Most ancient philosophers alluded to intuition as being the ticket for direct access. The big question also remained constant: intuition for what? Was it intuition for obvious, or intangible, objects, numbers, appearances, or their elemental properties — or, all our emotional contexts? Plato, for one, thought of intuition as being our mind's most primal mode of interacting openly with our quintessential identities and contexts — with or without of the advantage of reflection, experience, reason, or purpose.
For Immanuel Kant, the German philosopher, intuition was aligned to space and time. He articulated that our senses interrelate, or act, with our mystical, intuitive abilities to yield a certain mock-up of previous knowledge. This natural resource holds the key to 'accepted' intuition. It, of course, does not, in any way, preclude the idea that intuition is autonomous of, and to, our senses. The reason is simple: our intuitions are not always the result of our accumulated sensory records, or processes, including manoeuvring of one’s intuitive compass, or radar. Kant's idea of 'appearance' of objects to our senses was also essentially a form of 'sense-intuition.' It was processed by the substance and its cause, or effect.
To go a tad backwards, we’d cull the French philosopher René Descartes' famed maxim, "I think, therefore I am," as that pristine, classical intuitive element that unravelled the composite prism of intuition from the portals of transcendental mysticism to essential reality. Or, instinctive, compassionate intuition to be at the core of objects, elements, and individuals, while equating with them as being a part of the whole, or sum of the parts. Descartes suggested that this was celestial intervention — where knowledge was derived from not just absolutes, but also our resident souls, or prana in Eastern philosophy. He also outlined, that, if one were to use one’s intelligence to 'tap' one’s intuition, it would not elevate, but falsify reality. On the other hand, if one were to use their skilful or creative instincts, it would open up their access to reality — and, hold a mirror to it.
Most ancient Greek philosophers thought of the intuitive knowledge of the world as the interconnected whole, or what Edward Wilson, the modern biologist, calls as 'consilience,' the interconnectedness of things, wherever you look, or turn. The Dutch philosopher Baruch Spinoza thought of it contextually, no less. He presupposed intuitive knowledge as being far too superior to empirical knowledge and reason. This was precisely why it united the mind with divinity, or divine reality, in our organised, interconnected and collective universe, or the cosmos.
This isn’t the only manner in which our intuitive capabilities are expressed. There is something called as 'emergent intuition,' where the individual can 'grasp at straws and float on gossamers,' as it were, for intuitive sparks to emerge, through a linear thought process, based on trial and miscalculation. This type of intuition emerges from myriad possibilities, like a surreal, abridged thought process. This could range from the magical, or amazing, or a flash of brilliance, to flaws, failures and cul-de-sacs. Most mathematicians and physicists are part of this school of thought — they often use emergent intuitions to solving problems through equations, not guesswork.
For Aristotle, intuition was part of science. It demonstrated the ability for one to get at the truth about invariable or eternal things through logic, induction and syllogism — beginning with things that one already knew. He believed that intuition flowed, in effect, through the précis of thought principles wherefrom we’d begin to use science to derive the rest of our knowledge about interminable facts. He emphasised on 'ideal intuition' too, where thoughts and feelings preceded intellectual analysis.