Concept

Post Hoc Ergo Propter Hoc

Intro

Post hoc ergo propter hoc is Latin for "after this, therefore because of this." It is the move where someone notices that B happened after A, or that A and B keep showing up together, and jumps to "A must be causing B." The related Latin tag cum hoc ergo propter hoc covers the correlation version: A and B are correlated, therefore A causes B.

The classic kid version: a rooster crows every morning right before the sun rises. The rooster must be causing the sun to rise.

A grown-up version: ice cream sales and drowning deaths both go up in July. Ice cream must cause drowning. (No; both go up because it is summer and people are outside near water.)

Both sides of the religion debate fall into this. Atheists run it against Christianity: "Christian-majority countries had slavery, therefore Christianity caused slavery." Christians run it against atheism: "Stalin and Mao were atheists, therefore atheism causes mass murder." In both cases the correlation is real but the causal arrow has not been established.

This is rated major rather than critical because correlation actually can be evidence for causation when the work is done right. The cardiac prayer studies, randomized controlled trials with proper blinding, are correlation-from-causation arguments under conditions that do support an inference. The fallacy is not in noticing the pattern; it is in jumping from pattern to cause without ruling out alternatives, demonstrating a mechanism, or running the proper test.

In full

The informal fallacy of inferring causation from temporal succession or correlation alone, without independent evidence of a causal mechanism, without engagement with alternative explanations, and without controlled-experimental or quasi-experimental design supporting the inference. The Latin slogans:

Post hoc ergo propter hoc, "after this, therefore because of this", inferring causation from sequence (A happened, then B; therefore A caused B).
Cum hoc ergo propter hoc, "with this, therefore because of this", inferring causation from correlation (A and B occur together; therefore A causes B).

The two are typically treated together in informal-logic textbooks as the correlation-causation fallacy cluster (Walton Informal Logic 2008; Hurley A Concise Introduction to Logic; Copi-Cohen-McMahon Introduction to Logic). The popular formulation is "correlation does not imply causation", an aphorism that is technically imprecise (statistical correlation IS evidence for causation under appropriate conditions) but captures the diagnostic spirit: temporal-sequence + statistical-association are insufficient on their own.

In apologetic discourse the fallacy is bidirectionally deployed:

Atheist deployment against Christianity: "Christianity correlates with witch trials / Inquisition / slavery defense, therefore Christianity caused these atrocities"; "religious people correlate with [bad outcome] in surveys, therefore religion produces [bad outcome]"; "Christian-majority countries had Y problem, therefore Christianity caused Y."
Christian counter-deployment: "Atheist regimes correlate with mass murder (Stalin / Mao / Pol Pot), therefore atheism causes mass murder" (when poorly framed); "decline of Christianity correlates with social-decline indicators, therefore Christian decline causes the decline"; "prayer correlates with positive health outcomes, therefore prayer works" (when not engaging the controlled-trial methodology that distinguishes the cardiac-prayer studies from naive post-hoc).

The fallacy is major-severity rather than critical because legitimate causal inference from correlation IS possible under controlled conditions, established mechanism, IBE, and ruled-out alternatives. The false-fallacy diagnostic that runs through this folder is particularly important here: the cardiac-prayer studies (Byrd Cardiac Prayer Study (1988) / Harris CCU Prayer Study (1999) / STEPP Mozambique Study (Brown 2010)) make statistical-correlation arguments under RCT-quality controlled conditions, NOT naive post-hoc claims.

Canonical structure

Two related forms:

Post hoc form

P1: A occurred before B
C: Therefore A caused B

The fallacy: temporal sequence is not sufficient evidence of causation. Many things happen in sequence without causal connection.

Cum hoc form

P1: A and B are statistically correlated
C: Therefore A causes B

The fallacy: correlation can arise from (a) genuine direct causation A→B; (b) reverse causation B→A; (c) common cause C→A and C→B; (d) selection bias / confounding; (e) chance / random coincidence in finite samples. Without engaging alternatives + the underlying mechanism, the inference is unsupported.

