Rob Moir, Department of Applied Mathematics, Western University

Toward A Computational Model of Scientific Discovery
Traditionally in philosophy of science, the process of discovery of theories or hypotheses in science has been regarded as being non-rational and therefore not accessible to philosophical scrutiny. For Reichenbach's famous epistemological distinction between the "context of discovery" (idea generation) and the "context of justification" (idea defense), it is the latter that is the focus of most philosophical scrutiny of science, and the former, in Reichenbach's view, only insofar as objective judgements of inductive evidential support can be made.[1] Indeed, Hempel (1985) stated that automatic genera- tion of interesting scientific hypotheses by computer is impossible.[2] With the advent of advanced computing machines and superior AI, this dogma is now coming into question.[3] Many philosophers of science now challenge this traditional view, and promote rational views of scientific discovery by emphasizing distinct structure to the discovery process, such as methodological patterns, analogical reasoning, mental modeling and reconstruction by explicit computation.[4] The approach I propose, which I believe is novel, could be construed as a mixture of the approaches just listed. I suggest that from a direct examination of historical evidence we can abstract a discovery pattern based on key aspects of the actual methods used, a pattern potentially limited by the range of evidence considered. I shall argue that the existence of this pattern shows not only that discovery processes can be rational but that they can even display an important algorithmic component. I will briefly review three examples of the discovery of important theories in physics (in optics, electromagetism and QED) and show how, subsequent to the identification of an appropriate problem space given empirical knowledge of the phenomenon, they all follow a pattern of recursive search through a problem space to solve a kind of inverse problem (combined with a refinement or variation of the characterization of the problem space).[5] These instances of success of a computational search method in several landmark discoveries in physics suggests that a deeper examination of the computational character of the discovery process in the history of science is needed.

[1] Glymour and Eberhardt, "Hans Reichenbach", The Stanford Encyclopedia of Philosophy,

[2] Hempel (1985) "Thoughts on the Limitations of Discovery by Computer".

[3] See, e.g., Schmidt and Lipson (2009) "Distilling Free-Form Natural Laws from Experimental Data", Science 324, 81, and Brunton, Proctor and Kutz (2015) "Discovering governing equations from data: Sparse identification of nonlinear dynamical systems", arXiv:1509.03580.

[4] Schickore, "Scientific Discovery", The Stanford Encyclopedia of Philosophy,

[5] There may be a case for modeling the examples in terms of the gradual formation and refinement of a (flexible) constraint satisfaction problem (CSP), followed by its solution, making a distinct connection to contemporary AI.