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.

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.

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.

The Philosophy of Dissonant Children : Stanley Cavell's Wittgensteinian Philosophical Therapies as an Educational Conversation

Education is often understood as a process whereby children come to conform to the norms teachers believe should govern our practices. This picture problematically presumes that educators know in advance what it means for children to go on the way that is expected of them. In this essay Viktor Johansson suggests a revision of education, through the philosophy of Stanley Cavell, that can account for both the attunement in our practices and the possible dissonance that follows when the teacher and child do not go on together. There is an anxiety generated by the threat of disharmony in our educational undertakings that may drive teachers toward philosophy in educational contexts. Here Johansson offers a philosophical treatment of this intellectual anxiety that teachers may experience when they, upon meeting dissonant children, search for epistemic justifications of their practices—a treatment whereby dissonant children can support teachers in dissolving their intellectual frustrations.