1. the quality or state of being unable to be reduced, simplified, or broken down into smaller or simpler parts
Usage: often used in philosophy, mathematics, and science
2. in philosophy and biology, the principle that certain complex phenomena cannot be fully explained by or reduced to their component parts alone
Usage: technical; used in discussions of emergence and holism

Examples

• The irreducibility of consciousness remains a central debate in philosophy of mind.
• Some scientists argue for the irreducibility of biological systems to purely chemical explanations.
• The mathematician demonstrated the irreducibility of the polynomial equation.
• Critics of reductionism emphasize the irreducibility of social phenomena to individual behavior alone.
• The irreducibility of certain quantum properties challenges classical physics.
• Philosophers have long grappled with the irreducibility of subjective experience.