How to spot it (diagnostic)

Causation inferred from sequence or correlation alone, without independent evidence of mechanism.
No causal mechanism articulated. A genuine causal claim requires a story of how A produces B.
Alternative explanations not engaged. Third common cause; reverse causation; chance; selection bias; confounding variables.
The argument doesn't engage why some correlations are non-causal. "Ice cream sales correlate with drowning deaths", both caused by summer heat, not by each other.
No controlled-experimental design. Causal claims from purely-observational data require explicit engagement with the limitations.
Sample-size + statistical-significance considerations absent. Small samples + multiple comparisons + p-hacking can produce spurious correlations.

Common apologetic deployment

Atheist deployment against Christianity

"Christianity correlates with witch trials / Inquisition / slavery defense, therefore Christianity caused these atrocities." Treated in Christians Behaving Badly + No True Scotsman Fallacy via the doctrinal-content distinction. The substantive Christian engagement: Christianity's grounding documents condemn the cited acts in pre-existing text (Mt 5-7; Lk 6:27-35; Mt 26:51-54; 1 Tim 1:10 anti-trafficking command); the temporal-correlation between Christian-majority cultures and these atrocities does not establish Christianity as the causal source, the alternative explanation is that the atrocities occurred despite Christian doctrinal-content rather than because of it.
"Religious people correlate with [bad outcome] in survey data, therefore religion produces [bad outcome]." Survey-correlation + behavioral-outcome studies often have selection effects + reverse causation + confounding (education / income / culture). Substantive engagement requires controlled-comparison + mechanism + alternatives. Examples: "religious people are more politically conservative therefore religion produces conservatism" (likely partly reverse-causal, political-conservatism may drive religious-affiliation rather than vice versa); "religious people are happier" (could be community effect; could be reverse causation; could be selection).
"Christian-majority countries had Y problem (slavery, colonialism, etc.), therefore Christianity caused Y." Geographic-religious correlation does not establish causation. The substantive engagement: Christianity's doctrinal content, abolitionist movements (Wilberforce, the Quaker abolition tradition, the Clapham Sect, all explicitly Christian), the historical record of Christian-influenced moral progress (Holland Dominion 2019). The correlation argument selectively cites the failure-cases while ignoring the success-cases that share the same religious-cultural context.

Christian counter-deployment

The Christian apologist needs to check their own correlation-causation deployments:

"Atheist regimes correlate with mass murder (Stalin / Mao / Pol Pot), therefore atheism causes mass murder." Christian counter-strain. The substantive Christian argument is stronger when framed as engagement with the doctrinal-content of Marxist-Leninist atheism (which authorized class-warfare violence + religious-institutional eradication; treated in No True Scotsman Charge Defeater P5 + Atheist Regime Body Count) rather than as bare correlation. The correlation alone wouldn't establish atheism-as-cause; it requires the doctrinal-content + grounding-text engagement.
"Decline of Christianity correlates with social-decline indicators, therefore Christian decline causes the decline." The correlation between secularization and various social indicators is observable but causal inference requires engagement with confounding variables (industrial / technological change; demographic transitions; cultural fragmentation; etc.). Substantive engagement requires mechanism + multi-line evidence + IBE.
"After I prayed, Y happened, therefore the prayer caused Y." Naive post-hoc as deployed in casual Christian discourse. The substantive Christian engagement is via controlled-trial evidence (Byrd Cardiac Prayer Study (1988) / Harris CCU Prayer Study (1999) / STEPP Mozambique Study (Brown 2010)) + the Miracles cluster's tier-vetted cases, not via naive post-hoc.

How to rebut it

1. Demand a causal mechanism

The proper response to a correlation-causation claim: "State the mechanism by which A produces B. Articulate the causal pathway. Without a mechanism, the correlation is suggestive, not conclusive." Many correlations dissolve under mechanism-scrutiny because no plausible pathway exists.

