Not so distinctively mathematical explanations: topology and dynamical systems 

2022, Synthese [Springer]

(Jha, A., Campbell, D., Wilson, P. & Montelle, C.)  

https://link.springer.com/article/10.1007/s11229-022-03697-9 

This paper argues that distinctively mathematical explanations are actually causal explanations in disguise because they sneak in reasoning about particular forces in the associated conditional.  

A mathematical model of Dignaga’s hetu-cakra 

2020, Journal of Indian Council of Philosophical Research [Springer]

https://doi.org/10.1007/s40961-020-00217-3 

This paper provides a formulation to deconstruct styles of analogical reasoning in Indian philosophy.  

[revise and resubmit: title changed] Is Temperature a Continuous Function? (draft available)

(With Campbell, D., Montelle, C. & Wilson, P.)

This paper dispels the misconception that the continuity of temperature is necessary in a non-causal sense, by examining evidence of inter-facial thermal resistance in phase transitions, in slip flows and at material interfaces. It further argues that, unlike the received view that continuum models are indispensable in providing explanations of physical phenomena, discontinuous models may actually have greater empirical adequacy and explanatory relevance.  

Geometry and dynamics: Tossed sticks and the bogus mathematical explanations of alleged physical facts (draft available)

(With Campbell, D., Montelle, C. & Wilson, P.)

This paper highlights a crucial difference between geometrical and dynamical reasoning in purported mathematical explanations of physical phenomena, which has been surprisingly neglected in the debate on mathematical explanations so far. This, we argue, makes for an appealing case that geometrical explanations may not ‘constrain’ physical phenomena in some non-causal sense.    

Are mathematical explanations (of physical phenomena) causal explanations in disguise? (draft available)

(with Skow, B.)

We argue that given how mathematical explanations conceal contingent facts in their conditionals, there is no fundamental difference between a mathematical explanation of a physical phenomenon and an ordinary application to mathematics to a physical phenomenon.  

The law of large numbers and other statistical generalities: Why do continuum models work, after all? 

We investigate the physical foundations for the claim that certain macro-level explanations and occurrences are probabilistically, or otherwise, independent of the micro-level details of a system. We argue that this the explanation for this fact may ultimately be forthcoming from deep conservation principles, and not only statistical generalities. 

Does topology provide sufficient structure for distinctively mathematical explanations? (draft available)

(With Campbell, D., Montelle, C. & Wilson, P.)

This paper argues that assumptions such as continuity or smoothness employed in a topological explanation are realised in the physical world only as contingent causal facts and packaging such assumptions in the conditional of a purported DME amounts to manipulating a run-of-the-mill causal explanation to appear like a non-causal explanation.

A Buddhist take on mathematical modelling (slides available)

(Proceedings of the University of Cambridge Postgraduate Conference: Dynamical Encounters Between Buddhism and the West)

This paper argues that a perspectival, contextual and mind-dependent view of mathematical models can be read closely to the ontological middle ground proposed by Buddhist philosophers like Nagarjuna, where no concept exists independently of human thought. 

The tale of a medieval Indian scroll: mathematical discoveries (slides available)

(Part of a University of Canterbury project on the history and mathematics of medieval astronomical scroll.