The operative word in 1 Cor 2:16 is νοῦς (nous), a word that means almost the same in English as the Greek. More specifically, BDAG ascribes three shades meanings to this word:
- the faculty of intellectual perception (a) mind, intellect, eg, Rom 7:22, 23, 25; (b) understanding, mind, eg,
Luke 24:45, Rev 13:18, Phil 4:7, 2 Thess 2:2
- way of thinking, mind attitude as the sum total of the whole mental and moral state of being, (a) as possessed by every person
... be transformed by the renewing of your mind, which come about
when Christians have their natural νοῦς penetrated and transformed by
the Spirit which they receive at baptism, Rom 12:2, Eph 4:23, Rom
1:28, Eph 4:17, Col 2:18, 2 Tim 3:8, 1 Tim 6:5, Titus 1:15, (b)
specifically of the Christian attitude or way of thinking, eg, 1 Cor
1:10
- result of thinking, mind, thought, opinion, decree, Rom 14:5, 1 Cor 2:16a. When Paul continues in the latter passage (1 Cor 2:16b) ... he
is using the Scriptural word νοῦςto denote what he usually calls
πνεῦμα (1 Cor 2:14). He can do this because his νοῦς (since he is a
'pneumatic' person) is filled with the Spirit (see 2a above), so that
in his case the two are interchangeable. Such a νοῦς is impossible
for a 'psychic' person.
Note #3 above and the BDAG extended explanation. Thus, "the mind of Christ" appears to be a Spirit-filled person - the distinction is explained in detail in Rom 8:5-9
5 Those who live according to the flesh set their minds on the things of the flesh; but those who live according to the Spirit set
their minds on the things of the Spirit. 6 The mind of the flesh
is death, but the mind of the Spirit is life and peace, 7
because the mind of the flesh is hostile to God: It does not submit to
God’s law, nor can it do so. 8 Those controlled by the flesh
cannot please God. You, however, are controlled not by the flesh,
but by the Spirit, if the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, he does not belong to
Christ.
Ellicott is more succinct in his comments about 2 Cor 2:16b
But we have the mind of Christ.—That is, spiritual men, including the Apostles. The Apostle here identifies Christ with the Spirit, whom
he has previously spoken of as the Teacher of spiritual things. He
does not mean to assert that the Apostles knew all that the mind of
Christ knew, but that all things which they did know were from Him and
spiritual (John 15:15).
Barnes is even briefer:
The mind of Christ - The views, feelings, and temper of Christ. We are influenced by his Spirit.