Tag Archives: tractatus

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 https://jhaponline.org/. Submissions welcome!

Resolute Readings of Wittgenstein and Nonsense

Volume 8.10 of The Journal for the History of Analytical Philosophy (JHAP) has now been published online, with full open-access.

It features an article by Joseph Ulatowski entitled, “Resolute Readings of Wittgenstein and Nonsense”. Here is the abstract:

The aim of this paper is to show that a corollary of resolute readings of Wittgenstein’s conception of nonsense cannot be sustained. First, I describe the corollary. Next, I point out the relevance to it of Wittgenstein’s discussion of family resemblance concepts. Then, I survey some typical uses of nonsense to see what they bring to an ordinary language treatment of the word “nonsense” and its relatives. I will subsequently consider the objection, on behalf of a resolute reading, that “nonsense” is a term of philosophical criticism. Finally, I conclude that resolute readings have not sufficiently accounted for how nonsense behaves in our language; they have failed to heed Wittgenstein’s warning: “don’t think, but look!”

JHAP is a free, open-access, peer-reviewed journal. It is available at https://jhaponline.org/. Submissions welcome!

On the Curious Calculi of Wittgenstein and Spencer Brown

Volume 6.10 of The Journal for the History of Analytical Philosophy (JHAP) has now been published online, with full open-access.

It features an article by Gregory Landini entitled “On the Curious Calculi of Wittgenstein and Spencer Brown”. Here is an abstract:

In his Tractatus, Wittgenstein sets out what he calls his N-operator notation which can be used to calculate whether an expression is a tautology. In his Laws of Form, George Spencer Brown offers what he calls a “primary algebra” for such calculation. Both systems are perplexing. But comparing two blurry images can reduce noise, producing a focus. This paper reveals that Spencer Brown independently rediscovered the quantifier-free part of the N-operator calculus. The comparison sheds a flood light on each and from the letters of correspondence we shall find that Russell, as one might have surmised, was a catalyst for both.

JHAP is a free, open-access peer reviewed journal. It is available at https://jhaponline.org/. Submissions welcome!

The Substance Argument of Wittgenstein’s Tractatus

Volume 4.7 of The Journal for the History of Analytical Philosophy (JHAP) has now been published.

It features an article by Michael Morris entitled “The Substance Argument of Wittgenstein’s Tractatus”. Here is an abstract:

In Morris (2008) I presented in outline a new interpretation of the famous ‘substance argument’ in Wittgenstein’s Tractatus (Wittgenstein 1922). The account I presented there gave a distinctive view of Wittgenstein’s main concerns in the argument, but did not explain in detail how the argument works: how its steps are to be found in the text, and how it concludes. I remain convinced that the interpretation I proposed correctly identifies the main concerns which lie behind the argument. I return to the argument here in order to elaborate in fuller detail the relation between those concerns and the actual course of the text.

JHAP is available at https://jhaponline.org. Submissions welcome!