19. Number

Reading Friedrich Nietzsche’s Human all too human

Read the introduction here

You can read the aphorism I discuss here in English, German and Dutch below the main article.

Synopsis, quote from the translation by Helen Zimmern and my take on it.

The discovery of the laws of numbers is made upon the ground of the original, already prevailing error, that there are many similar things (but in reality there is nothing similar), at least, that there are things (but there is no “thing”). The law of numbers is based on the (mistaken) belief in similarity and that there are things When you assume there is variety, you assume there are more things of one, but here we are mistaken and invent things that are not there. We see lots of different things and assume there are more of each Our sensations of space and time are false, for they lead consistently1 to logical contradictions. In science we know there are false quantities but as these quantities are at least constant, as, for instance, our sensation of time and space, the conclusions of science have still perfect accuracy and certainty in their connection with one another; Science works with false premises, but they work for specific questions like Newtonian and quantum physics one may continue to build upon them. Up to the point where our assumptions, the constant errors, no longer work with our conclusions like in the theory of atoms. You can work with these theories up to the point that they don’t work anymore There still we always feel ourselves compelled to the acceptance of a ” thing ” or material ” substratum”2 that is moved, Like with a theory of atoms, were our believe in numbers no longer works, we still belief in things whilst the whole scientific procedure has pursued the very task of resolving everything substantial (material) into motion ; here, too, we still separate with our sensation the mover and the moved and cannot get out of this circle, because the belief in things has from immemorial times been bound up with our being. We still separate the mover from the moved, there is no specific movement without our observation When Kant3 says, ” The understanding does not derive its laws from Nature, but dictates them to her, Nature has no order besides the order we give it to her” it is perfectly true with regard to the idea of Nature which we are compelled to associate with her (Nature = World as representation, that is to say as error), but which is the summing up of a number of errors of the understanding. The laws of numbers are entirely inapplicable to a world which is not our representation—these laws obtain only in the human world. Number work only for a world seen thru our eyes, a world created by our way of looking to the world, made of things, similarity, numbers.

In one sentence:

We exist but live in a man made world

1Zimmern translate the German “consequent” (konsequent) as “examined in sequence” is better translated as consequent or consistently.

2substratum” A foundation or basis of something.

3 In the Dutch translation is a note pointing to this quote of Kant from his book: Prolegomena zu einer jeden künftigen Metaphysik die als Wissenschaft wird auftreten können. Page 320 (82) 36 here you can read it.


Human, all too human a book for free spirits Part I translated by Helen Zimmern 1909

  1. NUMBER.—The discovery of the laws of numbers is made upon the ground of the original, already prevailing error, that there are many similar things (but in reality there is nothing similar), at least, that there are things (but there is no “thing”). The supposition of plurality always presumes that there is something which appears frequently,—but here already error reigns, already we imagine beings, unities, which do not exist. Our sensations of space and time are false, for they lead—examined in sequence—to logical contradictions. In all scientific determinations we always reckon inevitably with certain false quantities, but as these quantities are at least constant, as, for instance, our sensation of time and space, the conclusions of science have still perfect accuracy and certainty in their connection with one another; one may continue to build upon them—until that final limit where the erroneous original suppositions, those constant faults, come into conflict with the conclusions, for instance in the doctrine of atoms. There still we always feel ourselves compelled to the acceptance of a ” thing ” or material ” substratum ” that is moved, whilst the whole scientific procedure has pursued the very task of resolving everything substantial (material) into motion ; here, too, we still separate with our sensation the mover and the moved and cannot get out of this circle, because the belief in things has from immemorial times been bound up with our being. When Kant says, ” The understanding does not derive its laws from Nature, but dictates them to her,” it is perfectly true with regard to the idea of Nature which we are compelled to associate with her (Nature = World as representation, that is to say as error), but which is the summing up of a number of errors of the understanding. The laws of numbers are entirely inapplicable to a world which is not our representation—these laws obtain only in the human world.

