In this talk, I argue that eighteenth-century philosopher and mathematician Johann Heinrich Lambert (1728-1777) regards general concepts of geometrical figures as what we call non-propositional functions, rather than as unary predicates. According to Lambert, an expression like ‘equilateral triangle’ conceals the logical features of the concept of an equilateral triangle. Drawing on Friedman’s (1992) work on Kant, I show that Lambert holds that the concept of an equilateral triangle is better captured by the expression ‘the equilateral triangle constructed on a given finite straight line’, which can be viewed as a function-sign.
Lambert’s case sheds important light on the history of the notion of analytical truth: Although Lambert holds that mathematical truths flow from logical relations between concepts, we cannot conclude from this that he regards them as analytic in Kant’s sense. Lambert’s case also contributes to a more nuanced understanding of the extent to which ‘traditional’ or pre-Fregean logic could do justice to geometrical inference (cf. e.g. Hodges 2009).