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Henry comes to a third sort of intuition: he begins this section with Hume. Hume is the philosopher of empiricism: all know is what we sense. Period:

Hume’s most important contributions to the philosophy of causation are found in A Treatise of Human Nature, and An Enquiry concerning Human Understanding, the latter generally viewed as a partial recasting of the former. Both works start with Hume’s central empirical axiom known as the Copy Principle. Loosely, it states that all constituents of our thoughts come from experience. By learning Hume’s vocabulary, this can be restated more precisely. Hume calls the contents of the mind perceptions, which he divides into impressions and ideas. Though Hume himself is not strict about maintaining a concise distinction between the two, we may think of impressions as having their genesis in the senses, whereas ideas are products of the intellect. Impressions, which are either of sensation or reflection (memory), are more vivid than ideas. Hume’s Copy Principle therefore states that all our ideas are products of impressions.

The Internet Encyclopedia of Philosophy  Hume’s radical empiricism led to all sorts of problems:

Now as concerns inductive inference, it is hardly surprising to be told that the epistemological problem is insoluble; that there can be no formula or recipe, however complex, for ruling out unreliable inductions. But Hume’s arguments, if they are correct, have apparently a much more radical consequence than this: They seem to show that the metaphysical problem for induction is insoluble; that there is no objective difference between reliable and unreliable inductions.

The Stanford Encyclopedia of Philosophy Henry points to Kant as the one who saw the abyss of Hume’s philosophy and one who offered a solution:

Kant’s profoundest insight is that whoever professes, with Hume, to derive the categories of thought from experience, cannot consistently escape epistemological skepticism. He emphasized that human knowledge is possible only because of innate thought categories which guarantee the universal validity of human knowledge, and provide the basis for the truths of mathematics.

Carl F. H. Henry, God, Revelation, and Authority, vol. 1 (Wheaton, IL: Crossway Books, 1999), 75. Kant held to a sort of “sensuous intuition”, an intuition of space and time that permits us to under the world reasonably and to communicate with one another. But this comes at the cost of boxing God and the transcendent out of human knowledge. Henry notes the irony with Kant’s philosophical sequestration of God:

His postulation of a cognitively unknowable god encouraged the notion that one may experience what cannot be conceptually defined, that is, the ineffable. Intuition is therefore for Kant, in contrast to the view of rational intuitionists, not a means of cognitively knowing God.

Carl F. H. Henry, God, Revelation, and Authority, vol. 1 (Wheaton, IL: Crossway Books, 1999), 75.

Hegel tries to solve Kant’s problem by conflating human thought and God:

But, by equating the Absolute with the reflective self-consciousness of human minds, Hegel obscured any real created existence. For mankind in the image of God he substituted God externalized as the universe, so that destruction of man and the world would obliterate divine being and life. Hegel made God an inescapable reality by divinizing man, and thereby he caricatured both.

Carl F. H. Henry, God, Revelation, and Authority, vol. 1 (Wheaton, IL: Crossway Books, 1999), 76.