexity is added because the lower framework cannot account for the complexity of the behaviour of a higher one. So commensurability of concepts exists only in the borders. In this view Occam's razor is just an intellectual simplification. Nov 13, 2023 at 18:37
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    Anything that produces incomparables undermines the razor, and we do not need something as complex as incommensurability. As SEP notes in Simplicity, parsimony is a multicritereal objective which already produces incomparables even among commensurable theories. For example, Copenhagen is argued to be more ontologically parsimonious (no multiple branches), while MWI to be more conceptually parsimonious (drops the collapse postulate).
    – Conifold
    Nov 13, 2023 at 19:53
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    I would suggest that appeals to Occam's Razor are appeals to Bayes' Theorem (filtered through an heuristic for doing rough guesses of the outputs thereof). The "complexity" in Occam's Razor becomes well-defined as the Bayesian concatenation of prior probabilities; the heuristic usually works because prior probabilities are usually nontrivially less than 1, so concatenating many priors usually results in a lower probability than concatenating few priors.
    – g s
    Nov 13, 2023 at 20:02

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You have a lot going on, so I'm going to tackle what I see as the pith of the issue, and where the leverage in analysis lies.

Now, is it possible that a manifestation of scientific incommensurability might be explanatory incommensurability with regards to degrees of theoretical simplicity/complexity?

Yes, because incommensurability, the very notion of theoretical simplicity and complexity, is domain-specific language regarding the quantification and qualification of conceptual and linguistic structure. From WP:

Commensurability is a concept in the philosophy of science whereby scientific theories are said to be "commensurable" if scientists can discuss the theories using a shared nomenclature that allows direct comparison of them to determine which one is more valid or useful. On the other hand, theories are incommensurable if they are embedded in starkly contrasting conceptual frameworks whose languages do not overlap sufficiently to permit scientists to directly compare the theories or to cite empirical evidence favoring one theory over the other.

So, let's go to Searle's analysis of natural fallacy fallacy in his work Speech Acts where he makes a simple claim. Every claim of an objective and descriptive notion of logical inference relies on normative (or as he calls it evaluative) logical standards. There is no divorcing the logic that undergirds the conditional nature of language, particularly natural language, from evaluative logical criteria. Thus, any theory of complexity itself necessarily relies on normative criteria that two distinct camps of theoreticians might disagree on.

So, what this really boils down to is that Occam's razor presupposes a consistent normative framework on parsimony and complexity when being applied to distinct theories. That means one aspect of incommensurability is the dispute over the theory of parsimony that characterizes the theories themselves. Parties simply can dispute each other's claims on such matters.

Exemplification: Camp A asserts their theory is simpler, and camp B attempts to refute that claim asserting their theory is simpler. Any presumption that a third-party can make a determination objectively presumes that there is some non-normative framework from which two theories might be assessed. But what might such a framework look like? How does one measure the complexity of a theory? The number of words? The use of phrasal syntactic grammars to analyze natural language arguments? The topological characterization of natural language ontologies? The number of calculations or mathematical proofs involved? If one follows Alan Gross, should an analysis of the complexity of the rhetoric be a factor? It's easy to see how any sophisticated thinker could quickly become being at odds with another over what is parsimonious in a theory.

Without such a consensus on what constitutes "parsimonious scientific theory", the use of Occam's Razor has no teeth, because fundamentally, the notion of parsimony becomes just another aspect of incommensurability of scientific theory.

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  • I don't think that it is necessary to conclude that introducing a separate domain of discourse, let's say physicalism to mental questions, necessarily makes a theory more complicated. I can envision a theory with many simple domains of discourse, being more elegant than a massive theory that is full of ad hoc explanation in a monolithic domain of discourse.
    – J D
    Nov 13, 2023 at 19:37
  • Bringing up incommensurability in theories of Occam's razor itself is quite the illustrative maneuver. I hadn't thought to go meta on that level, so thank you for pointing me in that direction! Nov 14, 2023 at 13:33
  • Splitting hairs put me in therapy quite literally, so it's just nice to know there is some value in it somewhere. ; )
    – J D
    Nov 14, 2023 at 14:50

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