POST HOKE ER-go PROP-ter HOKE /poːst hoːk ˈer.ɡoː ˈprop.tɛr hoːk/
After this, therefore because of this. It can be defined as assuming causation solely from temporal priority.
Taxonomy - Causal fallacy, temporal causation error. Contrasts with genuine causal inference requiring independent evidence.
Informal Example - "The rooster crowed, then the sun rose; therefore the rooster caused the sunrise."
This section gives the elemental symbolic pattern of the fallacy.
Canonical Form:
(A < B) ⊢ (A → B)
Where:
The fallacy is the unjustified inference from "A earlier than B" to "A caused B." This expresses the core erroneous inference in bare propositional/temporal notation.
This is the explanatory logic showing why the inference structure fails.
Invalidity Statement:
(A < B) ⇏ (A → B)
Temporal succession does not entail causal implication.
Missing Necessary Condition
A valid causal inference would require at minimum:
¬∃C (C < A ∧ C → B)
There must be no earlier variable C that causes B. Assuming away confounders, this reveals the formal "gap" the fallacy commits.
Fallacious Assumed Model:
A → B
Correct Minimal Alternative Model:
A ← C → B
A hidden common cause C can explain both A and B without A → B. This demonstrates the fallacy as a model-selection error.
Let:
The fallacy corresponds to the invalid inference:
(A U B) ⊢ (A → B)
Or equivalently:
◇(A ∧ ◇B) ⇏ (A → B)
Temporal precedence does not entail causal implication.
Epistemic Misstep
𝔼(A < B) ⇏ □cause(A → B)
Where:
Evidence of succession is insufficient justification for believing causation. This captures the fallacy as a failure of evidential standards. Epistemic error formulation can be extremely useful across fallacies.
Coincidence Model
A < B ∧ ¬(A → B)
Reverse Causation Model
B → A ∧ A < B
Confounder Model
C → A ∧ C → B ∧ C < A
Multiple incompatible models fit the temporal data, defeating the inference.
The underlying error of inferring causation from mere succession is discussed by Aristotle, particularly in his treatment of non causa pro causa ("the non-cause taken as cause"). The exact phrase post hoc ergo propter hoc does not appear in Aristotle, but the fallacy is recognized as a mistaken causal inference based on temporal order.
During the medieval Scholastic period, the Latin expression becomes standard in logical handbooks, where it is treated as a subtype of fallacia causae falsae. Scholastic authors distinguish it from related forms such as cum hoc ergo propter hoc.
In the early modern era (16th-18th centuries), the phrase appears consistently in logic manuals and university textbooks throughout Europe, solidifying its canonical form.
By the 19th and 20th centuries, with the rise of inductive logic and later probabilistic and causal analysis, the fallacy is reinterpreted as a formal error of causal identification: assuming an arrow A → B without eliminating confounding factors or alternative causal models.
Modern treatments in statistics and the philosophy of science describe the fallacy as a structural error in causal reasoning, independent of temporal logic.