Without logic, understanding non existence of a self is impossible. If we look at the suttas and hundreds of cases where people have attained stream entry, we see that all did it though contemplating the higher dhamma. And what is the higher dhamma ? It's the technical explanation about how a being actually functions. When Buddha explained it to people, he first explained conditionality, then how the 5 aggregates work, sense bases, etc. and only at the end he explained no self.
The process is very similar to how a bushman would understand how a car works. When first seeing a car, he might believe it is an animal or that it's pushed by some form of spirit. But after a mechanic will show him how every piece of the engine and how the car works in general, he will understand the trickery about how a car actually functions, without the use of a tiger-spirit to push it and without being an animal, despite thing thing looking impossible to him at first.
Buddhism central notion is "the dhamma" - what does dhamma mean ? It means "things as they really are" or "how things really work". According to buddhism, things work in a specific way. And Buddha claims to have found out this specific way and claims to be able to show it to you, same as one could show you that cars work because of the engine, etc and not because of mysterious tiger forces pushing it.
More than this, postmodernism was the only one out of 64 philosophies of the time that Buddhism considers to be a product of sheer stupidity:
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What proponents of posmodernism always forget is
the very thing that makes it be so stupid. If no idea is correct, then how could postmodernism be correct ? How could things work in the way postmodernism says they do ?