Friedrich Waismann, a little-known mathematician and onetime student of Wittgenstein's, provides answers to problems that vexed Wittgenstein in his attempt to explicate the foundations of mathematics through an analysis of its practice. Waismann argues in favor of mathematical intuition and the reality of infinity with a Wittgensteinian twist. Waismann's arguments lead toward an approach to the foundation of mathematics that takes into consideration the language and practice of experts.

The predominant interpretation of Wittgenstein's later remarks on religion takes him to hold that all religious utterances are non-scientific, and to hold that the way to show that religious utterances are non-scientific is to identify and characterise the grammatical rules governing their use. This paper claims that though this does capture one strand of Wittgenstein's later thought on religion, there is an alternative strand of that thought which is quite different and more nuanced. In this alternative strand Wittgenstein stresses that (...) religious utterances and beliefs can come in both scientific and non-scientific varieties. More than that, he claims that the grammar of religious utterances, and the logic of religious beliefs, is often complex – in that individual utterances and beliefs will often be mixed between, indeterminate between, or fluid between being scientific and being non-scientific. This complexity means that it will often be unhelpful to try to pin down one particular grammar or logic for a given utterance or belief. Wittgenstein therefore suggests a new method of grammatical and logical investigation, which is less likely to distort complex grammars or logics by being overly simplistic or rigid. This method is to use simple examples of utterances and beliefs as objects of comparison, so as to illuminate the different aspects of the more complex actual utterances and beliefs under examination. This alternative strand in Wittgenstein's later remarks on religion is a manifestation of a broader strand of Wittgenstein's later thought as a whole, which was first described by Friedrich Waismann, and later developed by Gordon Baker and Oskari Kuusela. The paper concludes by providing examples of religious beliefs which are logically mixed, indeterminate, and fluid, and showing how simple objects of comparison can be used to illuminate them. (shrink)

A mysterious remark to Friedrich Waismann on 30 December 1929 marks the only occasion where Wittgenstein refers to both Heidegger and Kierkegaard. Yet although this has generated much controversy, little attention has been paid to the charge of nonsense that Wittgenstein here appears to bring against Heidegger; thus, the supporting argument that may be latent has not been unearthed. Through analysis of this remark, Wittgenstein's arguments in the Tractatus and 'A Lecture on Ethics', and Heidegger's account of anxiety (Angst) (...) in Being and Time, I argue that we can extract an argument against the central question of Heidegger's philosophy: the question of being. To understand this, I examine the Kierkegaardian ideas employed by Wittgenstein and Heidegger and attempt to show that this argument can be partly understood in Kierkegaardian terms. I further argue that examining what Heidegger means by 'being' (Sein) shows that Wittgenstein's argument does not meet its target. (shrink)