What I call ‘radical intuitionism’ can be thus summarized:
Intuition means the non-mediated perception that something is PRESENT.
A logical proposition is MADE of signs, but the IDENTITY BETWEEN TWO PROPOSITIONS is an object that is perceived by consciousness directly, not through signs, and is, therefore, the object of intuition.
Furthermore, understanding these propositions is THE SAME as understanding without mediation its apodictic truth.
Again, if the identity between two propositions is not PRESENT to consciousness WITHOUT MEDIATION, then it is simply impossible to perceive it.
Either the conection between two propositions is perceived in a single intuition, or it is never perceived at all (otherwise we would fall into and endless regression).
Therefore, the operation of reason itself is founded upon intuition or it has no founding at all.
Hence, there are not two kinds of knowledge, one rational and the other intuitive. There is only the difference between logical intuitions and sensible intuitions.
Reasoning is not, therefore, an operation specifically different from intuition, it is just the intuition of a special kind of object, which is the logical or ideal objects.
More generically, a thing may be thought indirectly through a sign, but the sign itself has to be perceived directly and not through another sign.