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What does irreducibly mean?

Looking for the meaning or definition of the word irreducibly? Here's what it means.

Adverb
  1. In an irreducible manner, or state.
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In Feyerabend's view, commonsense introspective reports are irreducibly immaterialist in content.
Accounting for new irreducibly complex structures by the foregoing mechanisms is a completely different proposition.
Here, it is crucial that there is no formula that connects them, that our experience is irreducibly multiform.
Prof. Torrance aligns himself with Athanasius and the Nicene fathers in holding that the divine identity and one human personality are irreducibly bound together.
It seems to the Jew irreducibly and scandalously unique because of its relationship to his own history.
It is clear that capitalism, with its ceaseless boom and bust cycles, is itself, fundamentally and irreducibly, bi-polar.

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