Most importantly, I strongly disagree with Bill's apparent view that experimental work in philosophy should avoid testing competing theories and instead stick to "unproblematic common ground" with minimal "theoretical baggage". How could you make theoretical progress with such a view?

This wasn't a "curious methodological choice" which supported a non-ontic picture "only by accident". It was a deliberate attempt to empirically test a prediction made by non-ontic Zelcer-like accounts. I don't see where the "confounded results" or "muddled interpretations" are.

4. They didn’t, therefore participants couldn’t have only used ontic criteria when making their judgements.

3. If they had only used ontic criteria, the two purported explanations would have ended up with similar CJ parameters.

2. We asked mathematicians to make ontic explanations about two 'identical' proofs (same underlying argument, different presentation).

1. Some people (e.g., Mark Zelcer) believe that ontic explanations don’t exist in mathematics. If they're right, then when you ask mathematicians to make judgements about the ontic notion of explanation, they will actually make judgements about the epistemic notion.

I'm very puzzled by this criticism. The logic of this methodological choice was the following.

Bill goes on to suggest that "experimentalists ought to avoid designing studies around controversial ideology" and that they should stick to "unproblematic common ground".

In a section entitled "Experiment and Ideology", Bill suggests that our decision to prompt participants to think about explanation onticly (roughly, in a manner independent of how a reader might react to the purported explanation) was a "curious methodological choice" which "courted confusion".

Bill discusses a comparative judgement study that Pablo Mejía Ramos, @drtanyaevansnz.bsky.social, Colin Rittberg and I did a few years ago, concerning mathematicians' intuitions about mathematical explanations: doi.org/10.1007/s105...