Henri Bergson, answered from the texts and cited to the page.
Intuition is not feeling, not inspiration, not disorderly sympathy. It is a precise philosophical method, one of the most fully developed methods in philosophy, with strict rules. The first rule: apply the test of true and false to problems themselves, and condemn false problems. False problems are of two sorts — nonexistent problems (nonbeing, disorder, the possible), which involve the retrograde movement of the true (mistaking the "more" for the "less"), and badly stated questions, which group together things that differ in kind.
The second rule: struggle against illusion and rediscover the true differences in kind, the natural articulations of the real. The third concerns the apprehension of real time. Intuition's distinctive work is to find the natural articulations, to follow each line of fact beyond the turn of pragmatic experience, and to converge on the virtual point at which the lines intersect again.
It is reciprocal to analysis, not opposed to it: analysis works from the outside in symbols; intuition works from the inside in the thing itself.12
Seen from within, an absolute is then a simple thing; but considered from without, that is to say relative to something else, it becomes, with relation to those signs which express it, the piece of gold for which one can never make up the change. Now what lends itself at the same time to an indivisible apprehension and to an inexhaustible enumeration is, by definition, an infinite.The Creative Mind, pp. 185–186
It was therefore not only a psychological theory, associationism, which I brushed aside; it was also and for a similar reason, a general philosophy such as Kantianism, and everything connected with it. Both of them, almost universally accepted at that time in their main outlines, appeared to me as impedimenta hindering philosophy and psychology from going ahead. The only thing to do, then, was to go ahead.The Creative Mind, pp. 27–29
Russell's 1912 Monist article fixed the analytic-tradition reception for half a century and contributed to the 1930s eclipse of Bergsonism in French university philosophy as Hegel, via Kojève, took the place Bergsonism had held since 1900. The reading was a misreading. Russell collapsed intuition-as-method into romantic feeling and mistook the demand for precision in metaphysics for an evasion of it. The Bergson-Einstein debate of 1922 produced a parallel public humiliation: the philosopher who would not concede that the physicist's coordinate-time exhausts the metaphysical question of time was widely declared to have failed to understand relativity. Duration and Simultaneity was withdrawn from circulation rather than continue the dispute. The withdrawal is in the record. The argument it carried, that the metaphysical question of time is distinct from the physics of relativity and that the question survives the answer, is also in the record, and the record has held up better than the verdict at the time.