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 (...) quasi-erotetic solution which provides a remedy to the problem in the form of an additional necessary condition on explanation. (shrink)

At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit, we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs guide their choices. Second, (...) RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later. (shrink)

A subarea of the debate over the nature of evolutionary theory addresses what the nature of the explanations yielded by evolutionary theory are. The statisticalist line is that the general principles of evolutionary theory are not only amenable to a mathematical interpretation but that they need not invoke causes to furnish explanations. Causalists object that construction of these general principles involves crucial causal assumptions. A recent view claims that some biological explanations are statistically autonomous explanations (SAEs) whereby phenomena are accounted (...) for statistically and which prescind from micro-causal details. I raise three major problems for this account and then advance a view which unifies SAEs as mathematical explanations: the MSAE view. The MSAE view not only resolves the issues bedeviling the original SAE account but serves to importantly broaden the class of non-causal explanations in population biology. (shrink)