Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

Angel of History. I can see for miles

Commissioned public artwork Focal Point Gallery, Southend 12 Sept - 22 Oct 2011 2.6 x 15M digital print for the railway bridge that spans Southend-on-Sea’s pedestrianised high street.

John of Worcester and the science of history

Although the ‘chronicle of chronicles’ compiled at Worcester c1095-c1140 is now firmly attributed to John of Worcester, rather than Florence, major questions remain. A central issue is that the semi-autograph manuscript of the chronicle (now Oxford, Corpus Christi College, Ms 157) underwent several alterations to its structure and contents, as codicological evidence demonstrates. These included the incorporation of important illuminations, which have been surprisingly little considered in their overall manuscript context. This article focuses on these illuminations, and will argue that their presence in this version of the chronicle makes it something even more distinctive than the learned, revisionist chronological work of Marianus Scotus upon which it was based. John of Worcester’s chosen images are linked not only to his political narrative but also to theological works and to cutting-edge science, newly translated from Arabic. The presence of such miniatures in a twelfth-century chronicle is unique, and they are central to the final form given to the Worcester chronicle by John of Worcester himself in this key manuscript. Their analysis thus brings into focus the impressive assembly of materials which the chronicle offered to readers, to shape their understanding of ongoing events.