Counterfactuals

A counterfactual is a claim about how outcomes would differ under non-actual conditions.

Counterfactuals have the form: If X had been different, Y would have been different.

For example:

• "If the glass had been made of rubber, it would not have shattered."
• "If they were still interested, they would have called."
• "If the premise were false, the conclusion would not follow."

Predictions

Counterfactuals are not predictions.

• Predictions concern what will happen given certain conditions.
• Counterfactuals concern what would have happened under conditions that didn't actually happen.

Predictions anticipate future outcomes; counterfactuals reason about alternatives to what already happened.

Probabilities

Counterfactuals apply at the level where constraints operate. In stochastic systems, the constraint operates on the distribution, not on individual outcomes.

"If I had flipped the coin differently, it would have landed heads" is not a counterfactual. No constraint determines the specific outcome of a fair coin flip.

"If the coin had been biased 70/30 instead of 50/50, heads would have been more likely" is a counterfactual. It identifies a constraint (the bias) and specifies how the distribution would differ.

The distinction matters: a counterfactual must identify something that is actually constrained. In a stochastic system, what is constrained is the probability, not the realization.

2026-01-28 Aaron Brinton