My argument in this paper is that humility is implied in the concept of teaching, if teaching is construed in a strong sense. Teaching in a strong sense is a view of teaching as linked to students’ embodied experiences (including cognitive and moral-social dimensions), in particular students’ experiences of limitation, whereas a weak sense of teaching refers to teaching as narrowly focused on student cognitive development. In addition to detailing the relation between humility and strong sense teaching, I will also (...) argue that humility is acquired through the practice of teaching. My discussion connects to the growing interest, especially in virtue epistemology discourse, in the idea that teachers should educate for virtues. Drawing upon John Dewey and contemporary virtue epistemology discourse, I discuss humility, paying particular attention to an overlooked aspect of humility that I refer to as the educative dimension of humility. I then connect this concept of humility to the notion of teaching in a strong sense. In the final section, I discuss how humility in teaching is learned in the practice of teaching by listening to students in particular ways. In addition, I make connections between my concept of teaching and the practice of cultivating students’ virtues. I conclude with a critique of common practices of evaluating good teaching, which I situate within the context of international educational policy on teacher evaluation. (shrink)

The mathematical prowess of pure mathematician J. E. Littlewood (1885-1977), and of his elder cousin the mathematical educator Philippa Fawcett (1868-1948), is illustrated in the context of the Mathematical Tripos examination at Cambridge. Littlewood’s brilliant though highly condensed treatment in his splendid Miscellany (1953) of a perplexing problem from an old Tripos paper – familiar to some as “The Paradox of the Second Ace” – is then expanded with reference to Coxeter’s treatment of it in his revision of Rouse Ball’s (...) Mathematical Recreations (1939) and ultimately explained in the light of Wittgenstein’s later philosophy. The discussion touches on the nature of mathematical supposition. (shrink)

Sand drawings are introduced in relation to the fieldwork of British anthropologists John Layard and Bernard Deacon early in the twentieth century, and the status of sand drawings as mathematics is discussed in the light of Wittgenstein’s idea that “in mathematics process and result are equivalent”. Included are photographs of the illustrations in Layard’s own copy of Deacon’s “Geometrical Drawings from Malekula and other Islands of the New Hebrides” (1934). This is a brief companion to my article “Wittgenstein on string (...) figures as mathematics” (2022), published in the journal Philosophical Investigations. (shrink)

Wittgenstein's farcical clash with literary critic F. R. Leavis over the analysis of Empson's poem "Legal Fiction" is well known to devotees of Wittgenstein's life (Ludwig Wittgenstein: Personal Recollections (1981), edited by Rush Rhees, Oxford: Basil Blackwell, 80). Less well known is the value of studying Empson's artistic and intellectual achievement as part of the wider cultural background for the appreciation of Wittgenstein's views and influence, early and late. This talk sketches some diverting byways awaiting further exploration. A recurrent theme (...) is contradiction. (shrink)