Transfinite Number in Wittgenstein’s Tractatus / Review of work on Ramsey

Volume 9.2 of The Journal for the History of Analytical Philosophy (JHAP) has now been published online, with full open-access.

It features an article by James Connelly entitled, “Transfinite Number in Wittgenstein’s Tractatus”. Here is the abstract:

In his highly perceptive, if underappreciated introduction to Wittgenstein’s Tractatus, Russell identifies a “lacuna” within Wittgenstein’s theory of number, relating specifically to the topic of transfinite number. The goal of this paper is two-fold. The first is to show that Russell’s concerns cannot be dismissed on the grounds that they are external to the Tractarian project, deriving, perhaps, from logicist ambitions harbored by Russell but not shared by Wittgenstein. The extensibility of Wittgenstein’s theory of number to the case of transfinite cardinalities is, I shall argue, a desideratum generated by concerns intrinsic, and internal to Wittgenstein’s logical and semantic framework. Second, I aim to show that Wittgenstein’s theory of number as espoused in the Tractatus is consistent with Russell’s assessment, in that Wittgenstein meant to leave open the possibility that transfinite numbers could be generated within his system, but did not show explicitly how to construct them. To that end, I show how one could construct a transfinite number line using ingredients inherent in Wittgenstein’s system, and in accordance with his more general theories of number and of operations.

The volume also contains a review of Cheryl Misak, Frank Ramsey: A Sheer Excess of Powers (Oxford University Press, 2020), written by Matthew Simpson.

JHAP is a free, open-access, peer-reviewed journal. It is available at Submissions welcome!