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An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductivemathematical account, because it is modelled on the deductivenomological account, is unlikely to satisfy these desiderata. I provide a counterfactual account of DME, the Narrow (...) 

Socalled ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any ntuple pendulum system on the ground that such explanations are (...) 

This paper advances the view that some explanations in cognitive science are extramathematical explanations. Demonstrating the plausibility of this interpretation centers around certain efficient coding cases which ineliminably enlist information theoretic laws, facts and theorems to identify inprinciple, mathematical constraints on neuronal information processing capacities. The explanatory structure in these cases is shown to parallel other putative instances of mathematical explanation. The upshot for cognitive mathematical explanations is thus twofold: first, the view capably rebuts standard mechanistic objections to nonmechanistic explanation; (...) 

Lange’s collection of expanded, mostly previously published essays, packed with numerous, beautiful examples of putatively noncausal explanations from biology, physics, and mathematics, challenges the increasingly ossified causal consensus about scientific explanation, and, in so doing, launches a new field of philosophic investigation. However, those who embraced causal monism about explanation have done so because appeal to causal factors sorts good from bad scientific explanations and because the explanatory force of good explanations seems to derive from revealing the relevant causal (or (...) 





Proponents of ontic conceptions of explanation require all explanations to be backed by causal, constitutive, or similar relations. Among their justifications is that only ontic conceptions can do justice to the ‘directionality’ of explanation, i.e., the requirement that if X explains Y , then notY does not explain notX . Using topological explanations as an illustration, we argue that nonontic conceptions of explanation have ample resources for securing the directionality of explanations. The different ways in which neuroscientists rely on multiplexes (...) 

Marcello Barbieri has presented code biology as an alternative to the Peircean approach to biosemiotics. Some critics questioned the viability of code biology on grounds that Barbieri’s conception of science is limited. It has been argued that code biology’s mechanistic tendency is the cause of the allegedly limited conception of science. In this paper, I evaluate the scientific viability of the code model from the perspective of scientific realism in the philosophy of science. To be more precise, I draw on (...) 

Opinionated state of the art paper on mathematical explanation. After a general introduction to the subject, the paper is divided into two parts. The first part is dedicated to intramathematical explanation and the second is dedicated to extramathematical explanation. Each of these parts begins to present a set of diverse problems regarding each type of explanation and, afterwards, it analyses relevant models of the literature. Regarding the intramathematical explanation, the models of deformable proofs, mathematical saliences and the demonstrative structure of (...) 

It is generally accepted that, in the cognitive and neural sciences, there are both computational and mechanistic explanations. We ask how computational explanations can integrate into the mechanistic hierarchy. The problem stems from the fact that implementation and mechanistic relations have different forms. The implementation relation, from the states of an abstract computational system to the physical, implementing states is a homomorphism mapping relation. The mechanistic relation, however, is that of part/whole; the explaining features in a mechanistic explanation are the (...) 

The increasing preponderance of opinion that some natural phenomena can be explained mathematically has inspired a search for a viable account of distinctively mathematical explanation. Among the desiderata for an adequate account is that it should solve the problem of directionality and the reversals of distinctively mathematical explanations should not count as members among the explanatory fold but any solution must also avoid the exclusion of genuine explanations. In what follows, I introduce and defend what I refer to as a (...) 

In the last two decades, philosophy of neuroscience has predominantly focused on explanation. Indeed, it has been argued that mechanistic models are the standards of explanatory success in neuroscience over, among other things, topological models. However, explanatory power is only one virtue of a scientific model. Another is its predictive power. Unfortunately, the notion of prediction has received comparatively little attention in the philosophy of neuroscience, in part because predictions seem disconnected from interventions. In contrast, we argue that topological predictions (...) 

A popular view presents explanations in the cognitive sciences as causal or mechanistic and argues that an important feature of such explanations is that they allow us to manipulate and control the explanandum phenomena. Nonetheless, whether there can be explanations in the cognitive sciences that are neither causal nor mechanistic is still under debate. Another prominent view suggests that both causal and noncausal relations of counterfactual dependence can be explanatory, but this view is open to the criticism that it is (...) 



This paper provides a sorelyneeded evaluation of the view that mathematical explanations in science explain by unifying. Illustrating with some novel examples, I argue that the view is misguided. For believers in mathematical explanations in science, my discussion rules out one way of spelling out how they work, bringing us one step closer to the right way. For nonbelievers, it contributes to a divideandconquer strategy for showing that there are no such explanations in science. My discussion also undermines the appeal (...) 

Lange argues that some natural phenomena can be explained by appeal to mathematical, rather than natural, facts. In these “distinctively mathematical” explanations, the core explanatory facts are either modally stronger than facts about ordinary causal law or understood to be constitutive of the physical task or arrangement at issue. Craver and Povich argue that Lange’s account of DME fails to exclude certain “reversals”. Lange has replied that his account can avoid these directionality charges. Specifically, Lange argues that in legitimate DMEs, (...) 

Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to refocus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one. 

Recent literature on noncausal explanation raises the question as to whether explanatory monism, the thesis that all explanations submit to the same analysis, is true. The leading monist proposal holds that all explanations support changerelating counterfactuals. We provide several objections to this monist position. 1Introduction2ChangeRelating Monism's Three Problems3Dependency and Monism: Unhappy Together4Another Challenge: Counterfactual Incidentalism4.1Highgrade necessity4.2Unity in diversity5Conclusion. 