If the mathematical structure of infinity is coherent and does not generate the contradictions Aristotle alleges, his reductio ad absurdum arguments lose their logical force entirely.

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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.
Logical force(describing how arguments work): The power of an argument to prove or support a conclusion; how strongly an argument makes its point.
Mathematical structure(what structural realists claim is what we actually know about reality): The abstract patterns, equations, and relationships that describe how something works, stripped of real-world details.
coherent(de Finetti's usage in the context of the Dutch Book argument for probabilism): A subject is coherent if their unconditional degrees of belief do not permit a Dutch Book (a guaranteed loss through a combination of bets) to be made against them

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