Are mathematical explanations causal explanations in disguise? 

2024, Philosophy of Science

(with Campbell, D., Montelle, C. and Wilson, P.)

https://doi.org/10.1017/psa.2024.8 

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

On the continuum fallacy: is temperature a continuous function?  

2023, Foundations of Physics 

(with Campbell, D., Montelle, C., and Wilson, P.)  

https://doi.org/10.1007/s10701-023-00713-x 

This paper argues against the widely-held misconception that temperature is necessarily represented as a continuously varying function. It also argues that discontinuum models of temperature variation may actually have greater explanatory relevance and empirical adequacy in some cases.   

Does topology provide sufficient structure for non-causal explanations?

2023, PhD thesis (Foundations of Applied Mathematics), University of Canterbury, NZ

https://ir.canterbury.ac.nz/items/abeca6d2-8aea-4d0a-a456-a4fce5a823b0

This thesis examines some foundational issues in the applicability of topology to the natural world and their bearing on allegedly non-causal (topological) explanations of dynamical and complex systems. 

Not so distinctively mathematical explanations: topology and dynamical systems 

2022, Synthese  

(with Campbell, D., Montelle, C., and Wilson, P.)

https://doi.org/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

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

This paper provides a formulation to deconstruct styles of analogical reasoning in Indian philosophy using the ideas of bounded rationality and the Buddhist method of reasoning through analogies.  

Foundations of Thermodynamics and Statistical Mechanics

1. On the heat-work distinction: a response to Robertson and Prunkl (draft available)

In a recent paper, “Is Thermodynamics Subjective?”, Robertson and Prunkl (Philosophy of Science, 2023) suggest  that Quantum Statistical Mechanics (QSM) provides an objective way to draw the heat-work  distinction. This is because, so they argue, one does not need to appeal to anthropomorphic  notions of (dis)order and ignorance in order to draw this distinction, as would be in the case  of Classical Statistical Mechanics (CSM) or phenomenological Thermodynamics (TD). I show  the limitations of this argument by arguing that a) the heat-work distinction drawn in QSM  is actually analogous to that in CSM, in that QSM does not provide any additional physical  insights into this distinction, and b) the heat-work distinction in both QSM and CSM is fixed  no more objectively than in TD.

2. Irreversibility as underdetermination (draft available)

I suggest that it is possible to bring together the different views of irreversibility as in Thermodynamics (TD) and Boltzmannian Statistical Mechanics (BSM) via an appeal to an epistemic notion of irreversibility. The epistemic notion that I suggest is based on underdetermination of the past states of a system, an idea that, I show, is popular in the SM literature (as Markovian dynamics) but not so popular in the TD literature. I further show why Markovian dynamics is not intrinsic  to large statistical systems, unlike mainstream views, and is instead a byproduct of the way statistical systems are idealised and studied in their infinite  limits. 

3. Projection operators and non-equilibrium temperature

(with te vrugt, Michael and Hoyningen-Huene, Paul)

We look into the interpretations of temperature fields in Mori-Zwanzig formalism and examine its implications for obtaining a consistent definition of non-equilibrium temperature when the assumption of local thermal equilibrium is relaxed.   

4. Logical and thermodynamic irreversibility: the schism 

I take a critical look at the account of Ladyman et al. (2007) and make a case for a sharper distinction between logical and thermodynamic irreversibility by taking a stronger view of irreversibility as irrecoverability, specifically by looking into many-to-one dissipative mappings in Landauer's Principle.  

Philosophy of Mathematical Modelling 

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

(with Campbell, D., Montelle, C. and 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.

2. Physical and mathematical reasoning

(with Campbell, D., Montelle, C. and Wilson, P.)

We argue that the applications of mathematics to the physical world are not dictated by Platonic connections but rather tangible physical principles, such as conservation principles. Mathematical reasoning, as applied to the physical world, works because it invokes or reflects physical principles. We demonstrate this by building upon Mark Levi's brilliant book, The Mathematical Mechanic (Princeton University Press, 2012) that provides various ways of understanding the physical basis of various mathematical results.  

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

(with Campbell, D., Montelle, C. and Wilson, P.)

We investigate the physical foundations for the observation that certain macro-level explanations and occurrences are probabilistically, or otherwise, independent of the micro-level details of a system in a way that stable statistical generalities are observed at the macro-level. We argue that the explanation for this observation may ultimately be forthcoming from the way complex micro-level phenomena are mathematically approximated via the central limit theorem. 

Buddhist Philosophy and the History of Indian astronomy 

1. A Buddhist take on mathematical modelling (slides available)

(Proceedings of the Asia-Pacific Philosophy of Science Conference, 2023) 

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 the Buddhist philosophical school of Madhyamaka, which argues no concept exists independently of human thought. 

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

(with Montelle, C., Cidami, S. and Dhammaloka, J. : part of a University of Canterbury project on the history and mathematics of medieval astronomical scroll)

We investigate the historical and the mathematical origins of a rare seven-metre-long-medieval-Sanskrit scroll which, we believe, holds important lessons for historians of science.