This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students (...) learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future. (shrink)

Different inferences in probabilistic logics of conditionals 'preserve' the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability I when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...) conclusions must have positive probability when premisses do, and in the last case conclusions must be at least as probable as their least probable premisses. Precise definitions and well known examples are given for each of these properties, characteristic principles are shown to be valid and complete for deriving conclusions of each of these kinds, and simple trivalent truthtable 'tests' are described for determining which properties are possessed by any given inference. Brief comments are made on the application of these results to certain modal inferences such as "Jones may own a car, and if he does he will have a driver's license. Therefore, he may have a driver's license.". (shrink)

Now I may not be an educated man . . . But it seems to me to go against common sense to ask what the poet is ‘trying to say’. The poem isn’t a code for something easily understood. The poem is what he is trying to say.

This paper is inter-disciplinary. Its disadvantage is that the author is not sufficiently conversant with the disciplines it is inter. He may however, like Lord Wavell, claim that at least the thread that binds them is his own.The paper is of philosophic interest in that it is inspired by, and hopes to shed some light on, the notion of an ideal language. It is of interest to social anthropology in that its main subject is kinship structure. It may be of (...) interest to mathematicians in setting a task. (shrink)

Preface.-- Introduction.--I. The problem of consciousness.-- II. Modern idealism.--III. The alogical and the logical as ultimate elements.--IV. The individual conciousness.--V. Reality and truth.--VI. The higher conciousness.--VII. The final goal of all things.--VIII. Problem of metaphysic.--IX. Survey of results.-- Index.