De l’Esprit géométrique et de l’art de persuader (On the spirit of geometry and the art of persuasion) (1657-8?) is a yet more sophisticated presentation of the new scientific outlook. Pascal begins by conceding that definitions in geometry are nominal and not real, and that what are taken for axioms are intuitive perceptions which can neither be demonstrated nor reasonably be doubted. The four terms which he identifies in this way are number, space, movement and time. All share the property of being infinitely divisible and infinitely extensible. This insight is counter-intuitive to those who conceive knowledge as finite but, unless it can be grasped, then the geometric spirit itself cannot be comprehended. Pascal is not claiming that man’s capacity for knowledge is unlimited; merely that the immediate information of his senses and his reason have to be transcended if scientific advances are to be made. Geometry emerges from this as superior to logic, in that it can both provide axioms and engage in demonstration, whereas logic can only do the latter.

The second part of the work is devoted to the thorny problem of persuasion; here the will comes into question as the path through which human assent to a given argument is to be obtained. Even here, however, a method or a set of rules are supplied for the correct conduct of an argument. Terms must be given clear definitions, axioms must be incontrovertible and must all be explicit, and conclusions should be checked by substituting definitions for the terms used. Pascal’s discussion of scientific method is therefore distinct from Bacon’s negative use of induction although, like Bacon, he conceives of science in evolutionary terms; nor does it evince Descartes’ greater reliance on the resources of human reason; it harnesses the arguments of the sceptics, but escapes from their epistemological dilemma by positing intuitive truths which do not come to us from the exercise of our intellect.

6 Theology and the human condition