Abstract: According to current accounts, a satisfactory mechanistic explanation should include all the relevant components of the mechanism (entities, activities and organizational features) and exhibit productive continuity from input to output conditions. It is not specified, however, how this kind of ‘mechanistic completeness’ can be demonstrated. Experimental interventions can demonstrate that a mechanism is necessary to produce a phenomenon. Nevertheless, interventions do not demonstrate that a mechanism is sufficient for producing a phenomenon. This creates a cluster of related problems: it is not clear to what extent the explanation is complete, whether the mechanism postulated by the explanation can be detached from the system in which it is embedded and treated as an independent module, and where a mechanistic explanation can safely bottom out.
I argue that mathematical modeling of mechanisms can provide a solution to these sufficiency related issues. More and more studies in leading journals complement traditional descriptions of mechanisms supported by the experimental practices of molecular biology with quantitative models aiming to demonstrate that the proposed mechanism can generate the quantitative-dynamic aspects of a phenomena in the right amount/intensity, and thus support the claim that the mechanism is sufficient to produce the phenomenon. While this kind of extrapolative inferences from surrogate mathematical models need to be carefully regimented, they provide a workable solution to the ‘explanatory leakage’ problem whereby it is not clear how systemic a mechanism needs to be and how deep it needs to bottom out in order to explain a phenomenon.
Different concepts define species at the pattern-level grouping of organisms into discrete clusters, the level of the processes operating within and between populations leading to the formation and maintenance of these clusters, or the level of the inner-organismic genetic and molecular mechanisms that contribute to species cohesion or promote speciation. I argue that, unlike single-level approaches, a multi-level framework takes into account the complex sequences of cause-effect reinforcements leading to the formation and maintenance of various patterns, and allows for revisions and refinements of pattern-based characterizations in light of the gradual elucidation of the causes and mechanisms contributing to pattern formation and maintenance.
The emergence of systems biology is marked by a revival of mathematical modeling approaches to causal-mechanistic explanations and associated experimental practices in molecular biology. From a philosophical standpoint, this ‘mathematical turn’ in biology constitutes an excellent opportunity to investigate the relationship between deductive-nomological and causal-mechanistic accounts of scientific explanation. I argue that mathematical models in systems biology integrate substantial knowledge of molecular mechanisms with the application of laws, modeling and analysis strategies borrowed from chemistry, cybernetics and systems theory in order to yield quantitative mechanistic explanations. Mechanism schemas obtained by abstracting high-resolution biochemical details act as bridges between molecular mechanistic explanations and mathematical models of networks. In turn, mathematical models account for poorly understood aspects of biological phenomena, most notably minute quantitative-dynamic features. Thus, in actual scientific practice, deductive-nomological and casual-mechanistic approaches to explanation are not mutually exclusive, but complementary. Furthermore, mathematical models can reveal unsuspected ‘black boxes’ and motivate revisions of mechanistic explanations. This interplay between mechanistic explanations and their mathematical counterparts constitutes a progressive research approach that generates explanations of novel phenomena, and reveal strange properties of molecular mechanisms that have thus far escaped our attention.