Academic journal article The Review of Metaphysics

MIND: Vol. 109, No. 435, July 2000

Academic journal article The Review of Metaphysics

MIND: Vol. 109, No. 435, July 2000

Article excerpt

The Two-Envelope Paradox, MICHAEL CLARK and N. SCHACKELL

Previous claims to have resolved the two-envelope paradox have been premature. The paradoxical argument has been exposed as manifestly fallacious if there is an upper limit to the amount of money that may be put in an envelope; but the paradoxical cases which can be described if this limitation is removed do not involve mathematical error, nor can they be explained away in terms of the strangeness of infinity. Only by taking account of the partial sums of the infinite series of expected gains can the paradox be resolved.

Embedded Definite Descriptions: Russellian Analysis and Semantic Puzzles, STEVEN KUHN

A sentence containing a number of definite descriptions, each lying within the scope of its predecessor, is naturally read as asserting the uniqueness of a sequence of objects satisfying the descriptions. The project of providing a general uniform procedure for eliminating embedded definite descriptions that gets this and other logical forms right is impeded by several puzzles.

Weaseling Away the Indispensability Argument, JOSEPH MELIA

According to the indispensability argument, the fact that we quantify over numbers, sets and functions in our best scientific theories gives us reason for believing that such objects exist. This paper examines a strategy to dispense with such quantification by simply replacing any given platonistic theory by the set of sentences in the nominalist vocabulary it logically entails. The author argues that, as a strategy, this response fails: for there is no guarantee that the nominalist world goes beyond the set of sentences in the nominalist language that such theories entail. However, the author argues that what such theories show is that mathematics can enable us to express possibilities about the concrete world that may not be expressible in nominalistically acceptable language. While the author grants that this may make quantification over abstracta indispensable, he deny that such indispensability is a reason for accepting them into our ontology. …

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