This volume analyzes and studies how vagueness occurs and matters as a specific problem in the context of theories that are primarily about something else.

This volume focuses on constructivism, which is here intended as a general philosophical attitude arising from reflection upon mathematics. We are concerned with the ways in which this idea is applied in science and with the theoretical reflections these applications give rise to. For this purpose this volume presents different sides of the general idea of constructivity, with the intention of getting a broader, and hopefully insightful, understanding of questions such as ‘what is a construct...

This volume focuses on constructivism, which is here intended as a general philosophical attitude arising from reflection upon mathematics. We are concerned with the ways in which this idea is applied in science and with the theoretical reflections these applications give rise to. For this purpose this volume presents different sides of the general idea of constructivity, with the intention of getting a broader, and hopefully insightful, understanding of questions such as ‘what is a construct...

Material kept in the National Library of Finland shows that from 1963 until 1969 Erik Stenius (1911–1990) worked on a book on antinomies , having been invited by the Dutch logician Evert Beth (1908–1964) to contribute a monograph to the North-Holland series Studies in Logic and the Foundations of Mathematics . The book was never published, but the manuscript has been found, and it is the purpose of this note to report on this finding.

Richard Tieszen's new book1 is a collection of fifteen articles and reviews, spanning fifteen years, presenting the author's approach to philosophical questions about logic and mathematics from the point of view of phenomenology, as developed by Edmund Husserl in the later phase2 of his philosophical thinking known as transcendental phenomenology, starting in 1907 with the Logical Investigations and characterized by the introduction of the notions of ‘reduction’. Husserlian transcendental phenomenology as philosophy of mathematics is described as one that ‘cuts across’ (...) different philosophical positions, such as platonism, nominalism, fictionalism, Hilbertian formalism, etc. but, at the same time, as having built in the conceptual tools which allow one not to incur the kinds of problems which are usually related to one's preferred approach. Phenomenology centers around the notion of intentionality3 or aboutness, i.e. the characteristic of acts of cognition of being about something. The ‘something’ a cognitive act is about is called its ‘intentional object’, meaning the object of an intentional act. Any kind of object can be seen as an intentional object irrespective of whether it is concrete, illusory, abstract, etc. Indeed the emphasis is on the intentional act, as it is in the intentional act that the object—which need not be claimed to exist—is present. In order to achieve knowledge of an object the phenomenologist investigates the consciousness of the knowing subject when performing the act directed to that particular object.Characterized in this way, it is not difficult to see that phenomenology has a straightforward bearing on almost everything, philosophy of mathematics included. As Tieszen puts it , ‘[…] our mathematical beliefs are always about something. They are about certain objects, such as numbers, sets, functions or groups […]’. …. (shrink)