The superiority of economics and the economics of externalism – a sketch

ArgumentThe article takes as its starting point the relationship of academic economists and the wider society. First, various bodies of literature that deal empirically with this matter are discussed: epistemologically, they range from a bold structuralism via a form of symbolic interactionism to a form of radical constructivism. A Bourdieusian approach is recommended to complement these perspectives with a comprehensive perspective that is sensible to the cultural differences between social groups. Starting from the established notions of field, capital and habitus, the article then attempts to go the initial steps towards formulating a theory of the specificity of academic economics, taking Germany as its example. For that it uses and compares in-depth interviews of recognized and non-recognized German economics students. It shows the thorough interweaving of specific normative and positive dispositions into a conviction of objectivity and disinterestedness. This exploratory empirical induction furthers follow-up questions, the empirical answering of which may help to gain a more complete understanding of the actions and thoughts of economists in their specific contexts.

Recursive Abduction and Universality of Physical Laws: A Logical Analysis Based on Case Studies

The paper studies some cases in physics such as Galilean inertia motion and etc., and hereby, presents a logical schema of recursive abduction, from which we can derive the universality of physical law in an effective logical path without infinite induction asked. Recursive abduction provides an effective logical path to connect a universal physical law with finite empirical observations basing on the both quasi-law tautology and suitable recursive dimension, the two new concepts introduced in this paper. Under the viewpoint of recursive abduction, the historically lasting difficulty from Hume’s problem naturally vanishes. In Hume’s problem one always misunderstood the universality of natural law as a product of empirical induction and the time-recursive issue as an infinitely inductive problem and, thus, sank into the inescapable quagmire. The paper gives a concluding discussion to Hume’s problem in the new effective logical schema.

Generality, generalization, and induction in Poincaré’s philosophy

This article examines Henri Poincaré’s philosophical conceptions of generality in mathematics and physics, and more specifically his claim that induction in experimental physics does not consist in extending the domain of a predicate. It first considers Poincaré’s view that generalization is not a means to reach generality and that the issue of infinity is related to the theme of generality. It then shows how generality in mathematics and physics is construed by Poincaré in a very specific way and how he analyzes empirical induction in physics. It also analyzes the distinction suggested by Poincaré between generalizations used in mathematical physics and generalizations used by ‘naturalists’. In particular, it explains the distinction between mathematical generality and the so-called predicative generality. Finally, it compares Poincaré’s concern regarding empirical induction with Nelson Goodman’s ‘new riddle of induction’, arguing that ‘the new riddle of induction’ was originally formulated by Poincaré half a century earlier.

From numerical concepts to concepts of number

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas.