Key Principle
Natural laws are "principles of impossibility" — they declare certain events physically impossible, carrying modal force that accidentally true generalizations lack. "Were there a natural law limiting the age of any moa-like organism to fifty years, then it would not be possible for any moa to live longer" (Appendix *x). Natural necessity differs from logical necessity: a world violating Newton's inverse square law is conceivable; a world violating the law of non-contradiction is not.
The distinction matters because falsifiability alone cannot separate genuine laws from accidentally true universal statements — both are universal, both are falsifiable, both may survive all tests.
Why This Matters
Without natural necessity, Popper's framework cannot explain why scientists treat "all copper conducts electricity" differently from "all coins in my pocket are silver." Both are universal statements, both happen to be true, both are falsifiable. But only the first supports counterfactuals ("if this were copper, it would conduct electricity") and grounds genuine scientific explanation.
This appendix acknowledges a gap in the main text rather than fully closing it. Falsifiability sorts theories into scientific vs. non-scientific, but within the class of scientific theories, something more is needed to distinguish laws from accidents. Popper points toward the concept of natural necessity as part of the answer, while acknowledging it requires further philosophical elaboration.
Good Examples
The moa example: "No moa lives beyond fifty years" might be accidentally true (all moas happened to die young because of some contingent circumstance) or nomologically necessary (there is a biological law limiting their lifespan). The truth-value is the same, but the modal force differs: the law would support counterfactuals about hypothetical moas, the accident would not (Appendix *x).
Copper conductivity vs. pocket coins: "All copper conducts electricity" is treated as a law because it supports counterfactuals and generalizes beyond observed instances. "All coins in my pocket are silver" is accidentally true and would not survive a different pocket. Falsifiability cannot distinguish them — both are universal and testable (Appendix *x).
Physical vs. logical necessity: Newton's inverse square law could conceivably be different (an inverse cube law is coherent). The law of non-contradiction cannot be different. Natural necessity occupies a middle ground between logical necessity and mere accident.
Counterpoints
Humean skepticism about necessity: Hume argued that we never observe necessity, only constant conjunction. Popper partially agrees — natural necessity is not directly observable — but insists the distinction is real and scientifically indispensable, even if not fully formalizable.
Incomplete account: Popper acknowledges this concept "requires further philosophical elaboration." The appendix opens a question rather than settling it, pointing toward work he would continue in Conjectures and Refutations and the Postscript.
Goodman's "grue" problem: Nelson Goodman later sharpened this challenge: how do we distinguish law-like generalizations from accidental ones that happen to match all observations? Popper's appeal to natural necessity gestures at the answer but does not formalize it.
Key Quotes
"Were there a natural law limiting the age of any moa-like organism to fifty years, then it would not be possible for any moa to live longer." — Karl Popper, Appendix *x
Rules of Thumb
- Not all true universal statements are laws — ask whether the statement supports counterfactuals
- A genuine law declares certain events impossible, not merely absent
- Natural necessity is stronger than accidental truth but weaker than logical necessity
- Falsifiability is necessary for science but not sufficient to identify genuine laws
Related References
- Falsifiability and the Logic of Deductive Testing — Falsifiability as the baseline criterion that natural necessity supplements
- Content, Testability, and Degrees of Falsifiability — How laws with higher content are preferred, beyond mere accidental truth
- The Formal Probability Calculus and Zero-Probability Proof — The zero-probability result that applies to all universal statements, law-like or accidental