The Collaborative International Dictionary
Irreducible \Ir`re*du"ci*ble\, a.
Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia.
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(Math.) Incapable of being reduced to a simpler form of expression; as, an irreducible formula.
Irreducible case (Alg.), a particular case in the solution of a cubic equation, in which the formula commonly employed contains an imaginary quantity, and therefore fails in its application. -- Ir`re*du"ci*ble*ness, n. -- -- Ir`re*du"ci*bly, adv.
Wiktionary
adv. In an irreducible manner, or state.
Usage examples of "irreducibly".
This is all the more surprising in light of his previously mentioned assertions that the ontology of the mental is an irreducibly first-person ontology and that mental states exist only as subjective, first-person phenomena.