"Le present est plein de l’avenir, et chargé du passé" : Vorträge des XI. Internationalen Leibniz-Kongresses, 31. Juli – 4. August 2023, Leibniz Universität Hannover, Deutschland. Band 2

[No abstract available]Deutschen Forschungsgemeinschaft (DFG)/Projektnr. 517991912VGH VersicherungNiedersächsisches Ministerium für Wissenschaft und Kultur (MWK

Reasoning with Attitude:Foundations and Applications of Inferential Expressivism

Certain combinations of sounds or signs on paper are meaningful. What makes it the case that, unlike most combinations of sounds answers to these questions are based on the idea that words stand for something, but it is difficult to say what words such as good, if, or probable stand for. This book advances novel answers based on the idea that words get their meaning from the way they are used to express states of mind and what follows from them. It articulates a precise version of this idea, at a time when the shortcomings of the traditional answers are hotly discussed

Vagueness in mathematics talk

The Cockcroft Report claimed that "mathematics provides a means of communication which is powerful, concise and unambiguous". Such precision in language may be a conventional aim of mathematics, particularly when communicated in writing. Nonetheless, as this thesis demonstrates, vagueness is commonplace when people talk about mathematics. In this thesis, I examine the circumstances in which vagueness arises in mathematics talk, and consider the practical purposes which speakers achieve by means of vague utterances in this context. The empirical database, which is considered in Chapters 4 to 7, consists almost entirely of transcripts of mathematical conversations between adult interviewers (including myself) and one or two children. The data were collected from clinical interviews focused on a small number of tasks, and from fragments of teaching. For the most part, the pupils involved in the study were aged between 9 and 12, although the age-range in Chapter 7 extends from 4 to 25. I draw on a number of approaches to discourse associated with 'pragmatics' -a field of linguistics - to analyse the motives and communicative effectiveness of speakers who deploy vagueness in mathematics talk. I claim that, for these speakers, vagueness fulfills a number of purposes, especially 'shielding', i. e. self-protection against accusation of being wrong. Another purpose is to give approximate information; sometimes to achieve shielding, but also to provide the level of detail that is deemed to be appropriate in a given situation. A different purpose, associated with a particular form of vagueness (of reference), is to compensate for lexical gaps in pursuit of effective communication of concepts and ideas. I show, in particular, how speakers use the pronouns 'it' and 'you' in mathematics talk to communicate concepts and generalisations. Some consideration is given to the intentions of 'expert speakers of mathematics when they deploy vague language. Their purposes include some of those identified for novices. Teachers also use vagueness as a means of indirectness in addressing pupils; this strategy is associated with the redress of 'face threatening acts'. My thesis is that vagueness can be viewed and presented, not as a disabling feature of language, but as a subtle and versatile device which speakers can and do deploy to make mathematical assertions with as much precision, accuracy or as much confidence as they judge is warranted by both the content and the circumstances of their utterances. I report on the validation and generalisation of my findings by an Informal Research Group of school teachers, who transcribed and analysed their own classroom interactions using the methods I had developed

"Logic is a geometry of thinking". Space and Spatial Frameworks in Wittgenstein's Writings

The thesis investigates the history and functions of space concepts in Wittgenstein’s philosophy. It is based on a Kantian account which conceives of space not as a thing, but as an a priori framework which constitutes possibilities, not facts. The increasing abstraction and formalisation of geometry in the 19th century enabled Wittgenstein in his Tractatus Logico-Philosophicus to extend this formal account and to devise his concept of “logical space” as a universal and necessary manifold for all meaningful states-of-affairs. After his return to philosophy in 1929, he holds up the idea that necessity is not an extraordinary fact, but a feature of the logical framework which constitutes possibilities. Unlike in the Tractatus, however, he then speaks of spaces in the plural and highlights the differences between different “geometries” or “grammars”. I emphasise the plurality of Wittgenstein’s later space concept by presenting the various fields in which spatial terminology is used, as well as the similarity of these various instances by pointing out commonalities in the way in which they are used: the emphasis on possibility instead of truth, the distinction between “geometry” and “physics”(between logic and experience), but also the distinction between different kinds of geometries. These similarities allow me to recognise a number of concepts as closely connected to “space” – and thereby to one another – instead of highlighting their differences. Against views which argue for the complete disappearance of spaces and grammar in the late Wittgenstein’s philosophy, I suggest that these concepts are not dismissed, but transformed after the middle period. The reasons for this transformation are the increasing importance of time, notably the change from static spaces to more dynamic frameworks, and the acknowledgement of empirical factors in logic: instead of an ontological separation of logic and experience it makes more sense to speak of different grammatical roles.The thesis has been supported by the AHRC DTP (Fees only Award for EU-students) and the Vice Chancellor's Awards of the Cambridge Trus

Being up for grabs: On speculative anarcheology

This is a book on the metaphysics of contingency. It looks at what could be otherwise, at what lacks the weight of necessity, at what is up for grabs. Aristotle maintained that there could be no knowledge of the impermanent. Since then, metaphysics has endeavored to find out what really is permanent, non-accidental and resilient – substances that endure, substrata underneath different qualities, fixed principles, necessary connections. In contrast, Bensusan draws on the growing philosophical attention to the contingent. It explores how we can counter Aristotle and develop a metaphysics of what ain’t necessarily so. The endeavor renegotiates the accepted familiarity between ontology and the search for an arché. Being Up For Grabs explores this in connection to what is up in the air, what is out of the blue and what is up for grabs. It is a metaphysical exercise that dialogues with several philosophical resources. It is also a speculative and anarcheological effort, as it tries to reach a broad and encompassing view of the sensible world while conceiving it as lacking any arché. The book emerges as an exercise in speculative anarcheology

EBook proceedings of the ESERA 2011 conference : science learning and citizenship

This ebook contains fourteen parts according to the strands of the ESERA 2011 conference. Each part is co-edited by one or two persons, most of them were strand chairs. All papers in this ebook correspond to accepted communications during the ESERA conference that were reviewed by two referees. Moreover the co-editors carried out a global reviewing of the papers.ESERA - European Science Education Research Associatio