¹⁶ Kritik der reinen Vernunft, A 125 abridged. 17 ibid., B 15 and 22 (note).

¹⁸ ibid., A 126.

¹⁹ Prolegomena, A 111.

²⁰ K. d. r. V., A 127.

²¹ Hume's inconsistency with the fundamental thesis of Empiricism is clearly evidenced in the sentences which introduce Section II of the Enquiry: “All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact.

“Of the first kind are the sciences of Geometry, Algebra, and Arithmetic, and in short, every affirmation which is either intuitively or demonstratively certain. … Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe….

“Matters of fact, which are the second objects of human reason are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. … This proposition, that causes and effects are discoverable, not by reason but by experience, will readily be admitted with regard to such objects, as we remember to have once been altogether unknown to us….”

Hume's argument goes on to show that what is generally admitted in the particular case must, on reflection, be seen to hold in all cases in which we assert that a given event follows from such and such a cause, or is followed by such and such an effect.

Huxley's criticism of the first of these propositions, recognizing the non-empirical nature of our acceptance of the theorems of mathematics, is to be found in the early paragraphs of his Essay on Hume, Chapter VI.

That the ultimate reflections which we have put into the thoughts of the radical Empiricist do not materially depart from those which this radical has himself put into words is sufficiently established in the following quotation from the same chapter of Huxley:

“The axiom of causation [“Every event has a cause.”] cannot possibly be deduced from any general proposition which simply embodies experience. But it does not follow that the belief, or expectation, expressed by the axiom, is not a product of experience, generally antecedently to, and altogether independently of, the logically indefensible language in which we express it.”

²² K. d. r. V., A 126.

²³ Leibnitz called it the principium identitatis indiscernibilium.

²⁴ Timaeus, 52.

²⁵ A slight departure of Kant's formal logic from the traditional texts, being of no interest to later logic or to the present study, is passed over.

²⁶ K. d. r. V.

²⁷ ibid.

²⁸ Prolegomena, A 44.

²⁹ Phaedo, 76.

³⁰ Metaphysics, B 1.993 b9; De anima, III, Vol. 2.

³¹ Descartes to Mersennes, 15 Avril 1630, Oeuvres, ed. Adam and Tannery, I, 145.

³² Essay, Book 1.

³³ Notae in Programma, ed. Adamnd and Tannery, VIII, 358 B a.

³⁴ “Analytic”, for Kant, was any judgment whose predicate was part of the definition of the subject, “synthetic”, one whose predicate added to the attributes belonging to the subject by definition. Thus “A triangle is three-sided” would be an analytic judgment. “A triangle is a figure whose interior angles taken together equal two right angles” would be synthetic. Cf. K. d. r. V., 10–17 B.

³⁵ Walter Frost, Naturphilosophie, I, pp. 199–202, selected. A similar “physiological” or “empirical” a priori is proposed by Rehmke in his discussion of space perceptions:

“Apriorische Ursprünglichkeit des Raumbewusstseins will sagen, dass die Seele, wann immer sie da ist und Empfindungen hat, zugleich, aber kraft einer in ihr Bewusstsein liegenden Eigenart allein, Raumbewusstsein hat, also ohne eine seiner Bedingungen in vorausgehenden Vorgängen des Nervensystems habe. Empirische Ursprünglichkeit des Raumbewussteins dagegen behauptet eine physiologische Bedingung für dasselbe … für jene ist das menschliche Bewusstsein der “Schöpfer”, für diese aber ist es nur die eine Bedingung des ursprunglichen Raumbewusstseins.

“Wir finden keine Veranlassung, zu einer apriori-Theorie des Raumbewusstseins unsere Zuflucht zu nehmen und von unsere Meinung der empirischen Ursprünglichkeit des Raumbewusstseins abzulassen.” Lehrbuch der Allgemeinen Psychologie, pp. 209–211, selected.

³⁶ Charles Reade, The Cloister and the Hearth, 1, 6

So, too, the illusory character of “immediate and certain self-knowledge”, seems frequently to have impressed itself on the mind of Lawrence Sterne. Two of his sermons have this “lesson” as their central theme; the one was later introduced into Tristram Shandy as a homily of Yorick; the other, delivered on the text, “Thou art the man. …” 2 Samuel, XII, 7, is worth recalling:

“There is no historical passage in Scripture, which gives a more remarkable instance of the deceitfulness of the heart of man to itself than this. … To know one's self, one would think could be no very difficult lesson;—for who, you will say, can well be truly ignorant of himself and the disposition of his own heart? If a man thinks at all, he cannot be a stranger to what passes there—he must be conscious of his own thoughts and desires, he must remember his past pursuits, and the true springs and motives which have directed the actions of his life: he may hand out false colors to the world, but how can a man deceive himself? That a man can is evident, because he daily does so.—Scripture tells us, and gives us many historical proofs of it, besides this to which the text refers—‘that the heart of man is treacherous to itself and deceitful above all things,’ and experience and every hour's commerce with the world confirms the truth of this seeming paradox, ‘That though man is the only creature endowed with reflection, and consequently qualified to know the most of himself—yet so it happens, that he generally knows the least—and with all the power which God has given him of turning his eyes inward upon himself, and taking notice of the chain of his own thoughts and desires—yet … he is as much, nay often a much greater stranger to his own disposition and true character, than all the world besides.”