If the geometric contradictions Aristotle derives depend on treating infinite magnitudes as though they behave like arbitrarily large finite ones, the arguments are category errors, not valid reductions.

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Aristotle: Aristotle was an ancient Greek philosopher who lived over 2,000 years ago and is one of the most influential thinkers in Western history. He studied nearly every subject—from animals and plants to politics and ethics—and developed practical ways of thinking that shaped how people understand the world. His ideas on logic, nature, and how to live a good life are still taught and debated today because he focused on observing the real world rather than just abstract theories.
Category error(as used in logic and philosophy of language): A logical mistake where you apply a rule or concept to something it doesn't actually fit, like using a math formula on a poem.
geometric contradictions(as Aristotle's mathematical arguments): Logical problems or paradoxes that arise when dealing with shapes, space, and infinity in mathematics—situations where something seems to break the normal rules.
infinite magnitudes(as mathematical objects being discussed): Quantities or sizes that have no end or limit—they go on forever, like the concept of infinity itself.
reductions(computer science and logic): Transformations that convert one problem into another to show they have similar difficulty—like proving two puzzles are equally hard by showing how to solve one if you can solve the other.

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