Brouwer formulates his foundational philosophy using a single a priori notion, that of time; expressing the kernel of his idea thus :
(neo)intuitionism considers the falling apart of moments of life into qualitatively different parts, to be reunited only while remaining separate in time, to be the fundamental phenomenon of the human intellect.
(All quotes given are taken from “Intuitionism and Formalism” by L.E.J. Brouwer.)
Brouwer gives a name to this concept (that of the falling apart of moments and reuniting them). He calls it two-oneness (and we note this concept is clearly analogous to collectivisation - i.e., set formation).
Brouwer then states his two acts of intuitionism. The first act gives rise to the natural numbers, while the second act gives rise to the continuum. Again quoting Brouwer :
This intuition of two-oneness, the basal intuition of mathematics, creates not only the numbers one and two, but also all finite ordinal numbers, inasmuch as one of the elements of the two-oneness may be thought of as a new two-oneness, which process may be repeated indefinitely; this gives rise still further to the smallest infinite ordinal number ω. Finally this basal intuition of mathematics, in which the connected and the separate, the continuous and the discreet are united, gives rise immediately to the intuition of the linear continuum, i.e., of the “between,” which is not exhaustible by the interposition of new units and therefore can never be thought of as a mere collection of units.
Thus, it is Brouwer’s intuition of betweenness that gives rise to his continuum, and we see that Brouwer’s continuum is not equivalent to the classical continuum.
In particular, Brouwer’s continuum does not fall apart into individual points (“can never be thought of as a mere collection of points”). Yet the intuition of “between” must surely apply to moments of time, so Brouwer's notion of time appears to be that of continuum. But then, how does time fall apart into individual moments (as per the first quote)? What am I misunderstanding here?