In this paper I investigate two notions of concepts that have played a dominant role in 20th century philosophy of mathematics. According to the first, concepts are definite and fixed; in contrast, according to the second notion concepts are open and subject to modifications. The motivations behind these two incompatible notions and how they can be used to account for conceptual change are pres...

Causes of reduced visual function can be grouped into three broad categories, pre-retinal (i.e. optical), retinal/neural, and a combination of the two. It is now widely accepted that one of the penalties of longevity is the eventual development of cataracts, which scatter light and reduce visual performance. To date, the generally accepted form of treatment is the surgical removal of the catara...

BACKGROUND INFORMATION Marine nematodes belonging to the Stilbonematidae (Desmodoridae) family are described as living in obligatory association with sulfur-oxidizing chemoautotrophic ectosymbionts. The symbiotic bacteria carrying out this chemosynthesis should contain elemental sulfur in periplasmic granules as sulfur granules of chemoautotrophic endosymbionts described in various marine inver...

The Willmore energy for Frenet curves in quaternionic projective space HP is the generalization of the Willmore functional for immersions into S. Critical points of the Willmore energy are called Willmore curves in HP. Using a Bäcklund transformation on Willmore curves, we generalize Bryant’s result on Willmore spheres in 3–space: a Willmore sphere in HP has integer Willmore energy, and is give...

This announcement describes research concerning local quasiconvexity, coherence, compact cores, and local indicability for fundamental groups of certain 2-complexes.

Harmonic maps X:(S,h) --> N from a 2-manifold S with indefinite metric h to a semi-Riemannian manifold N are characterized, assuming that the induced metric I is nondegenerate. Except in one very special case, the characterizations involve a canonically determined holomorphic quadratic differential on a naturally chosen conformal structure. This is surprising because the Euler-Lagrange equation...

In this paper, we explicate the method of Investigative Ordinary Language Philosophy (IOLP). The term was coined by John Cook to describe unique philosophical approach Frank Ebersole. We argue that (i) IOLP is an overlooked yet valuable grounded in our everyday experiences and concerns; (ii) as such, Ebersole important but neglected figure history ordinary language philosophy.