2. Engage alternative explanations systematically

The standard alternatives:

Third common cause, both A and B caused by C (the "ice cream sales / drowning deaths / summer heat" classic)
Reverse causation, B causes A, not vice versa
Selection effect, the sample is non-representative in ways that produce correlation without causation
Confounding variables, uncontrolled factors that vary with A and produce B
Chance / random coincidence, finite-sample patterns that don't reflect underlying causal structure
Multiple-comparisons inflation, when many hypotheses are tested, some will appear significant by chance alone

The proper response engages each alternative: "Have you ruled out [common cause / reverse causation / selection / chance]? If not, the correlation alone is insufficient."

3. Distinguish suggestive correlation from established causation

Some correlations DO establish causation when supplemented by:

Controlled experimental design (randomized controlled trials)
Mechanism articulated and supported
Multiple-line evidence converging on causal claim (epidemiology + animal studies + mechanism + dose-response + temporal precedence + counterfactual reasoning)
Inference to best explanation when alternatives have been engaged and ruled out
Effect size + statistical significance appropriate to inference

The distinction is the work; the cardiac-prayer studies (controlled trials with explicit RCT design) are doing this work, while naive correlation-causation claims are not.

False-fallacy examples

Cases where what looks like post-hoc / cum-hoc is NOT actually fallacious, the inference from correlation has been supplemented by appropriate methodological work.

Controlled clinical trials with statistical significance. Byrd Cardiac Prayer Study (1988) (San Francisco General Hospital CCU; Southern Medical Journal 81:826-829; positive composite-severity-score result, P <.01); Harris CCU Prayer Study (1999) (Mid America Heart Institute; Archives of Internal Medicine 159:2273-2278; weighted MAHI-CCU score P=.04 favoring prayer); STEPP Mozambique Study (Brown 2010) (proximal-prayer protocol, Southern Medical Journal 103.9 pp. 864-869). Why these aren't post-hoc fallacy: RCT design controls for confounders; statistical significance excludes pure-chance interpretations within standard p-value thresholds; the inference to causation is probabilistic, not fallacious. Methodological critiques (Posner 1990 on Byrd; Hoover-Margolick 2000 on Harris) engage methodology + alternative interpretations rather than dismissing the studies as naive post-hoc.
Mechanism-supported causal claims (smoking → lung cancer). Started as epidemiological correlation in mid-20th-c. but became established causation through (a) mechanism (carcinogens binding DNA), (b) animal studies, (c) dose-response relationships, (d) controlled cessation studies showing reversal, (e) molecular-genetic evidence. Why this isn't post-hoc: multiple-line evidence + mechanism convergence supports causal inference.
Inference to the best explanation when alternatives have been engaged. When the alternatives (common cause; reverse causation; chance; selection) have been systematically ruled out, IBE supports causation. Standard scientific reasoning. Engaged in Argument from Origin of Life (the design-inference is IBE-not-gap-reasoning; engaged in God of the Gaps).
Universal generalizations from observation + theory. "Force = mass × acceleration" began as observation, became lawlike with mechanism + theoretical embedding (Newtonian mechanics + subsequent refinements). Not post-hoc but inductive-theoretical.
Historical-causal inferences supported by multi-line evidence. Tom Holland's Dominion (Basic 2019) argues Christianity → modern moral framework via multi-line evidence: doctrinal-content of NT moral teaching + counterfactual reasoning about non-Christian ancient cultures + sociological / institutional pathway tracing. Not naive post-hoc but multi-line historical-causal inference. Whether the inference succeeds is contested but the methodology is post-hoc-fallacy-resistant.
Statistical regression / experimental design. Properly controlled (RCTs; matched-pair studies; quasi-experimental designs; instrumental variables; regression discontinuity) can support causal inference from observational data. Modern econometrics + epidemiology + clinical-trial methodology engage these tools.
Mendelian randomization in epidemiology. Uses genetic variation as instrumental variable to support causal inference from observational data. Methodologically post-hoc-fallacy-resistant.
Convergent evidence from independent methodologies. When multiple methodologies (RCT + observational + mechanistic + theoretical) converge on the same causal claim, the convergence resists post-hoc-fallacy critique.

