You're right. As a minor point, note that not all Greeks believed in the immortality of the soul. If you read Homer, for example, the concept just isn't there. It seems to have entered Greece via the Pythagoreans, in about the 6th century BC. My guess is that they got it from India. (That can not be proven, as relevant evience has not survived, but it seems plausible. I dont think it came from Egypt. There are other hints of Indian influence in Greece around that time too. If you read the surviving fragments of Heraclitus, for example, you can't help but detect a faint whiff of India if you are familiar with early Indian religious thought..) The early Hebrews didn't believe in an afterlife either, a fact that christians always conveniently overlook.