## 26 Nov 2008

### Hegel, Science of Logic, Remark 4 §§170-175

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[Below is summary. At the end I cite the text in full. My interpretations not informed by a complete read of the text.]

Hegel

Science of Logic

Volume One: The Objective Logic

Book One: The Doctrine of Being

Section 1: Determinateness (Quality)

Chapter 1 Being

C Becoming

1. Unity of Being and Nothing

Remark 4: Incomprehensibility of the Beginning

§ 170

In the following, Hegel will prove that a beginning of the world or of anything at all is impossible.

§ 171

It is impossible for anything to begin, either in so far as it is, or in so far as it is not; for in so far as it is, it is not just beginning, and in so far as it is not, then also it does not begin.

For something to have begun, there must be a point of transition. But if at that point the beginning has begun, then it already has being, and thus it is no longer beginning. But if at that point the beginning has not yet begun, that it does not yet have being, and so it also is not beginning. Thus it is inconceivable that something might begin, because there is no way to account for the precise point of transition between being and non-being.

If the world, or anything, is supposed to have begun, then it must have begun in nothing, but in nothing — or nothing — is no beginning; for a beginning includes within itself a being, but nothing does not contain any being. Nothing is only nothing.

For the same reason, something cannot cease to be, because then being would have to contain nothing, "being is only being, not the contrary of itself."

§ 172

We are not here disproving becoming or the unity of being and nothing.

§ 173

So when we posit an absolute separatedness of being from nothing, we cannot account for beginning or becoming.

§ 174

This ambiguity of becoming as the unity of being and nothing is found also in infinitesimal magnitudes (treated later in more depth).

These magnitudes have been defined as such that they are in their vanishing, not before their vanishing, for then they are finite magnitudes, or after their vanishing, for then they are nothing.

Some object that these infinitesimal magnitudes must either be something or nothing, because there is no "intermediate state between being and non-being." (Hegel here parenthetically objects that the term 'state' is an "unsuitable, barbarous expression"). But Hegel has already shown that there is "nothing which is not an intermediate state between being and nothing." By adopting such a stance, mathematics has attained "its most brilliant successes."

§ 175

Reasoning that makes the false absolute separation between being and non-being is sophistry, not dialectic, because "sophistry is an argument proceeding from a baseless presupposition which is uncritically and unthinkingly adopted." However, dialectic is

the higher movement of reason in which such seemingly utterly separate terms pass over into each other spontaneously, through that which they are, a movement in which the presupposition sublates itself.

Through their "dialectical immanent nature," being and nothing "manifest their unity, that is, becoming, as their truth."

From the translation:

Remark 4: Incomprehensibility of the Beginning

§ 170

What has been said indicates the nature of the dialectic against the beginning of the world and also its end, by which the eternity of matter was supposed to be proved, that is, the dialectic against becoming, coming-to-be or ceasing-to-be, in general. The Kantian antinomy relative to the finitude or infinity of the world in space and time will be considered more closely under the Notion of quantitative infinity. This simple, ordinary dialectic rests on holding fast to the opposition of being and nothing. It is proved in the following manner that a beginning of the world, or of anything, is impossible:

§ 171

It is impossible for anything to begin, either in so far as it is, or in so far as it is not; for in so far as it is, it is not just beginning, and in so far as it is not, then also it does not begin. If the world, or anything, is supposed to have begun, then it must have begun in nothing, but in nothing — or nothing — is no beginning; for a beginning includes within itself a being, but nothing does not contain any being. Nothing is only nothing. In a ground, a cause, and so on, if nothing is so determined, there is contained an affirmation, a being. For the same reason, too, something cannot cease to be; for then being would have to contain nothing, but being is only being, not the contrary of itself.

§ 172

It is obvious that in this proof nothing is brought forward against becoming, or beginning and ceasing, against this unity of being and nothing, except an assertoric denial of them and an ascription of truth to being and nothing, each in separation from the other. Nevertheless this dialectic is at least more consistent than ordinary reflective thought which accepts as perfect truth that being and nothing only are in separation from each other, yet on the other hand acknowledges beginning and ceasing to be equally genuine determinations; but in these it does in fact assume the unseparatedness of being and nothing.

§ 173

With the absolute separateness of being from nothing presupposed, then of course — as we so often hear — beginning or becoming is something incomprehensible; for a presupposition is made which annuls the beginning or the becoming which yet is again admitted, and this contradiction thus posed and at the same time made impossible of solution, is called incomprehensible.

§ 174

The foregoing dialectic is the same, too, as that which understanding employs the notion of infinitesimal magnitudes, given by higher analysis. A more detailed treatment of this notion will be given later. These magnitudes have been defined as such that they are in their vanishing, not before their vanishing, for then they are finite magnitudes, or after their vanishing, for then they are nothing. Against this pre notion it is objected and reiterated that such magnitudes are either something or nothing; that there is no intermediate state between being and non-being ('state' is here an unsuitable, barbarous expression). Here too, the absolute separation of being and nothing is assumed. But against this it has been shown that being and nothing are, in fact, the same, or to use the same language as that just quoted, that there is nothing which is not an intermediate state between being and nothing. It is to the adoption of the said determination, which understanding opposes, that mathematics owes its most brilliant successes.

§ 175

This style of reasoning which makes and clings to the false presupposition of the absolute separateness of being and non-being is to be named not dialectic but sophistry. For sophistry is an argument proceeding from a baseless presupposition which is uncritically and unthinkingly adopted; but we call dialectic the higher movement of reason in which such seemingly utterly separate terms pass over into each other spontaneously, through that which they are, a movement in which the presupposition sublates itself. It is the dialectical immanent nature of being and nothing themselves to manifest their unity, that is, becoming, as their truth.

Hegel. Science of Logic. Transl. A.V. Miller. George Allen & Unwin, 1969.
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