The diagnostic test: does the inference rest on correlation/sequence alone, or is it supplemented by mechanism / controlled design / alternative-elimination / multi-line evidence / IBE? If correlation alone, fallacy; if supplemented, legitimate.

When it's actually fallacious

Clear cases where the post-hoc / cum-hoc charge sticks:

"Christianity correlates with witch trials / Inquisition, therefore Christianity caused these atrocities." Engaged in Christians Behaving Badly + No True Scotsman Fallacy via doctrinal-content distinction. The temporal-correlation does not establish causation; Christianity's grounding documents condemned the acts in pre-existing text.
"Religious people are X% more likely to vote conservatively, therefore religion produces conservatism." Selection / reverse-causation / cultural-confounding alternatives not engaged.
"After I prayed, Y happened, therefore the prayer caused Y." Naive post-hoc; many sequences without causal connection.
"Atheist regimes had mass killings, therefore atheism causes mass killings" (Christian counter-instance, when not framed as engagement with Marxist-Leninist doctrinal content). The substantive case requires mechanism + grounding-text engagement (treated in No True Scotsman Charge Defeater P5 + Atheist Regime Body Count), bare correlation is insufficient.
"Decline of Christianity correlates with social-decline indicators, therefore Christian decline causes the decline." Christian counter-instance; confounding variables (industrialization / demographic / cultural fragmentation) not engaged.
Conspiracy-theory correlation arguments (vaccines/autism temporal correlation, refuted by RCT data + mechanism + epidemiology).
"Eat ice cream → catch a cold", common cause (cold weather) produces both ice-cream-craving and infections without direct causation.
"Crowing rooster causes sunrise", temporal sequence without causal mechanism.

Christian scholarly resources

Douglas Walton, Informal Logic 2nd ed. (Cambridge, 2008). Standard taxonomic treatment of post-hoc / cum-hoc cluster.
Patrick Hurley, A Concise Introduction to Logic (Cengage, multiple eds.). Textbook treatment.
Irving Copi, Carl Cohen, & Kenneth McMahon, Introduction to Logic (Routledge, 14th ed.). Alternate canonical textbook.
Norman Geisler & Ronald Brooks, Come, Let Us Reason: An Introduction to Logical Thinking (Baker, 1990). Christian-apologetic logic primer.
Judea Pearl + Dana Mackenzie, The Book of Why: The New Science of Cause and Effect (Basic, 2018). Modern causal-inference framework, Pearl's do-calculus + structural causal models address correlation-causation rigorously.
Tom Holland, Dominion: How the Christian Revolution Remade the World (Basic, 2019). Multi-line historical-causal inference engaged carefully, Christianity → modern moral framework with mechanism + counterfactual + sociological pathway tracing.
Candy Gunther Brown, Testing Prayer: Science and Healing (Harvard, 2012). Engages cardiac-prayer-studies methodology + correlation-causation question carefully; the academic text complementing the STEPP Mozambique Study (Brown 2010) research.
Edward Feser, The Last Superstition (St. Augustine's Press, 2008). Engages atheist correlation-causation arguments against Christianity from natural-law tradition.
Vincent Carroll & David Shiflett, Christianity on Trial: Arguments Against Anti-Religious Bigotry (Encounter, 2002). Engaging anti-Christian correlation-causation cluster arguments with the historical record.
John Lennox, God's Undertaker: Has Science Buried God? (Lion, 2007). Engages correlation-causation in the science-religion debate.