First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This (...) historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic. (shrink)

The paper argues that no criterion-referenced assessment system can achieve both reliability and validity at one and the same time. It shows that the reasons for this are conceptual, and hence that empirical research into the‘problem’ is a waste of money and effort. Considerable discussion is devoted to ideas of knowledge and understanding, and to proper educational objectives pertaining to these. Much reference is made to the current National Curriculum context in the United Kingdom, and conclusions are drawn for appropriate (...) educational policy in this area. (shrink)

Professor Whitty has endorsed the consensus that research into education is empirical social science, distinguishing ‘educational research’ which seeks directly to influence practice, and ‘education research’ that has substantive value but no necessary practical application.The status of the science here is problematic. The positivist approach is incoherent and so supports neither option. Critical educational science is virtually policy-inert. The interpretive approach is empirically sound but, because of the value component in education, does not support education research either, or account for (...) this component.A solution to the latter problem is sought in the debate between Carr and Hirst on the relationship between philosophy and education. This shows Carr making claims that rely on a conception of philosophy that he rejects, while Hirst insists on this conception, uses it to justify practical claims, but denies that this is possible.To achieve a practically relevant analysis of educational research, both need to include second-order, normative, conceptual enquiry into the philosophies that drive educational policy-making and partly regulate teaching methodology. Deweyan, first-order, ‘reflective practice’ needs, then, to be supplemented with second-order reflection.Educational research is philosophy- not science-driven, and is value-led. Consequently, it has the status not of scientific discovery but of practical recommendation. (shrink)

This new work provides an approachable introduction to the complex system that Making It Explicit mapped out.

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This (...) historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic. (shrink)

In this work the distinguished physical chemist and philosopher, Michael Polanyi, demonstrates that the scientist's personal participation in his knowledge, in ...

When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: "The theories contained in this new work . . . are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who likes simplicity, I should like to think that they are not, but (...) from what I have read of them I am quite sure that he ought to have an opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy." "[ Philosophical Remarks ] contains the seeds of Wittgenstein's later philosophy of mind and of mathematics. Principally, he here discusses the role of indispensable in language, criticizing Russell's The Analysis of Mind . He modifies the Tractatus 's picture theory of meaning by stressing that the connection between the proposition and reality is not found in the picture itself. He analyzes generality in and out of mathematics, and the notions of proof and experiment. He formulates a pain/private-language argument and discusses both behaviorism and the verifiability principle. The work is difficult but important, and it belongs in every philosophy collection."--Robert Hoffman, Philosophy "Any serious student of Wittgenstein's work will want to study his Philosophical Remarks as a transitional book between his two great masterpieces. The Remarks is thus indispensible for anyone who seeks a complete understanding of Wittgenstein's philosophy."--Leonard Linsky, American Philosophical Association. (shrink)

The purpose of this paper is to raise some questions about the idea, which was first made prominent by Gilbert Ryle, and has remained associated with him ever since, that there are at least two types of knowledge (or to put it in a slightly different way, two types of states ascribed by knowledge ascriptions) identified, on the one hand, as the knowledge (or state) which is expressed in the ‘knowing that’ construction (sometimes called, for fairly obvious reasons, ‘propositional’ or (...) ‘factual’ knowledge) and, on the other, as the knowledge (or state) which is ascribed in the ‘knowing how’ construction (sometimes called ‘practical’ knowledge). This idea, which might be said to be Ryle's most lasting philosophical legacy, has, in some vague form, remained part of conventional wisdom in philosophy since he put it forward. My purpose here is fairly accurately described as ‘raising questions’, since both the criticisms of the received view (as I interpret it), and the positive alternative suggestions to be advanced, are, to some extent, tentative and exploratory. The aim is to assemble a broad range of evidence for the conclusion that we need to replace the standard account, to query especially what Ryle suggested as evidence for it, and to explore what seems to me to be the indicated replacement for it. (shrink)

Essays analyze the nature of the human mind, thought, and imagination and explore the connection of thought to teaching.

ACT, CONTENT, AND OBJECT THE TITLE I have chosen for this work is a mere label for a set of problems; the controversial views that have historically been ...

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

No previous experience in formal studies in either philosophy or education is a requirement for a full comprehension of the text.

This radical reading of Wittgenstein's third and last masterpiece, On Certainty, has major implications for philosophy. It elucidates Wittgenstein's ultimate thoughts on the nature of our basic beliefs and his demystification of scepticism. Our basic certainties are shown to be nonepistemic, nonpropositional attitudes that, as such, have no verbal occurrence but manifest themselves exclusively in our actions. This fundamental certainty is a belief-in, a primitive confidence or ur-trust whose practical nature bridges the hitherto unresolved categorial gap between belief and action.