I recently read some materials about intuitionism in the philosophy of mathematics, such as Intuitionism and Formalism by Brouwer himself, and some relative interpretations, I maybe understand how he treats infinite sets as potential infinite, a procedure that constructs its elements, and why he rejects uncountable sets and treats them as other things (e.g. the Choice Sequence of real numbers) for this reason, but I don't understand why, in his paper, choose the time as the only a priori concept, and the so-called "two-oneness" he built upon this, particularly in the phrase:
[...] This neo-intuitionism considers the falling apart of moments of life into quantitatively different parts, to be reunited only while remaining separated by time, as the fundamental phenomenon of the human intellect, passing by abstracting from its emotional content into the fundamental phenomenon of mathematical thinking, the intuition of the bare two-oneness [...]
and how he constructs the numbers (or in his quote the finite and smallest infinite ordinal number) using this.
To me, it seems like he is defining ordinal numbers by using the moments of time. I don't know whether my interpretation of this is correct or not, even if it's right, I still don't understand how he constructs numbers upon the moments of time, and the connection between time and the Intuitionism
Brouwer is alluding to an intuitive idea that is inherently temporal. The only possible way of suggesting this to others is the use of analogy: It is like an unending line of domino blocks tipping over, or a walk toward the horizon with each step. What Brouwer frequently calls a "move of time" is analogous to one of the domino blocks hitting the ground, or the planting of one foot on the ground in front of the other at each moment. To Brouwer, repeating this as many times as one pleases and keeping each instance in memory while doing so is what constitutes counting. This kind of thinking is briefly displayed at the beginning of Brouwer's original 1907 dissertation, where he builds natural number arithmetic from the ground up.
As for why he chooses time, in short and as far as I understand it, he observes that the succession of sensations in time is the most he can pin down as a fixed part of our experience, and he contends that this is how the intellect organizes experiences in one's memory, making the (unmeasured) sense of time the only a priori intuition. This is to be contrasted with conventions of time measurement used in science and communication; and it is in contradistinction with Kant's time and space, as Brouwer thinks that no form of space as in any geometry can be a priori, since they are all derived as subsystems of projective geometry done through homogeneous coordinate arithmetic, which is really all borne by time in Brouwer's eyes. He talks about this in his 1909 The Nature of Geometry.