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In ‘Beyond good and evil’, chapter 1, section 4, Nietzsche uses the words ‘counterfeiting of the world by means of numbers’:

The question is, how far an opinion is life-furthering, life- preserving, species-preserving, perhaps species-rearing, and we are fundamentally inclined to maintain that the falsest opinions (to which the synthetic judgments a priori belong), are the most indispensable to us, that without a recognition of logical fictions, without a comparison of reality with the purely IMAGINED world of the absolute and immutable, without a constant counterfeiting of the world by means of numbers, man could not live - that the renunciation of false opinions would be a renunciation of life, a negation of life.

I’ve no idea what these words mean, or refer to

  • what does Nietzsche mean by these words?
  • He means that the value of opinions depends not on whether they are true but on whether they are life-sustaining, and hence the value we are inclined to place on describing the world mathematically (as in mathematical physics of Newton, for example) has nothing to do with its truth. This is Nietzsche's subversion of Kant. For Kant, synthetic a priori judgments at the basis of mathematics come from the conditions of possibility of experience, and hence are true, but to Nietzsche they only come from the conditions of possibility of life, and hence are only useful fictions. – Conifold Jun 19 at 22:16
  • You conveniently/opportunistically fail, @Conifold, to include the last sentence of that section in your revision of the question: "TO RECOGNISE UNTRUTH AS A CONDITION OF LIFE; that is certainly to impugn the traditional ideas of value in a dangerous manner, and a philosophy which ventures to do so, has thereby alone placed itself beyond good and evil." Why so? – gonzo Jun 19 at 23:22
  • @gonzo I also omitted the first sentence because both are irrelevant to the meaning of the phrase asked about. They frame this into Nietzsche's broader argument. – Conifold Jun 19 at 23:26
  • The last, @Conifold, is but a more precise iteration of the first. But he issue, most poignantly raised in the modern world by Rorty's suggestion that "objectivity" [read truth] be sacrificed at the altar of "solidarity" remains alive and well. "TO RECOGNISE UNTRUTH AS A CONDITION OF LIFE," is a slogan which underlies and undergirds the contemporary post modern, "post truth," ethos, which essentially gave birth to the current leader of the free world, who, much to the chagrin of many, realized that he could play that game too. – gonzo Jun 20 at 0:09
  • In short, it is by ignoring the, if nothing else, regulative notion of truth/objectivity as the goal of inquiry, not as the synthetic a priori, that we have delivered our world to the polarity and chaos that we find ourselves in. – gonzo Jun 20 at 0:10
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If you go on to the next section, you find the following paragraph which clarifies things (well, a bit...). Note the passage I bolded:

[Philosophers] all pose as though their real opinions had been discovered and attained through the self-evolving of a cold, pure, divinely indifferent dialectic (in contrast to all sorts of mystics, who, fairer and foolisher, talk of "inspiration"), whereas, in fact, a prejudiced proposition, idea, or "suggestion," which is generally their heart's desire abstracted and refined, is defended by them with arguments sought out after the event. They are all advocates who do not wish to be regarded as such, generally astute defenders, also, of their prejudices, which they dub "truths,"-- and VERY far from having the conscience which bravely admits this to itself, very far from having the good taste of the courage which goes so far as to let this be understood, perhaps to warn friend or foe, or in cheerful confidence and self-ridicule. The spectacle of the Tartuffery of old Kant, equally stiff and decent, with which he entices us into the dialectic by-ways that lead (more correctly mislead) to his "categorical imperative"-- makes us fastidious ones smile, we who find no small amusement in spying out the subtle tricks of old moralists and ethical preachers. . Or, still more so, the hocus-pocus in mathematical form, by means of which Spinoza has, as it were, clad his philosophy in mail and mask--in fact, the "love of HIS wisdom," to translate the term fairly and squarely--in order thereby to strike terror at once into the heart of the assailant who should dare to cast a glance on that invincible maiden, that Pallas Athene [...]

Nietzsche's point is that math — numbers — aren't used for any philosophical purpose; they aren't integral to any philosophical process. Numbers are a shield that gives a philosophical opinion and air of solidity and invincibility. I mean, consider the following two statements:

  • It's very likely that John will pick up the book
  • There's a 85% chance that John will pick up the book

On the face of it, there is absolutely no difference between these two statements. Both state my opinion that John will (in all likelihood) pick up some book. But substituting in that number gives a sense of authority, as though I had measured something and come to a definitive conclusion that the chance of this happening is exactly so much. It's strange how much numerical measurement impacts our daily lives... Think about how we arbitrarily point to certain positions on a clock face, positions which then come to designate 'on-time' and 'late', which in turn creates an assortment of social challenges, risks, rewards, and punishments.

Or perhaps think of it in terms of Nietzsche's invocation of 'mystics' and 'inspirations'. A mystic looks at the sky and notes that it is blue. He doesn't need to pull out an instrument and measure whether the wavelength of light he's perceiving is between 450 and 485 nanometers (the wavelengths we associate with 'blue'), and in most cases that kind of measurement would add nothing useful to a discussion of the sky. But there's an appealing power in saying "the sky is at 457 nanometers." That feels like we've said something more significant than "The sky is blue."

More broadly, we can go back to section two, where Nietzsche says:

The fundamental belief of metaphysicians is THE BELIEF IN ANTITHESES OF VALUES.

Every philosopher (in Nietzsche's view) wants to set up the world as a system of opposing values. Every set of opposing values needs a metric (a system of measurement) so that objects or events can be placed in relationship to those values. And every metric relies on numbers to carry its value judgements. To suggest that X is good is to imply that some Y is bad, and then we must lay things out on a tortuous path between X and Y; we must put them in order, implying some scale that maps to a number line. It's this move that Nietzsche finds problematic, because he questions not just the imposed value ordering, but the very act of creating antithetic values.

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Pretty simple, really, the expression addresses the shortcomings of the quantification of reality, i.e. formally generalizing experience:

"In mathematics and empirical science, quantification (or quantitation) is the act of counting and measuring that maps human sense observations and experiences into quantities. Quantification in this sense is fundamental to the scientific method." See https://en.wikipedia.org/wiki/Quantification_(science); https://plato.stanford.edu/entries/quantification/

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