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Answer for the clue "Auguste Comte's positivistic philosophy that metaphysics and theology should be replaced by a hierarchy of sciences from mathematics at the base to sociology at the top ", 7 letters:
comtism

Word definitions for comtism in dictionaries

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
Comtism \Com"tism\ (? or ?), n. [Named after the French philosopher, Auguste Comte.] Positivism; the positive philosophy. See Positivism .

Usage examples of comtism.

If Comtism had spread the world would have been converted, not by the Comtist philosophy, but by the Comtist calendar.

In the days of my youth the Religion of Humanity was a term commonly applied to Comtism, the theory of certain rationalists who worshipped corporate mankind as a Supreme Being.