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Cliquer sur les phrases pour les voir dans leur contexte. Les textes de Immanuel Kant et David Hume sont disponibles auprès du Projet Gutenberg.

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Nay, it may even be said that the true value of mathematics- that pride of human reason--consists in this; that she guides reason to the knowledge of nature--in her greater as well as in her less manifestations--in her beautiful order and regularity--guides her, moreover, to an insight into the wonderful unity of the moving forces in the operations of nature, far beyond the expectations of a philosophy building only on experience; and that she thus encourages philosophy to extend the province of reason beyond all experience, and at the same time provides it with the most excellent materials for supporting its investigations, in so far as their nature admits, by adequate and accordant intuitions.

 As you vary this experience, he varies his reasoning. Axioms are, for this reason, always self-evident, while philosophical principles, whatever may be the degree of certainty they possess, cannot lay any claim to such a distinction. 

Mathematics, indeed, are useful in all mechanical operations, and arithmetic in almost every art and profession: But it is not of themselves they have any influence: Mechanics are the art of regulating the motions of bodies to some designed end or purpose; and the reason why we employ arithmetic in fixing the proportions of numbers, is only that we may discover the proportions of their influence and operation.

 If they contain the unconditioned, they relate to that to which all experience is subordinate, but which is never itself an object of experience--that towards which reason tends in all its conclusions from experience, and by the standard of which it estimates the degree of their empirical use, but which is never itself an element in an empirical synthesis. if we consider this reality as cause (be it of sensation or of another reality in the phenomenon, for example, a change), we call the degree of reality in its character of cause a momentum, for example, the momentum of weight; and for this reason, that the degree only indicates that quantity the apprehension of which is not successive, but instantaneous.