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# Unifying the debates: mathematical and non-causal explanations

**Workshop**: Unifying the debates: mathematical and non-causal explanations

** Venue**: IHPST, Paris

** Dates**: 28-29 June, 2017 .

** Participants**:

- Robert Batterman (University of Pittsburgh);
- Marc Lange (University of North Carolina at Chapel Hill);
- André Ariew (University of Missouri Columbia);
- Holly Andersen (Simon Fraser University);
- Lina Jansson (The University of Nottingham);
- Juha Saatsi (University of Leeds);
- Denis Walsh (IHPST/University of Toronto);
- Philippe Huneman (IHPST/CNRS/University Paris 1 Sorbonne);
- Daniel Kostic (IHPST/CNRS/University Paris 1 Sorbonne);
- Max Kistler (IHPST/CNRS/University Paris 1 Sorbonne);
- Francesca Merlin (IHPST/CNRS/University Paris 1 Sorbonne);
- Francesca Poggiolesi (IHPST/CNRS/University Paris 1 Sorbonne) ;
- Jean Gayon (IHPST/CNRS/University Paris 1 Sorbonne).

**Workshop description**

In the last couple of years a few seemingly independent debates on several specific features of scientific explanation have emerged. There is a debate about the nature of mathematical explanations in sciences and their explanatory power (Batterman 2009; Batterman and Rice 2014; Bokulich 2008, 2011; Lange 2013, 2015). In this debate, on the one hand Batterman claims that the story that helps us delimit models into universality classes is that which makes the mathematical explanations explanatory (Batterman 2009, Batterman and Rice 2014). On the other hand Lange claims it’s their modality, i.e. the mathematical necessity which makes the explanandum logically inevitable (Lange 2013, 2015). There is also a debate on the nature of non-causal explanations (Chirimuuta 2016; Jansson forthcoming; Kostic manuscript; Pinnock 2014; Saatsi and Pexton 2013; Skow 2014) in which various features of non-causal explanations are discussed, e.g. are non-causal explanations symmetrical and whether explanatory symmetry is a bad thing in non-causal context (Jansson), or if they support traditionally conceived counterfactuals, such as interventionism (Saatsi and Pexton 2013; Kostic manuscript). There is of course the debate about the relation between causal and non-causal explanations, especially the issue of whether non-causal explanations can be seen as an alternative, or sometimes a complement to mechanistic and causal ones (Andersen 2015; Huneman 2015), given that the mechanistic and causal explanations seem to be well understood by now (Craver 2007, 2013; MDC 2000; Salmon 1984; Woodward 2003). There is a debate on statistical interpretation of the Modern Synthesis theory of evolution, according to which the post-Darwinian theory of natural selection explains evolutionary change by citing statistical properties of populations and not the causes of change (Walsh 2015). And finally there is an emerging debate on the nature of so called topological explanations (Bechtel and Levy 2013; Craver 2016; Darasson 2015; Huneman 2010; 2015; Kostic 2016, Rathkopf 2015), which is another type of explanation that is not yet fully understood. This type of explanation is considered by some to be a variety of mechanistic explanation (Bechtel and Levy 2013; Craver 2016) because they believe that representation of causal relations or representation of ontic structures plays an important explanatory role or that good explanations have to take into account (at the very least) how the mathematical (in this case specifically topological) structure is instantiated in a real system. On the other hand, Huneman, (2010, 2015), Rathkopf (2015) Darrason (2015) and Kostic (2016) argue that the mathematical structure itself can be explanatory on its own regardless of the instantiations.

The aim of the workshop is to unify all these debates around several overlapping questions. These questions are:

- Are there genuinely or distinctively mathematical and non-causal explanations?
- Are all distinctively mathematical explanations also non-causal?
- In virtue of what are they explanatory, is it the finding of critical exponents which delimit universality classes (Batterman) or logical necessity underlying a mathematical structure (Lange)?
- Does the instantiation, implementation or in general, does applicability of mathematical structures to variety of phenomena and systems play any explanatory role?
- What makes them universally applicable?
- Is it the generacity (Huneman) in which generic and rudimentary features of particular types of mathematical explanations (such as topological) that make them universally applicable?
- Or is it because they explain by providing an understanding of mathematical structure independently from being instantiated in any particular system (Kostic)?
- Or if they can be explanatory only when the details of instantiation are provided (Craver), is it then some ontological fact that makes them universally applicable to a variety of very diverse phenomena, e.g. is there some fundamental physical fact in virtue of which many real world systems exhibit or instantiate certain topologies?

The participants of the workshop are the proponents of opposing views in each of the debates, some of whom take part in several of the debates, not just in one. The workshop will provide a platform for unifying the debates around several key issues and thus open up avenues for better understanding of mathematical and non-causal explanations in general, but also, it will enable even better understanding of key issues within each of the debates.

**Contact person**: Daniel Kostic (IHPST/CNRS/University Paris 1 Sorbonne); Email: daniel.kostic@gmail.com