Think of Venn Diagrams, only part of Turkey is part of Europe. There's overlap, but one isn't inside the other. Turkey is, like Russia, considered a transcontinental country. They aren't "in" either continent, but part of them is.

> And if history is important, the Ottoman empire has a history very much involved with the rest of Europe.

As an adversary/attacker, yes. But that's not a reasonable foundation for declaring membership.