Intermittently, from 1927 until 1936, Waismann had extensive conversations with Ludwig Wittgenstein about topics in philosophy of mathematics and philosophy of language. These conversations, recorded by Waismann, were published in Ludwig Wittgenstein and the Vienna Circle. Other members of the Circle also spoke with Wittgenstein, but not to Waismann's extent. At one point in 1934, Wittgenstein and Waismann considered collaborating on a book, but these plans fell through after their philosophical differences became apparent. Waismann later accused Wittgenstein of obscurantism because of what he considered to be his betrayal of the project of logical positivism and empirically-based explanation. Ultimately the texts for the project, written or just transcribed by Waismann, have been published by Gordon Baker in 2003.
In Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics, Waismann argued that mathematical truths are true by convention rather than being necessarily true. His collected lectures, The Principles of Linguistic Philosophy, and How I See Philosophy, a collection of papers, were published posthumously.
Waismann introduced the concept of open texture, or porosity to describe the universal possibility of vagueness in empirical statements. It is based on the Wittgenstein, Philosophical Investigations, particularly Section 80. According to the philosopher, even after measures have been taken to ensure that a statement is precise, there remains an inexhaustible source of vagueness due to an indefinite number of possibilities. Waismann's notion of vagueness is slightly different from his concept of open texture. He explained that open texture is more like the possibility of vagueness. The latter can also be remedied so that it can be made more precise while the former cannot. Open texture has been found in legal philosophy through the writings of H. L. A. Hart. According to Hart, vagueness constitutes a fundamental feature of legal languages. It is cited, however, that Waismann's conceptualization has limited practical application since it is more for the extraordinary while Hart's view of open texture concerned the more mundane, favoring to approach the term in the context of a particular norm.
