Part I: Foundations

Scale-Relative Truth

Introduction
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Scale-Relative Truth

A proposition pp is true at scale σ\sigma if it accurately describes the cause-effect structure at that scale:

Trueσ(p)  ⟺  p minimizes prediction error for scale-σ interactions\text{True}_\sigma(p) \iff p \text{ minimizes prediction error for scale-$\sigma$ interactions}

Example (Scale-Relative Truths).

  • Quantum scale: "The electron has no definite position" is true.
  • Chemical scale: "Water is H2_2O" is true.
  • Biological scale: "The cell is dividing" is true.
  • Psychological scale: "She is angry" is true.
  • Social scale: "The company is failing" is true.

None of these truths reduces without remainder to truths at other scales. Each accurately describes structure at its scale.

Scale-relative truths must be consistent across adjacent scales, in the sense that:

Trueσ(p)∧Trueσ′(q)  ⟹  ¬(p contradicts q at shared interface)\text{True}_\sigma(p) \land \text{True}_{\sigma'}(q) \implies \neg(p \text{ contradicts } q \text{ at shared interface})

But they need not be inter-translatable. Chemical truths constrain but do not replace biological truths.