Science indisputably provides us with explanations. It is natural to 
think that these include non-contingent explanations: explanations where 
the explanans and the explanandum necessarily co-vary. Potential 
examples in contemporary science include mathematical explanations, 
geometrical explanations, topological explanations and grounding 
explanations. While some progress has been made in understanding how 
these explanations are used, their metaphysical foundation remains 
shaky. I raise a general puzzle about non-contingent explanations, in 
the form of a trilemma facing scientific realists who endorse them: 
either scientific explanation is disjunctive in character, or 
non-contingent explanations are not genuinely explanatory, or 
non-contingent explanations incur a substantial metaphysical commitment 
in terms of objective structure amongst (physical and metaphysical) 
impossibilities. I then raise some objections against each horn of the 
trilemma.


Some relevant background reading in case that's helpful:

Jansson, L. and Saatsi, J. [2019]. “Explanatory Abstractions”, The 
British Journal for the Philosophy of Science 70 (3): 817–844

Shaheen, J. [2017]. “The Causal Metaphor Account of Metaphysical 
Explanation, Philosophical Studies 174(3): 553-578.

Wilson, A. [2018]. “Grounding Entails Counterpossible Non-Triviality”, 
Philosophy and Phenomenological Research 96(3): 716-728.