This word has widely varied meanings when it is used to designate things that people regard as not destined to pass away.. They think of a person's fame as immortal if it endures forever. They think of various institutions as immortal if their endurance is unending in time.
But then they are not thinking philosophically, or they are not thinking of personal immortality as an article of faith in the three great religions of the West -- Judaism, Christianity, and Islam.
The schoolbook syllogism "Socrates is a man, all men are mortal, Socrates is mortal" asserts that, as a matter of observable fact, Socrates is not immortal. The affirmation that the soul is immortal is an article of faith. It is not provable by reason.
It is sometimes said that the existence of God, the immortality of the soul, and the freedom of the will are all articles of faith. But the immortality of the soul differs from the existence of God and the freedom of the will. The latter two are in the sphere of reason. They are provable by reason in purely philosophical theology. But unlike the existence of God and free will, the immortality of the human soul is not within the province of philosophical theology. It is entirely in the sphere of religious faith.
In purely philosophical theology, all that can be affirmed by human reason is that the human intellect, being immaterial, is capable of subsisting after the death of the body. But the intellect's capacity for existing apart from the mortal body requires divine intervention to assure it of imperishable existence, either in heaven or in hell. (See Heaven and Hell.)
Adler's Philosophical Dictionary (1995)
Great Ideas from the Great Books (1963)
by Mortimer J. Adler