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.

"The Poet of Science": how scientists read their Tennyson

Tennyson’s responses to science have been thoroughly documented and discussed, but how did scientists respond to his poetry? Through examining in detail the work of three scientists who wrote at length about Tennyson--the astronomer Norman Lockyer, the physicist Oliver Lodge, and the American geologist William North Rice--it is possible to see how Tennyson went from being respected by contemporary scientists to being feted as the Poet of Science itself after his death. As a materialist, a Spiritualist, and a Darwinian Methodist respectively, Lockyer, Lodge, and Rice had very different conceptions of how science worked and what it implied about the universe, yet each looked to Tennyson and his poetry to confirm and extend his own judgements and values.

The appliance of science

One in four people will experience a mental health problem in any given year. Of those, the vast majority will not receive any psychological or pharmacological help. Even when psychological help is received, it frequently lacks a strong scientific basis. This article describes the extent of the problem in the dissemination and implementation of evidence-based psychological therapies and examines some of the solutions proposed.

The rise of Western rationalism: Paul Feyerabend’s story

I summarise certain aspects of Paul Feyerabend’s account of the development of Western rationalism, show the ways in which that account is supposed to run up against an alternative, that of Karl Popper, and then try to give a preliminary comparison of the two. My interest is primarily in whether what Feyerabend called his ‘story’ constitutes a possible history of our epistemic concepts and their trajectory. I express some grave reservations about that story, and about Feyerabend’s framework, finding Popper’s views less problematic here. However, I also suggest that one important aspect of Feyerabend’s material, his treatment of religious belief, can be given an interpretation which makes it tenable, and perhaps preferable to a Popperian approach.

Applied philosophy of language

This chapter explores the extent to which philosophy of language can be considered an applied discipline. I consider, first, ways in which sub-sections of philosophy of language may be considered as applied in terms of their subject matter and/or the kinds of questions being addressed (e.g. philosophy of language which deals with derogatory or inflammatory uses of language, or the role of philosophy of language within feminist philosophy). Then, in the second part of the chapter, I turn to consider a more general (and perhaps more controversial) conception of philosophy of language as applied, which arises from the methodology adopted and the relationship of the discipline to empirical data.

Children's preconceptions of science: how these can be used in teaching

This paper focuses on young children’s initial ideas about science prior to any teaching and discusses teachers’ identification of these ‘preconceptions’ when teaching science in the early years. The research focuses on early years teaching in public and private kindergartens with children from three to five. The area of the children’s preconceptions has been extensively investigated by other researchers in the past. However, research focusing on children’s preconceptions and how teachers work with these in the early years is still limited in comparison, especially within Cypriot context. A case study was employed which facilitated in-depth investigation employing different methods of data collection including interviews and observations. The results indicate that teachers tend to avoid identification of the children’s preconceptions when planning and teaching science. This suggests a lack of appreciation of the children’s preconceptions and the consequences when they are not acknowledged. To help teachers respond to the children’s preconceptions, this paper provides a number of suggestion on how to identify children’s preconceptions.

Experimental philosophy of language

Experimental philosophy of language uses experimental methods developed in the cognitive sciences to investigate topics of interest to philosophers of language. This article describes the methodological background for the development of experimental approaches to topics in philosophy of language, distinguishes negative and positive projects in experimental philosophy of language, and evaluates experimental work on the reference of proper names and natural kind terms. The reliability of expert judgments vs. the judgments of ordinary speakers, the role that ambiguity plays in influencing responses to experiments, and the reliability of meta-linguistic judgments are also assessed.