Saying they don't work because Aristotle didn't use them is like throwing out Newtons laws because Aristotle didn't use them.
There have been whole schools of mathematics that reject the law of the excluded middle: https://en.wikipedia.org/wiki/Constructivism_(mathematics)
Newer logics also don't use that law but instead deal with undecidability, which is less than a century old but is the most import result in logic since it's invention.
Saying they don't work because Aristotle didn't use them is like throwing out Newtons laws because Aristotle didn't use them.
There have been whole schools of mathematics that reject the law of the excluded middle: https://en.wikipedia.org/wiki/Constructivism_(mathematics)
Newer logics also don't use that law but instead deal with undecidability, which is less than a century old but is the most import result in logic since it's invention.