XXI. The idea of space is not an absolutely necessary condition of sensation.
XXII. The idea of extension has a real objectiveness.
XXIII. The transition from the subjective to the objective in relation to extension is a primitive fact of our nature.
XXIV. Therefore bodily phenomena have a real existence outside of us.
XXV. Therefore a real certainty, scientific as well as phenomenal, arises from the testimony of the senses.
XXVI. Reason justifies the instinct of nature when it examines the relation of subjectiveness with objectiveness in sensations.
XXVII. Geometry considers extension in the abstract; but with the certainty that when the principle exists in the real order, the consequences cannot fail to be produced, and that the consequences will be more or less exact in proportion as the principle is more or less exactly realized.
XXVIII. Notwithstanding our certainty of the existence of the external world we do not know its essence.
XXIX. We do not know what this world is when seen by a pure spirit.
XXX. Sensible intuition, to which our geometry relates, does not constitute the essence of scientific knowledge, and may be separated from it.