Abstraction Necessarily Discards Information

This is an axiom because it defines an irreducible property of abstraction itself: information loss is not an accidental feature but the very essence of what makes something an abstraction. The act of abstracting is fundamentally the act of discarding—selecting some features as relevant while ignoring others.

From information theory, any compression requires information loss (unless the data is perfectly redundant). Abstraction is lossy compression applied to reality. A map that included every feature of the territory at full fidelity would be the territory itself, making it useless as a map. The utility of abstractions comes precisely from their selectivity—they highlight certain patterns by suppressing others. This connects to Korzybski's "the map is not the territory" and Borges's fictional map at 1:1 scale that becomes useless. Every model, category, or representation trades completeness for tractability.

This axiom is foundational for the curriculum because it establishes that all our knowledge is necessarily incomplete—not due to lack of effort but due to the nature of abstraction itself. It explains why multiple models of the same phenomenon can be valuable (they discard different information), why edge cases reveal abstraction boundaries, and why applying abstractions to novel contexts can fail. This axiom justifies teaching students to ask "what information does this abstraction discard?" as a fundamental analytical move.