I. The Three Intuitions
IA. Eidetic Intuitions
Intuition is supposed to be a form of direct access. Yet, direct access to what? Does it access directly "intuitions" (abstract objects, akin to numbers or properties - see "Bestowed Existence")? Are intuitions objects of mental act of Intuition? Perhaps intuition is mind's way of interacting directly with Platonic ideals or Phenomenological "essences"? By "directly" I mean without intellectual mediation of a manipulated symbol system, and without benefits of inference, observation, experience, or reason.
Kant thought that both (Euclidean) space and time are intuited. In other words, he thought that senses interact with our (transcendental) intuitions to produce synthetic a-priori knowledge. The raw data obtained by our senses -our sensa or sensory experience - presuppose intuition. One could argue that intuition is independent of our senses. Thus, these intuitions (call them "eidetic intuitions") would not be result of sensory data, or of calculation, or of processing and manipulation of same. Kant's "Erscheiung" ("phenomenon", or "appearance" of an object to senses) is actually a kind of sense-intuition later processed by categories of substance and cause. As opposed to phenomenon, "nuomenon" (thing in itself) is not subject to these categories.
Descartes' "I (think therefore I) am" is an immediate and indubitable innate intuition from which his metaphysical system is derived. Descartes' work in this respect is reminiscent of Gnosticism in which intuition of mystery of self leads to revelation.
Bergson described a kind of instinctual empathic intuition which penetrates objects and persons, identifies with them and, in this way, derives knowledge about absolutes - "duration" (the essence of all living things) and "élan vital" (the creative life force). He wrote: "(Intuition is an) instinct that has become disinterested, self-conscious, capable of reflecting upon its object and of enlarging it indefinitely." Thus, to him, science (the use of symbols by our intelligence to describe reality) is falsification of reality. Only art, based on intuition, unhindered by mediating thought, not warped by symbols - provides one with access to reality.
Spinoza's and Bergson's intuited knowledge of world as an interconnected whole is also an "eidetic intuition".
Spinoza thought that intuitive knowledge is superior to both empirical (sense) knowledge and scientific (reasoning) knowledge. It unites mind with Infinite Being and reveals to it an orderly, holistic, Universe.
Friedrich Schleiermacher and Rudolf Otto discussed religious experience of "numinous" (God, or spiritual power) as a kind of intuitive, pre-lingual, and immediate feeling.
Croce distinguished "concept" (representation or classification) from "intuition" (expression of individuality of an objet d'art). Aesthetic interest is intuitive. Art, according to Croce and Collingwood, should be mainly concerned with expression (i.e., with intuition) as an end unto itself, unconcerned with other ends (e.g., expressing certain states of mind).
Eidetic intuitions are also similar to "paramartha satya" (the "ultimate truth") in Madhyamika school of Buddhist thought. The ultimate truth cannot be expressed verbally and is beyond empirical (and illusory) phenomena. Eastern thought (e.g. Zen Buddhism) uses intuition (or experience) to study reality in a non-dualistic manner.
IB. Emergent Intuitions
A second type of intuition is "emergent intuition". Subjectively, intuiting person has impression of a "shortcut" or even a "short circuiting" of his usually linear thought processes often based on trial and error. This type of intuition feels "magical", a quantum leap from premise to conclusion, parsimonious selection of useful and workable from a myriad possibilities. Intuition, in other words, is rather like a dreamlike truncated thought process, subjective equivalent of a wormhole in Cosmology. It is often preceded by periods of frustration, dead ends, failures, and blind alleys in one's work.