Menschliches allzu menschlich 1878/80

  1. Die Zahl. – Die Erfindung der Gesetze der Zahlen ist auf Grund des ursprünglich schon herrschenden Irrthums gemacht, dass es mehrere gleiche Dinge gebe (aber thatsächlich giebt es nichts Gleiches), mindestens dass es Dinge gebe (aber es giebt kein “Ding”). Die Annahme der Vielheit setzt immer voraus, dass es Etwas gebe, das vielfach vorkommt: aber gerade hier schon waltet der Irrthum, schon da fingiren wir Wesen, Einheiten, die es nicht giebt. – Unsere Empfindungen von Raum und Zeit sind falsch, denn sie führen, consequent geprüft, auf logische Widersprüche. Bei allen wissenschaftlichen Feststellungen rechnen wir unvermeidlich immer mit einigen falschen Grössen: aber weil diese Grössen wenigstens constant sind, wie zum Beispiel unsere Zeit- und Raumempfindung, so bekommen die Resultate der Wissenschaft doch eine vollkommene Strenge und Sicherheit in ihrem Zusammenhange mit einander; man kann auf ihnen fortbauen – bis an jenes letzte Ende, wo die irrthümliche Grundannahme, jene constanten Fehler, in Widerspruch mit den Resultaten treten, zum Beispiel in der Atomenlehre. Da fühlen wir uns immer noch zur Annahme eines “Dinges” oder stofflichen “Substrats”, das bewegt wird, gezwungen, während die ganze wissenschaftliche Procedur eben die Aufgabe verfolgt hat, alles Dingartige (Stoffliche) in Bewegungen aufzulösen: wir scheiden auch hier noch mit unserer Empfindung Bewegendes und Bewegtes und kommen aus diesem Zirkel nicht heraus, weil der Glaube an Dinge mit unserem Wesen von Alters her verknotet ist. – Wenn Kant sagt “der Verstand schöpft seine Gesetze nicht aus der Natur, sondern schreibt sie dieser vor”, so ist diess in Hinsicht auf den Begriff der Natur völlig wahr, welchen wir genöthigt sind, mit ihr zu verbinden (Natur = Welt als Vorstellung, das heisst als Irrthum), welcher aber die Aufsummirung einer Menge von Irrthümern des Verstandes ist. – Auf eine Welt, welche nicht unsere Vorstellung ist, sind die Gesetze der Zahlen gänzlich unanwendbar: diese gelten allein in der Menschen-Welt.

19. Het getal. – De uitvinding van de getallenwetten is gedaan op grond van de oorspronkelijk al heersende dwaling dat er verschillende identieke dingen zijn (maar in feite is er niets identieks), of althans dat er dingen zijn (maar er is geen ‘ding’). De veronderstelling van de veelheid gaat er altijd al van uit dat eriets is wat veelvuldig voorkomt: maar juist hier regeert de dwaling al, reeds hier fingeren wij wezenheden, eenheden die niet bestaan. – Onze gewaarwordingen van ruimte en tijd zijn vals, want bij consequent onderzoek blijken zij tot logische tegenstrijdigheden te leiden. Bij al onze wetenschappelijke bevindingen rekenen we onvermijdelijk altijd met enkele valse grootheden: maar omdat deze grootheden ten minste constant zijn, zoals bijvoorbeeld onze gewaarwording van tijd en ruimte, krijgen de resultaten van de wetenschap toch een volmaakte strengheid en zekerheid in hun onderlinge samenhang: men kan erop voortbouwen – tot aan dat uiterste punt, waarop de verkeerde basisveronderstellingen, de genoemde constante fouten, in conflict komen met de resultaten, bijvoorbeeld in de atomenleer. We voelen ons hier nog steeds gedwongen uit te gaan van een ‘ding’ of stoffelijk ‘substraat’ dat bewogen wordt, terwijl de hele wetenschappelijke procedure juist heeft gepoogd al het dingachtige (stoffelijke) tot bewegingen te ontleden: ook hier blijven we ten slotte zitten met onze gewaarwording van iets wat beweegt en iets wat bewogen wordt en we komen deze tovercirkel niet uit omdat het geloof aan dingen van oudsher met onze natuur verweven is. – Als Kant zegt ‘het verstand put zijn wetten niet uit de natuur, maar schrijft ze haar voor’ dan is dit volledig waar ten aanzien van het begrip van de natuur dat wij genoodzaakt zijn met haar te verbinden (natuur = wereld als voorstelling, dat wil zeggen als dwaling), maar dat de optelsom is van een grote hoeveelheid dwalingen van het verstand. – Op een wereld die niet onze voorstelling is zijn de getallenwetten in het geheel niet toepasbaar: zij gelden alleen in de mensenwereld.

 

Sources:

I will read a Dutch translation that is based on the work of researchers Colli and Montinari. I also use a translation from R.J.Hollingdale and the Gary Handwerk translation from the Colli-Montinari edition. Both are more modern than the copyright free translation I use here. This is a translation from 1909 by Helen Zimmern, who knew Nietzsche personally, but there was no critical study of Nietzsche’s work done back then and this translation suffers from that. The same goes for the translation from Alexander Harvey. My German is not good enough to pretend that I can translate it better than the professionals do but I will use the original as a referee.

  1. Menselijk al te menselijk een boek voor vrije geesten, translated by Thomas Graftdijk, 2000. Buy it here
  2. Human, all too human a book for free spirits, translated by R.J.Hollingdale, 1986
  3. Human, all too human a book for free spirits I V3, translated by Gary handwerk 1997
  4. Human, all too human a book for free spirits Part I, translated by Helen Zimmern 1909. Read it  here
  5. Human, all too human a book for free spirits, translated by Alexander Harvey, 1908. Read it here
  6. Menschliches allzu menschlich 1878/80. Read it here

 

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