If motion is defined purely by relational facts about contiguous neighborhoods, then rules four and five describe identical physical situations, and the asymmetric outcomes violate Descartes' own relationist commitments.

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Asymmetric outcomes(as a logical problem with the rules being discussed): Results or situations that are lopsided or unequal—where things don't match up the way they should or are treated differently even though they shouldn't be.
Contiguous neighborhoods(as spatial references used to define motion): The areas immediately surrounding something; basically, what's right next to it.
Descartes: # Descartes René Descartes was a French philosopher and mathematician from the 1600s who fundamentally changed how people think about knowledge and the mind. He's famous for the idea "I think, therefore I am" (cogito ergo sum), which means that the very fact that you can think proves you exist—a foundation for modern philosophy. He also invented the coordinate system used in mathematics (the x and y axes on a graph), which connects geometry and algebra in practical ways we still use today.
Relational facts(as used in metaphysics): True statements about how two or more things are connected to or compared with each other, rather than facts about a single thing alone.

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