The Nature and Status of Concepts in Phenomenology

This essay examines the debate that arose immediately following the publication of the first volume of Edmund Husserl's Ideas regarding the model of concept formation that Husserl sketches in that work. After a brief overview of the relevant passages from the Ideas, I take up essay-length responses to Husserl by August Messer, Theodor Elsenhans, and Heinrich Gustav Steinmann. Reflecting a variety of empiricist commitments, all three authors are skeptical that concepts can be expected to embody the essence of a corresponding phenomenon. Subsequently, I review the responses to these critiques offered by Husserl, his then-assistant Edith Stein, and Paul Linke. For Linke, it is at least highly probable that certain concepts derive their content from an apprehension of essence. The empiricist alternative, he argues, is fatally unstable. Husserl and Stein, meanwhile, offer a more forceful defense of this position. Unless we allow that certain kinds of concepts can originate from a grasp of essence, they argue, we will be unable to explain how certain manifest cognitive accomplishments are possible.

Sense-Perception, Reasoning and Forms in Plotinus

This paper discusses the role of innate concepts derived from Intellect in Plotinus’ account of cognition of the sensible realm. Several passages have been claimed as evidence for such innateness, but an analysis of them shows that they do not support this claim. It is tentatively suggested that, nevertheless, some very general concepts such as difference, sameness and being are integral to the faculty of sense and play a crucial role in concept formation. It is further argued that reasoning about the sensible realm takes place to a large extent without the involvement of the higher realms of Plotinus’ hierarchy of being. Clearly, however, for value concepts such as those of goodness, justice and beauty human beings are dependent upon an illumination from Intellect.

Domestication of Mathematical Pathologies

Certain mathematical objects bear the name “pathological” (or “paradoxical”). They either occur as unexpected and (temporarily) unwilling in mathematical research practice, or are constructed deliberately, for instance in order to delimit the scope of application of a theorem. I discuss examples of mathematical pathologies and the circumstances of their emergence. I focus my attention on the creative role of pathologies in the development of mathematics. Finally, I propose a few reflections concerning the degree of cognitive accessibility of mathematical objects. I believe that the problems discussed in the paper may attract the attention of philosophers interested in concept formation and the development of mathematical ideas.

Materiality and the Prehistory of Number

Modern humans produce number systems with striking cross-cultural similarities. Understanding prehistoric numerical cognition, however, requires looking at when cognitive prerequisites emerged: morphological factors like parietal encephalization; abilities like quantity perception, language, concept formation and manipulation, categorization, and ordinality; and demographic factors suggesting societal motivations for numerical development. These establish the “probably not before” timeline for numerical emergence. The question is then approached from the earliest emergence of unambiguous numbers in Mesopotamia, clay tokens used in the late 4th millennium and subsequent numerical notations. With tokens and notations, the archaeological and textual evidence of precursor technologies like tallies and fingers form a sequence capable of elaborating the innate perceptual experience of quantity into simple counting sequences and complex mathematics. Along with the cognitive prerequisites, the sequence of material forms also provides insight into potential archaeological evidence (material forms and demographic factors) that might indicate numerical emergence in prehistoric times.