Conjectures and refutations
The minimal cycle through which all knowledge grows.
Objective
Define the process of knowledge growth in a form precise enough to be used daily.
Context
Drawn directly from Karl Popper’s critical rationalism in Conjectures and Refutations [1].
Result
P₁ → TT → EE → P₂
- P₁ : Problem. Any difficulty, anomaly, contradiction, or open question in our present understanding.
- TT : Tentative Theory. A bold, imaginative conjecture offered as a possible solution to P₁.
- EE : Error Elimination. Ruthless critical discussion and empirical tests designed to refute the TT if it is false.
- P₂ : New Problem. The sharper, deeper, richer problem situation that emerges after EE.
The arrow means “gives rise to”. The cycle never ends; each iteration removes error and raises understanding.
Example
A desk lamp fails to light up when switched on (P₁).
- TT₁: The light bulb is burnt out.
- EE₁: Replace the bulb with a known working one. The lamp still does not light. The theory is falsified.
- P₂: Why does a lamp with a working bulb fail to light?
- TT₂: The wall outlet is not providing power.
- EE₂: Plug a different device into the same outlet. It works. Theory falsified.
- P₃: Why is power reaching the outlet but not the bulb socket? (The problem is now sharper: we have eliminated the bulb and the house grid, pointing toward the lamp’s internal wiring or switch).
Discussion
This schema replaces passive accumulation of data with active creation followed by merciless criticism. Knowledge does not begin with "observations," but with a problem and our imaginative attempts to solve it.
Conclusion
Knowledge grows exactly as problems are solved by conjectures that survive attempted refutations.