The OED defines “intuition” as “immediate apprehension by the intellect alone” (among other meanings). Intuitive knowledge, then, is knowledge by the intellect alone—knowledge by pure intellection. The senses play no part in it. Empirical knowledge, by contrast, is defined as knowledge by means of the senses, perhaps allowing a contribution by the intellect in addition to sense experience. Intuitive knowledge is often regarded as problematic, even unintelligible, while empirical knowledge is thought to be pellucid and paradigmatic. Thus empiricism has enjoyed ascendancy over rationalism since its inception in the seventeenth century. I will argue that this assessment is mistaken. The subject is large, but I will keep it brief.
The first point to note is that intuitive knowledge employs a single mental faculty in producing knowledge—the faculty of intellect. Its inputs are intellectual and so are its outputs; it doesn’t go outside itself. However, empirical knowledge employs a pair of faculties of very different nature: intellect in which the knowledge is stored, and the senses that yield sensations. Somehow sensations are supposed to produce states of knowledge. But how can sensations, which are non-propositional, give rise to knowledge, which is propositional? How could sensations constitute knowledge? The two are like chalk and cheese. Only by attempting to reduce intellect to sensation, which is hopeless. Call this the problem of epistemic mismatch. Second, skepticism stands in the way of basing knowledge of the world on experience, since the two are not logically connected—as with dreams, evil demons, and brains in a vat. Sense experience cannot justify such knowledge claims, so it can hardly be a sound basis for knowledge. Intuitive knowledge has no such problem and is generally regarded as certain (e.g. knowledge of logical laws). There is thus no such thing as empirical knowledge (true justified belief). Third, it is completely unclear what sense experience is such that it can produce knowledge. If we take it to be concept-infused, we impose intellect on sense from outside; if we rigorously exclude concepts from it, the residue will be incapable of creating knowledge (the bare “given”). More basically, it is impossible to say, or discern, what sense experience actually contains: the more you stare at it the more it looks impotent to justify our typical claims about the world. Blooming buzzing confusion can’t yield propositional knowledge of reality. The only way to save empiricism is to inject it with rationalism by invoking intellect. Maybe sensations can somehow trigger knowledge but they can’t act as justifiers of knowledge (“only knowledge can justify knowledge”).
Here is another way to look at the matter. The senses evolved in collaboration with the motor system to form the sensorimotor system. This system operates to regulate the organism’s relation to its environment and exists independently of cognition. It is not designed to produce knowledge or to interact with the intellect (all animals have it). The empiricist in effect believes that this primitive system can also give rise to propositional knowledge and is indeed its only legitimate basis. But seen from the proper biological perspective, this claim is vastly implausible; the intellectual system might never have evolved while the sensorimotor system would still be doing its job. It would be completely accidental if the senses could perform both functions. Perhaps there is some sort of epistemic hookup between the senses and the intellect, but the idea that knowledge of the world can be exhaustively explained by sensory inputs is quixotic at best. One can certainly imagine a rationalist philosopher (Plato?) holding that no knowledge can be derived from sensation, i.e. sensations can play no justificatory role. This isn’t to say that states of sensory seeming can’t function as justifications, as in “It seems to me that there’s a book on my desk”, but the states so reported are heavily imbued with concepts and capacities drawn from the intellectual faculty; they aren’t simply raw data existing antecedently to the operations of intellect. We really have no clear idea of what empirical knowledge could be construed in the traditional way (“impressions”, “ideas”, “sense-data”, etc.). So as a theory of knowledge, supposedly superior to rationalist theories, empiricist theories are woefully under-described, if not demonstrably incoherent. It is simply not true that knowledge is “based on experience”.