- Two discourses about the natural fact Many exist, both called Mathematics. One suppresses the other.
- Two discourses about learning exist, both called education. One is based upon European Bildung, the other upon North-American Enlightenment.
The French post-structuralist thinker Michel Foucault gives one understanding of competing discourses.
The victorious discourse called ‘deduced mathematics’ consists of concepts defined as examples of the abstrac-tion Set; and of theorems deduced from metaphysical axioms. It presents the outside world as its applications.
The suppressed discourse called ‘induced mathematics’ consists of concepts defined as abstractions from examples of the natural fact many; and theorems validated by testing deduced predictions. It presents the outside world as its roots.
The educational discourse called ‘enlightenment’ originates in the Enlightenment period and was developed in its US democracy wanting as many as possible to be enlightened as much as possible to practise democracy.
The educational discourse called ‘Bildung’ originates in the post-Enlightenment period and was developed in Germany to stop enlightenment and democracy in spreading from France, the place of the second Enlightenment-democracy; and to sort out the elite for a central administration patronizing its population.
As a professor on the history of thought systems, Michel Foucault created a discourse on discourses claiming to be scientific, especially human sciences. Foucault has shown how a human discipline disciplines itself and its objects, in contrast to a natural discipline disciplining itself by its objects. Thus human disciplines discipline its writers through conceptual force forcing researchers to research and teachers to teach and learners to learn inside the victorious discourse; and disciplines its human objects by forcing individuals to accept the identity-verdicts stated by the discourse’s IS-statements, thus imprisoning humans in an invisible identity-prison created and guarded by the pastoral power of the discourse.
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