Quite the opposite. The Greeks probably learned this from the Hebrews. And the term "immortal" does not apply to souls. Mortality and immortality are strictly about the human body. Hence "mortality rates".
But souls and spirits are imperishable, therefore we read about the OT saints in Sheol/Hades (which is in "the heart of the earth", or "the lower parts of the earth") after they died. Here is "The writing of Hezekiah king of Judah, when he had been sick, and was recovered of his sickness":
I said in the cutting off of my days, I shall go to the gates of [Sheol]: I am deprived of the residue of my years. (Isaiah 38:10 KJV) [Note: the KJV translators should not have substituted "the grave" for Sheol, which has led to a lot of confusion]
I said, “In the prime of my life I shall go to the gates of Sheol; I am deprived of the remainder of my years.” (Isaiah 38:10 NKJV)
אֲנִ֣י אָמַ֗רְתִּי בִּדְמִ֥י יָמַ֛י אֵלֵ֖כָה בְּשַׁעֲרֵ֣י שְׁאֹ֑ול פֻּקַּ֖דְתִּי יֶ֥תֶר שְׁנֹותָֽי
Strong's Concordance (H7585)
sheol: underworld (place to which people descend at death)
Original Word: שְׁאוֹל
Part of Speech: Noun Feminine
Transliteration: sheol
Phonetic Spelling: (sheh-ole')
Definition: underworld (place to which people descend at death)
But souls and spirits are imperishable, therefore we read about the OT saints in Sheol/Hades (which is in "the heart of the earth", or "the lower parts of the earth") after they died. Here is "The writing of Hezekiah king of Judah, when he had been sick, and was recovered of his sickness":
I said in the cutting off of my days, I shall go to the gates of [Sheol]: I am deprived of the residue of my years. (Isaiah 38:10 KJV) [Note: the KJV translators should not have substituted "the grave" for Sheol, which has led to a lot of confusion]
I said, “In the prime of my life I shall go to the gates of Sheol; I am deprived of the remainder of my years.” (Isaiah 38:10 NKJV)
אֲנִ֣י אָמַ֗רְתִּי בִּדְמִ֥י יָמַ֛י אֵלֵ֖כָה בְּשַׁעֲרֵ֣י שְׁאֹ֑ול פֻּקַּ֖דְתִּי יֶ֥תֶר שְׁנֹותָֽי
Strong's Concordance (H7585)
sheol: underworld (place to which people descend at death)
Original Word: שְׁאוֹל
Part of Speech: Noun Feminine
Transliteration: sheol
Phonetic Spelling: (sheh-ole')
Definition: underworld (place to which people descend at death)
SO then what is being said is our SPIRIT goes back to God,our SOULS wait in either a place of rest or torment until judgment and resurrection because the body decays those are then placed into an incorruptible and immortal new body?