By means of a reductio argument, Wittgenstein’s Tractatus calls into question the very idea that we can represent logical form. My paper addresses three interrelated questions: first, what conception of logical form is at issue in this argument? Second, whose conception of logic is this argument intended to undermine? And third, what could count as an adequate response to it? I show that the argument construes logical form as the universal, underlying correlation of any representation and the reality it represents. (...) I further show that the argument seeks to undermine core commitments of Frege’s and Russell’s. But the reductio, as I read it, is not intended to establish the falsity of any of their specific assumptions. Rather, its aim is to make manifest the indeterminacies that underlie the language in which these assumptions are framed, and establish the need for a transformation of that language. So understood, Wittgenstein’s argument exemplifies his idea that philosophy is not a theory, but an activity of elucidation. The interpretation I propose bears on one of the central debates in the literature, namely how we should understand Wittgenstein’s contention that his elucidations succeed despite being nonsensical. (shrink)

The main question addressed by this article is this: How should one understand the role of the sentences of the Tractatus, given Wittgenstein’s statement that they are nonsensical? I begin with a presentation of three general principles of interpretation in order to avoid answering the question in an inappropriate way. I then move on to a short presentation and commentary on a selection of readings – namely, the ineffabilist, resolute and elucidatory ones – and elaborate the answers given by advocates (...) of these to the question explored here. I agree on many points with resolute and elucidatory readings: the Tractatus presents an austere conception of nonsense, and is not a book that seeks to present ontological or semantic theories. I point out, however, that these readings cannot fully explain the nature of Tractarian elucidations. Then I discuss those parts of the Tractatus which refer to the sentences of the book itself. The main proposal of my own approach is this: Tractarian elucidations should be construed as rules of translation, in that they show how to substitute certain expressions for others. They enable us to construct a notation in which everything that is expressible in ordinary language can be said perspicuously. (shrink)

This paper concerns Wittgenstein’s conception of philosophical and mathematical problems. Both in his earlier and in his later writings Wittgenstein grapples with the tendency of philosophers to misconstrue the nature of the difficulties that they are facing. Whereas philosophers tend to assume that their problems are comparable to those that come up in the sciences, and take these problems to consist in questions the answers to which will provide them with substantive knowledge, Wittgenstein compares philosophical problems with riddles. What is (...) characteristic of riddles is that solving them involves an alteration of the use of language, but it does not tend to involve the acquisition of new knowledge. In his middle and later period, the comparison with riddles serves to highlight and resolve a related confusion in the way philosophers of mathematics understand the nature of mathematical problems. Wittgenstein rejects the realist approach according to which every mathematical theorem, whether proven or not, meaningfully specifies a possible fact which would make it true or false. By contrast, Wittgenstein construes unproven conjectures on the model of riddle phrases, whose meaning, prior to our finding the solution to them, has not been determined. Moreover, Wittgenstein draws our attention to the fact that we can be caught up in an attempt to solve a riddle even if the riddle does not have a solution; the same applies, in his mind, to our engagement with philosophical and mathematical problems. When it comes to philosophical riddles, Wittgenstein is convinced that they do not have a solution at all. The specific difficulty presented by unproven mathematical conjectures is different; in this case, we cannot tell in advance whether or not they present us with a solvable riddle. The paper situates these issues in the context of ongoing debates in the scholarship concerning Wittgenstein’s conception of nonsense, his methodology, his engagement with mathematical realism and verificationism, and his response to skepticism. (shrink)

This paper investigates a particular philosophical puzzle via an examination of its status in the writings of Wittgenstein. The puzzle concerns negation and can take on three interrelated guises. The first puzzle is how not-p can so much as negate p at all – for if p is not the case, then nothing corresponds to p. The second puzzle is how not-p can so much as negate p at all when not-p rejects p not as false but as unintelligible – (...) for if p is unintelligible, then p is nothing but scratches and sounds and does not seem apt for negation. And the third puzzle is how “not” could be anything but hopelessly equivocal if it sometimes (per the first puzzle) requires, and sometimes (per the second puzzle) precludes the intelligibility of p. The paper investigates these three puzzles, their respective structures, and their relations to each other. The second puzzle is expounded as the centre of gravity, and in countering two objections to the threefold puzzle, a special predicament is expounded with regard to the second puzzle’s concern with unipolar propositions – propositions that do not admit of an intelligible negation. The text concludes by indicating the first steps that could potentially lead us out of the threefold puzzle. (shrink)