https://jhaponline.org/jhap/issue/feed 2021-02-23T02:14:26+00:00 Audrey Yap ayap@uvic.ca Open Journal Systems <p>JHAP aims to promote research in and discussion of the history of analytical philosophy. <a href="/jhap/about">Read more ...</a></p> https://jhaponline.org/jhap/article/view/4029 2020-08-03T10:57:16+00:00 James R Connelly jamesconnelly@trentu.ca

<p>In his highly perceptive, if underappreciated introduction to Wittgenstein’s <em>Tractatus</em>, 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 <em>desideratum</em> 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 <em>Tractatus</em> 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.</p>

2021-02-23T00:00:00+00:00 Copyright (c) 2021 James R Connelly https://jhaponline.org/jhap/article/view/4642 2021-02-14T23:45:07+00:00 Matthew Simpson ms887@cam.ac.uk 2021-02-23T00:00:00+00:00 Copyright (c) 2021 Matthew Simpson