9/4/2026
The fallacy, in English
"Everything has a cause. Therefore, something is the cause of everything." The first sentence is a reasonable premise. The second does not follow from it — and mixing them up is a genuinely common move (it turns up, for instance, in causal versions of the cosmological argument). Logicians call this the *quantifier-shift fallacy*: swapping the order of `∀` and `∃` changes what is being claimed.
The diagram
Universe = {a, b, c}
C (Cause) = {(a,c),(c,b),(b,a) }, read as `Cause(y,x)` = "*y* causes *x*", drawn as three arrows: *a* causes *c*, *c* causes *b*, *b* causes *a*.
What we have in the diagram is a closed causal loop, each thing with exactly one cause, but no single universal cause among them.
Try it
Formula (e), `∀x∃yCause(y,x)`, is true — every individual has *some* cause (check: does *a* have a cause? yes, *b*. Does *b*? yes, *c*. Does *c*? yes, *a*). Formula (f), `∃y∀xCause(y,x)`, is false — no single individual causes all three. Endorse (e), then separately try to Endorse (f) and watch the game fail to find a witness for you — that gap between (e) and (f) *is* the fallacy, made playable. Formula (g), `∀x~Cause(x,x)`, confirms nothing causes itself in this model.