Definitions

from The American Heritage® Dictionary of the English Language, 5th Edition.

  • adjective Impossible to reduce to a desired, simpler, or smaller form or amount.

from The Century Dictionary.

  • Incapable of being reduced to a lower amount or degree; not to be diminished or degraded.
  • Incapable of being brought into a different state, condition, or form.
  • Incapable of being reduced to a desired form or condition by manipulation: as, an irreducible hernia or fracture.

from the GNU version of the Collaborative International Dictionary of English.

  • adjective Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition.
  • adjective (Math.) Incapable of being reduced to a simpler form of expression.
  • adjective (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.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • adjective Not able to be reduced or lessened.
  • adjective Not able to be brought to a simpler or reduced form.
  • adjective mathematics Unable to be factorized into polynomials of lower degree, as (x^2 + 1).
  • adjective mathematics, of an integer Unable to be factored into smaller integers; prime.
  • adjective topology, of a manifold Not containing a sphere of codimension 1 that is not the boundary of a ball.
  • adjective group theory impossible to divide further into representations of lower dimension by means of any similarity transformation
  • noun mathematics Such a polynomial

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • adjective incapable of being made smaller or simpler

Etymologies

from Wiktionary, Creative Commons Attribution/Share-Alike License

ir- +‎ reducible

Examples

  • Behe claims that evolutionary processes cannot generate structures that exhibit what he calls irreducible complexity.

    Desperately Dissing Avida - The Panda's Thumb

  • Nothing explains our phenomenology, but it's not the sort of physical stuff we usually think of as "physical" so I'm not physicalist, and it doesn't help to call it irreducible res cogitans either so I'm not dualist.

    Bunny and a Book

  • But thats precisely why you're definition of irreducible is useless, and why IC is relevant.

    Confirmation Bias and ID

  • The concept of coherence is implicit in the definition of irreducible complexity in the idea of parts that are “well matched” to a “system.”

    The Edge of Evolution

  • The concept of coherence is implicit in the definition of irreducible complexity in the idea of parts that are “well matched” to a “system.”

    The Edge of Evolution

  • The concept of coherence is implicit in the definition of irreducible complexity in the idea of parts that are “well matched” to a “system.”

    The Edge of Evolution

  • The concept of coherence is implicit in the definition of irreducible complexity in the idea of parts that are “well matched” to a “system.”

    The Edge of Evolution

  • The fundamental rhetorical argument of Intelligent Design was and remains the idea of "irreducible complexity" -- the existence of biological systems with functionally integrated parts that apparently cannot possibly arise by a succession of small changes produced by Darwinian evolution.

    Dan Agin: Book Review: God, Science, and the Story of the Human Eye

  • The fundamental rhetorical argument of Intelligent Design was and remains the idea of "irreducible complexity" -- the existence of biological systems with functionally integrated parts that apparently cannot possibly arise by a succession of small changes produced by Darwinian evolution.

    Dan Agin: Book Review: God, Science, and the Story of the Human Eye

  • Although he did not use the term irreducible complexity the interactive nature of the protein was implicit to his analysis of the evolution of chromatin.

    A Different Perspective on Irreducible Complexity

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