  This analysis left unresolved the status of scientific hypotheses. Do hypotheses provide genuine knowledge, despite their uncertainty? Or did Pascal anticipate the solution later adopted by Locke and restrict genuine knowledge to two categories: (a) what is perceived, and (b) what is ‘demonstrated’? De l'esprit géométrique adopts a foundationalist perspective on knowledge, in which ‘principles’ are first established and the certainty of other knowledge-claims derives from that of the principles. Such logically interconnected principles and conclusions were called ‘demonstrations’. Thus every demonstration requires that one first identify “the evident principles that it requires. For, if one does not guarantee the foundations, one cannot guarantee the building” (II, 175). One establishes the certainty of propositions if they are “deducible by infallible and necessary logical steps from such axioms or principles, on the certitude of which depends all the certitude of the consequences that are properly deduced from them” (letter to Father Noël: I, 378). This invites the question: does physical science provide demonstrations in this sense? Pascal limited ‘demonstration’ to mathematics and ‘whatever imitates it’ (II, 180). At the same time, he seems to have believed that his own physical investigations were sufficiently similar to mathematics that they amounted to demonstrated knowledge, and that experiments or observations provided their foundational principles.