Call it b what you wish, it is all arbitrary with no hard boundary. It is for this reason that any symbolic approach will utterly fail and the search for truth and facts will equally fail. All is in continuous flux and cannot be frozen. You can try but then the infinities and infinitesimals will start popping up all over. — Rich
How could what is perish? How could it have come to be? For if it came into being, it is not; nor is it if ever it is going to be. Thus coming into being is extinguished, and destruction unknown. (B 8.20–22)
Nor was [it] once, nor will [it] be, since [it] is, now, all together, / One, continuous; for what coming-to-be of it will you seek? / In what way, whence, did [it] grow? Neither from what-is-not shall I allow / You to say or think; for it is not to be said or thought / That [it] is not. And what need could have impelled it to grow / Later or sooner, if it began from nothing? Thus [it] must either be completely or not at all. (B 8.5–11)
[What exists] is now, all at once, one and continuous... Nor is it divisible, since it is all alike; nor is there any more or less of it in one place which might prevent it from holding together, but all is full of what is. (B 8.5–6, 8.22–24)
And it is all one to me / Where I am to begin; for I shall return there again. (B 5) — P
And it is all one to me / Where I am to begin; for I shall return there again. (B 5) — P
https://plato.stanford.edu/entries/weyl/#DasKon… the conceptual world of mathematics is so foreign to what the intuitive continuum presents to us that the demand for coincidence between the two must be dismissed as absurd. (Weyl 1987, 108)
… the continuity given to us immediately by intuition (in the flow of time and of motion) has yet to be grasped mathematically as a totality of discrete “stages” in accordance with that part of its content which can be conceptualized in an exact way. (Ibid., 24)[14]
The view of a flow consisting of points and, therefore, also dissolving into points turns out to be mistaken: precisely what eludes us is the nature of the continuity, the flowing from point to point; in other words, the secret of how the continually enduring present can continually slip away into the receding past. Each one of us, at every moment, directly experiences the true character of this temporal continuity. But, because of the genuine primitiveness of phenomenal time, we cannot put our experiences into words. So we shall content ourselves with the following description. What I am conscious of is for me both a being-now and, in its essence, something which, with its temporal position, slips away. In this way there arises the persisting factual extent, something ever new which endures and changes in consciousness. (Ibid., 91–92)
By 1919 Weyl had come to embrace Brouwer’s views on the intuitive continuum. Given the idealism that always animated Weyl’s thought, this is not surprising, since Brouwer assigned the thinking subject a central position in the creation of the mathematical world[18].
In his early thinking Brouwer had held that that the continuum is presented to intuition as a whole, and that it is impossible to construct all its points as individuals. But later he radically transformed the concept of “point”, endowing points with sufficient fluidity to enable them to serve as generators of a “true” continuum. This fluidity was achieved by admitting as “points”, not only fully defined discrete numbers such as 1/9, e
e
, and the like—which have, so to speak, already achieved “being”—but also “numbers” which are in a perpetual state of “becoming” in that the entries in their decimal (or dyadic) expansions are the result of free acts of choice by a subject operating throughout an indefinitely extended time. The resulting choice sequences cannot be conceived as finished, completed objects: at any moment only an initial segment is known. Thus Brouwer obtained the mathematical continuum in a manner compatible with his belief in the primordial intuition of time—that is, as an unfinished, in fact unfinishable entity in a perpetual state of growth, a “medium of free development”. In Brouwer’s vision, the mathematical continuum is indeed “constructed”, not, however, by initially shattering, as did Cantor and Dedekind, an intuitive continuum into isolated points, but rather by assembling it from a complex of continually changing overlapping parts. — Weyl
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