ABSTRACT
Mathematics must be based on the logic that underlies all truth-asserting language. But if arithmetic, the most basic of mathematics, is to be made healthy again, it is not only its health that must be in question, but also language, that natural language which had excluded mathematics and made it an outcast. If there was an estrangement between language and mathematics, the fault had to be on both sides. Gaps in mathematical reasoning are defects, but also defective is what had been solicited to fill those gaps: a thought and language essentially unclear. In the negotiation that is opened between language and mathematics in the Begriffsschrift, it is mathematics that is made chivalrously to offer the initial gestures of accommodation. If a sentence is to be seen as functional, a change is necessary in the notion of a mathematical function. It must be able to take all objects as arguments, and to have a truth value it must encompass equations.
