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to the paradox, I submitted in chapter 5, lies in an attitude of unconditional acceptance: our use of language is governed by a set of rules—rules that are partially meaning-constitutive of vague expressions—which, were they strictly ›enforced,‹ so to speak, would lead to frequent contradictions. The
Editor:
Joachim Bromand
Ludwig Wittgenstein selbst hielt seine Überlegungen zur Mathematik für seinen bedeutendsten Beitrag zur Philosophie. So beabsichtigte er zunächst, dem Thema einen zentralen Teil seiner Philosophischen Untersuchungen zu widmen. Tatsächlich wird kaum irgendwo sonst in Wittgensteins Werk so deutlich, wie radikal die Konsequenzen seines Denkens eigentlich sind. Vermutlich deshalb haben Wittgensteins Bemerkungen zur Mathematik unter all seinen Schriften auch den größten Widerstand provoziert: Seine Bemerkungen zu den Gödel’schen Unvollständigkeitssätzen bezeichnete Gödel selbst als Nonsens, und Alan Turing warf Wittgenstein vor, dass aufgrund seiner scheinbar toleranten Haltung gegenüber Widersprüchen Brücken einstürzen könnten, die Mithilfe mathematischer Berechnungen in Wittgensteins Sinne errichtet würden. Die Beiträge des Bandes erklären zentrale Überlegungen Wittgensteins zur Mathematik, räumen weit verbreitete Missverständnisse aus und analysieren kritisch Wittgensteins Bedeutung für die traditionelle Philosophie der Mathematik. Ebenfalls wird die Frage verfolgt, inwieweit Wittgensteins Bemerkungen zur Philosophie der Mathematik über seine Philosophischen Untersuchungen hinausführen.
have been jettisoned by various theorists of vagueness. Proponents of paraconsistent accounts (cf., e.g., Hyde, 2008: 93ff.) defend the possibility of true contradictions such as ›Prince William both is and is not bald,‹ and many theorists of vagueness have argued about the truth, falsity, or
would not go quite as far as Sainsbury and claim that the notion of a vague or fuzzy boundary is essentially a contradiction in terms; nevertheless, I think he is right to insist that vague predicates are, strictly speaking, boundaryless. Regarding our examples, the river and the hedge noticeably stand
never, or very rarely, actually led into contradiction« (Keefe, 2000: 20), and consider these facts in need of explanation. As Fischer observes, puzzlement in view of mundane facts is a characteristic point of departure for philosophical reflection and theory-building. However, questions concerning
-tautological status of the law of non-contradiction (LNC). According to Tye, the non-classical value ›indefinite‹ is not on a par with the two classical values, but indicates a truth-value gap. This suggests we conceive of the third value as representing a provisional truth state which, in principle, is resolvable
. On the usual definition of disjunction, and on the assumption that bivalence holds, then, both › Pa ‹ and › ¬ Pa ‹ are false, and their respective negations true—but › ¬ Pa ∧ ¬¬ Pa ‹ is a contradiction. Since Russell holds that vagueness ›infects‹ not only ordinary language, but—albeit to a lesser
run. According to biconditional B, then, item # n is both P and not- P . At first glance, this result appears to violate the law of non-contradiction. Through her introduction of a refined notion of context, however, Raffman avoids the semblance of contradiction. No item that lies within the
auch von der Skilehrerin behaupten. 122 In diesem Sinne hält Alva Noë beispielweise mit Blick auf das Beispiel der Pianistin (Maestra) fest: I agree that there would be no contradiction in supposing that Maestra knows how to play piano, even though she cannot now play. But this doesn’t show that