from The American Heritage® Dictionary of the English Language, 4th Edition
- adj. Impossible to reduce to a desired, simpler, or smaller form or amount: irreducible burdens.
from Wiktionary, Creative Commons Attribution/Share-Alike License
- adj. Not able to be reduced or lessened.
- adj. Not able to be brought to a simpler or reduced form.
- adj. Unable to be factorized into polynomials of lower degree, as (x^2 + 1).
- adj. Unable to be factored into smaller integers; prime.
- adj. Not containing a sphere of codimension 1 that is not the boundary of a ball.
- adj. impossible to divide further into representations of lower dimension by means of any similarity transformation
- n. Such a polynomial
from the GNU version of the Collaborative International Dictionary of English
- adj. Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition.
- adj. Incapable of being reduced to a simpler form of expression.
from The Century Dictionary and Cyclopedia
- 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 WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- adj. incapable of being made smaller or simpler
Behe claims that evolutionary processes cannot generate structures that exhibit what he calls irreducible complexity.
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.
But thats precisely why you're definition of irreducible is useless, and why IC is relevant.
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 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.
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.
The set of these indispensable parts is known as the irreducible core of the system.
Intelligent Design has something called irreducible complexity, all though all the examples have been shown to be reducible.
Michael Behe has basically conceded the validity of virtually every aspect of evolution, but fiercely clings to the idea of irreducible complexity even though every example he's come up with gets shot down.
As Roger Ruston has argued in a very important study of the development of rights language (Human Rights and the Image of God, 2004), the idea of irreducible or non-negotiable liberties for human beings has a strong theological basis in mediaeval thought.