Prototypes, exemplars, and theoretical & applied ethics

Concepts are mental representations that are the constituents of thought. EdouardMachery claims that psychologists generally understand concepts to be bodies of knowledge or information carrying mental states stored in long term memory that are used in the higher cognitive competences such as in categorization judgments, induction, planning, and analogical reasoning. While most research in the concepts field generally have been on concrete concepts such as LION, APPLE, and CHAIR, this paper will examine abstract moral concepts and whether such concepts may have prototype and exemplar structure. After discussing the philosophical importance of this project and explaining the prototype and exemplar theories, criticisms will be made against philosophers, who without experimental support from the sciences of the mind, contend that moral concepts have prototype and/or exemplar structure. Next, I will scrutinize Mark Johnson's experimentally-based argument that moral concepts have prototype structure. Finally, I will show how our moral concepts may indeed have prototype and exemplar structure as well as explore the further ethical implications that may be reached by this particular moral concepts conclusion. © 2011 Springer Science+Business Media B.V.

The abelianization of the Johnson kernel

We prove that the first complex homology of the Johnson subgroup of the Torelli group Tg is a non-trivial, unipotent Tg-module for all g ≥ 4 and give an explicit presentation of it as a Sym H 1(Tg,C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the infinitesimal Alexander invariant of the associated graded Lie algebra of G. In this setup, we also obtain a precise nilpotence test. © European Mathematical Society 2014.