Yeah, Spock liked to think that to be logical is the same as being emotionless.
I think that it’s more likely that being emotionless, or rather
controlling the emotions allows one to think more logically. The thought process isn’t clouded by emotion.
For example in the episode Amok Time, when Spock confronts T’Pring at the end of the Kal-if-fee:
SPOCK: T'Pring. Explain.
T'PRING: Specify.
SPOCK: Why the challenge, and why you chose my captain as your champion.
T'PRING: Stonn wanted me, I wanted him [to want is admittedly an emotion].
SPOCK: I see no logic in preferring Stonn over me.
T'PRING: You have become much known among our people, Spock. Almost a legend. And as the years went by, I came to know that I did not want to be the consort of a legend. But by the laws of our people, I could only divorce you by the kal-if-fee. There was also Stonn, who wanted very much to be my consort, and I wanted him.
If your Captain were victor, he would not want me, and so I would have Stonn. If you were victor you would free me because I had dared to challenge, and again I would have Stonn. But if you did not free me, it would be the same. For you would be gone, and I would have your name and your property, and Stonn would still be there.
SPOCK: Logical. Flawlessly logical.
T'PRING: I am honoured.
SPOCK: Stonn. She is yours.
After a time, you may find that having is not so pleasing a thing after all as wanting. It is not logical, but it is often true.
This exchange reminds me of a geometry proof. I had a love-hate relationship with them. And I love that last parting jab. Logical or not.