Olav Wiegand, Interpretationen der Modallogik: Ein Beitrag zur phanomenologischen Wissenschaftstheorie, 1998.
This book presents a very thorough, orderly exposition of the main features of Edmund Husserl’s phenomenological reflections on the formal sciences: formal logic and formal mathematics. The exposition is accurate, detailed and comprehensive from a scholarly viewpoint and clearly appreciative, from the critical perspective of an author who manifestly knows and is concerned about the themes covered. In addition, Wiegand enriches his exposition with helpful discussions relating Husserl’s approach to the prevailing trends of his own time, as well as to developments in the field since then. His discussion of affinities between Husserl and Hilbert, as well as of basic differences between them, is especially helpful.
Several distinctive features stand out in Wiegand’s approach. The first is his emphasis upon the centrality of semantic concepts, “truth” and “falsity,” warranting his singling out of what he calls “phenomenological semantics” as an independent component of the phenomenological theory of knowledge. Second is his comprehensive account of that discipline, whose object he takes to be the genetic analysis of concepts, “formal-logical truth and falsehood,” tracing their origins back to the regularities of natural language and of pre-predicative perception, at the same time emphasizing the difference between the typical generalities of experience and life-world language and the exact concepts of formal logic, the results of requisite formalization and idealization. Thirdly, his approach takes formal-logical truth and falsehood to be modalizations, thereby inserting phenomenological semantics within the context of interpretations of modal logic, predominantly those of Quine and Hintikka.
Based upon his careful exposition of Husserl’s position on the matter, Wiegand finally develops his own contribution to the field. In doing so, he aims at two results. First, he attempts to show that phenomenological semantics can provide a systematic explication of the outstaning phenomenological and epistemological problems involved in other approaches, as well as providing an analysis that is free of those difficulties. Secondly, by interpreting the concept of proof as a mathematical modality, he attempts to provide a sharp analysis of the distinction between formal logic and mathematics, despite their co-extensiveness. In that connection, he emphasizes the primacy of mathematical intuition over formal-logical reflection. In developing that crucial point, Wiegand provides an insightful discussion of Husserl’s commitment to the ideal of a definite manifold, as well as of Goedel’s theorm. Wiegand’s position even leads his to suggest that Husserl’s phenomenological semantics should have made him skeptical with regard to his own cherished concept of a definite manifold.