A Textual Study by Robert J. Fogelin
Taking Wittgenstein at His Word closely examines three concepts in Wittgenstein's philosophy: rule-following, private language and the philosophy of mathematics. The book is divided into two sections: rule-following and private language are examined in Part One, and the philosophy of mathematics is examined in Part Two. In particular, Fogelin stipulates that he is conducting a close textual reading, and - therefore - chooses not to engage at length with the vast secondary literature. The result is a book that asks, "what does Wittgenstein actually say on these topics?"
Part One includes a close examination of rule-following in the Philosophical Investigations. In relation to rule-following, Wittgenstein emphasises that any "rule" could be followed differently than intended. In other words, to follow a rule correctly, one needs to have access to examples and experience. For instance, one could be permitted to write the number "116" when asked, "what is the next number is the following series: 102, 104, 106, ...?" Why not? What would stop one from seeing "116" as a valid continuation of the series? An altogether different example would be rules of social decorum. Would a person be "wrong" if one chose not to extend a hand for a handshake when greeting a new person? What if the person was not schooled in that convention? What about the rules of child-rearing? Or the meaning of our concepts? Are forms of argumentation? Or of learning? Are these conventions and practices mere whimsy?
Obviously, we don't want to tumble into skepticism, which lead us to see our rules - which are so important to us and the way we live - as arbitrary and without justification. At the same time, it would arrogant to say that the rationale for our rules lies "deep in human nature", since that would brandish outsiders (or those who act differently) as somehow lacking in human nature. Instead, Fogelin argues that Wittgenstein suggests that we adopt a communitarian approach to find a justification for our rules. In Fogelin's reading, Wittgenstein is asking his readers (a) to examine how one's form of life [amongst others] presents contexts, training and justification for our rules, and (b) to examine the number and nature of encounters that one requires to be able to consistently act in accordance with such standards.
Part Two, then, is an examination of Wittgenstein communitarian views on the foundations of mathematics as presented in Remarks on the Foundations of Mathematics. In keeping with Part One, Fogelin sets off to show how Wittgenstein sees mathematics as a social invention. Therefore, mathematicians do not discover mathematical truths. Instead, they invent or extend mathematical methods, usually because the mathematical methods serve to solve practical problems or to clarify the conceptualisation of a problem faced by a community of users. In this case, mathematics starts out in its applied form before becoming purified as an abstract system before returning as a means of acting upon the world. In this reading, there is nothing particularly universal about mathematics or sacred about existing mathematical propositions.
Any claims at universality fail to acknowledge and appreciate the intricate social history of mathematics (and the cultures that do not share such a history). The fact that mathematics is used globally is more a testament to its utility as an invention than to its universality. Consequently, the "foundation" of mathematics isn't to be found "out there" in the world or "deep inside" the neural networks of the brain. Whilst mathematics may take advantage of the brain's architecture and also illuminate particular patterns in the world, the "foundations" of mathematics are to be found in the history of its use, transmission and extension within communities of practice.
The general theme of the Fogelin's reading can be summarised as follows: if one wants to seek a foundation for our practices, our language, our mathematics or our knowledge, then one must consider the contexts and interactions in which these elements occur. Taking Wittgenstein at His Word is an accessible, engaging book for those with a moderate understanding of Wittgenstein and the concepts being explored.