9/6/2026
The fallacy, in English
In Aristotelian philosophy there is the notion of Prime Mover (or Unmoved Mover). The idea here is most all of the things that are moved are moved by something else. Then, if these movement chains (or causal chains) were traced back in time, and the chains could not go back forever, there might be, or had to be, a Prime Mover, a first mover. At this point in the reasoning there is an issue, and it is an issue between 'a' and 'the'. That there is, or might be, a Prime Mover does not mean that there is only one of them i.e. the Prime Mover. There could be two of them (or more).
The same slip shows up in ordinary claims like "the tallest student in the class" — which presupposes there's exactly one, and breaks the moment there's a tie.
The diagram
Universe = {a, b, c}
P (PrimeMover) = {a,b} (two of them)
Try it
Formula (b), `∃x(PrimeMover(x)&∀y(PrimeMover(y)→y=x)) ` — 'there is exactly one Prime Mover' — is false. Endorse it and see how you get on. Then you can change the diagram so that there is exactly one and Endorse Formula (d), `∃x(PrimeMover(x)&∀y(PrimeMover(y)→y=x)) `
Generalization
The technique on display here can be generalized to different numbers of items. Suppose you suspected that there were two Prime Movers and you wished to say 'the two Prime Movers', you could do this with a formula like Formula (e)
∃x∃y(PrimeMover(x)&PrimeMover(y)&~(x=y)&∀w(PrimeMover(w)→(w=x)∨(w=y)))
This says 'there are two Prime Movers and any other Prime Mover is identical to one of those two.'