All naturally occurring configurations lie in the set L of living structure; human-made configurations may lie outside L because humans can create unnatural forms.

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• The structures where life occurs just cannot be made in any other way.quote0.824
  Categorical assertion about the necessity of the living process.
• The structures where life occurs just cannot be made in any other way — it is a categorical and mathematical must.claim0.818
• In nature the principle of unfolding wholeness creates living structure nearly all the time. Human designers, who are not constrained by this unfolding, can violate the wholeness if they wish to, and can therefore create non-living structure as often as they choose.quote0.814
  Encapsulates the distinction between natural and human-made order, central to Alexander's critique of contemporary architecture.
• The creation of living structure cannot be done in any other way.claim0.813
• Nature always produces living structure because it follows a process of unfolding wholeness; human designers can create non-living structure by violating this process.claim0.811
  Core distinction between natural and designed configurations, explaining why properties are ubiquitous in nature but rare in bad design.
• The entities which appear in a configuration are not merely cognitive; they have a real mathematical existence.claim0.811
  Rejects a purely psychological interpretation of centers in favor of an objective existence.
• The existence of living structure, as defined in The Nature of Order, requires modifications in our physical picture of the world, not only in the picture we have of architecture.claim0.808
  The closing claim of the chapter's mid-book appendix, asserting that the theory of centers has implications for physics.
• Life and living structure will appear in the world inevitably because the mathematical way space gives rise to structure necessarily reinforces wholeness as part of its most normal evolution.claim0.807
  Alexander's strongest ontological claim: living structure is not probabilistically improbable but mathematically necessary given the principle of unfolding wholeness