Is Brouwer's notion of time that of a continuum?

Question

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?

Answer 1

The experience of the current moment being different from the memory of the previous moment is a discrete phenomenon. Our memory is instantaneous and qualitatively isolated from any other remembered moment. Memory is not continuous, it is itemized. Each event we attend to has the feeling of two-oneness, of becoming an event.

But if we back away from our concrete memory and concentrate on the possible memories we might have had, we find that we might have had memories between any two we actually have. Consciousness is continuous, even if perception is not.

To put this in less vague frame, look at how it plays out in actual phenomenal experience near the limit of our processing resolution.

In "Consciousness, Explained", Daniel Dennett describes the experiment where a red light on one side of our peripheral vision and a green light on the other, when flashed too close together for them to be processed separately, get perceived as a single moving object that changes color.

We perceive the single event of there being a ribbon of light across our visual field which is red on one end and green on the other. But in retrospect we can identify the point where our brain assigns the (illusory) change in color because we naturally force continuity on our discrete sequential experience. So time is experience as continuous, but the experiences are discrete, and mapped onto the continuum artificially.

Since the interpolated continuity is at a different level of processing, and not made up of the actual discrete events, but interpolated from them, one cannot connect them in a way that makes the continuum a collection of points. We are prevented from undoing the illusion, because it is necessary to our narrative arc. From an extreme position, if we want to be intuitively motivated, we should respect this difficulty as natural to our psychology and not pretend we can remove it.