Enlightenment and mathematics

9 May, 2022 at 09:27 | Posted in Theory of Science & Methodology | 6 Comments

Dialectic of Enlightenment (Cultural Memory in the Present) - Kindle  edition by Horkheimer, Max, Adorno, Theodor W., Noeri, Gunzelin Schmid,  Jephcott, Edmund. Politics & Social Sciences Kindle eBooks @ Amazon.com.When in mathematics the unknown becomes the unknown quantity in an equation, it is made into something long familiar before any value has been assigned. Nature, before and after quantum theory, is what can be registered mathematically; even what cannot be assimilated, the insoluble and irrational, is fenced in by mathematical theorems. In the preemptive identification of the thoroughly mathematized world with truth, enlightenment believes itself safe from the return of the mythical. It equates thought with mathematics. The latter is thereby cut loose, as it were, turned into an absolute authority …

The reduction of thought to a mathematical apparatus condemns the world to be its own measure. What appears as the triumph of subjectivity, the subjection of all existing things to logical formalism, is bought with the obedient subordination of reason to what is immediately at hand. To grasp existing things as such, not merely to note their abstract spatial-temporal relationships, by which they can then be seized, but, on the contrary, to think of them as surface, as mediated conceptual moments which are only fulfilled by revealing their social, historical, and human meaning—this whole aspiration of knowledge is abandoned. Knowledge does not consist in mere perception, classification, and calculation but precisely in the determining negation of whatever is directly at hand. Instead of such negation, mathematical formalism, whose medium, number, is the most abstract form of the immediate, arrests thought at mere immediacy. The actual is validated, knowledge confines itself to repeating it, thought makes itself mere tautology. The more completely the machinery of thought subjugates existence, the more blindly it is satisfied with reproducing it. Enlightenment thereby regresses to the mythology it has never been able to escape …

The subsumption of the actual, whether under mythical prehistory or under mathematical formalism, the symbolic relating of the present to the mythical event in the rite or to the abstract category in science, makes the new appear as something predetermined which therefore is really the old. It is not existence that is without hope, but knowledge which appropriates and perpetuates existence as a schema in the pictorial or mathematical symbol.


  1. Related to the recent topics here of the Frankfurt School and Ukraine:


    • Thanx. Interesting reading!

      • I generally find that anything by Adam Tooze is going to be a good read.

    • Habermas wants his cake and to eat it also.
      He wants the Ukraine to win the war but then cautions the Germans not to turn away from “dialogue and peace”.
      There is no question that “dialogue and peace” are preferable to war.

      However, this is not possible when the antagonist displays a distinct preference for war and a terribly brutal one at that.
      “Dialogue and peace” can sound almost a euphemism for appeasement and history has taught us the value of appeasement.
      There can be no quarter given to a bellicose tyrant who displays evidence of derangement even if he has putative access to the deployment of nuclear weapons.
      Europe cannot cower in the face of such threats.
      Perhaps Tooze and Habermas should spend a week in Kharkiv enjoying directly the thrill of experiencing the deadening thud of explosives and the shattering of thousands of lives.

  2. Beware of false prophets, which come to you in sheep’s clothing, but inwardly they are ravening wolves. Ye shall know them by their fruits.
    Do men gather grapes of thorns, or figs of thistles?
    Wherefore by their fruits ye shall know them.
    – Matthew 12:15-20 KJV

    The technology, culture and liberties of modern Western countries are the fruits of The Enlightenment 1685 – 1815. The previous “Dark Ages” (nine centuries with little scientific and cultural advancement} were replaced by a new emphasis on reason, science, religious tolerance, and “natural rights”—life, liberty and property.

    What are the fruits of Horkheimer, Adorno and others in the “Frankfurt School”?
    None of these writers ever did practical scientific or technical work. So they were poorly qualfied to comment on the role of maths or The Enlghtenement which produced the freedoms an high living standards which they enjoyed.
    Instead these writers were armchair theorists whose clever books led to:
    – Racist indoctination aka “Equity, Diversity and Inclusion”
    – Race hatred aka “Black Lives Matter” (and peviously the Black Panthers etc)
    – Looting aka “consumer reparitions”
    – Promotion of gender fluidity among young children aka “Critical Sex Education”
    – “Queer Teory” and “Critical Feminism” which undermines marriage, family life and other social norms
    – Wokeism
    – Cancel culture

  3. Everything fundamentally wrong with neo-classical economics is summed up in this extraordinarily poignant passage.

    And the real world consequences of its failures are becoming ever more serious.

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