Romans 8:5

For they that are after the flesh
By flesh is meant the corruption of nature; and they may be said to be "after" it, not all that have flesh in them, for the best of saints have it in them; regenerating grace does not remove it from them; there is a difference between being in and after the flesh, and flesh being in us; but such who are as they were born, who have nothing but flesh, or corrupt nature in them, in whom that is the governing principle, whose minds are carnal, and whose whole walk and conversation is, such, are here meant: and these persons

do mind the things of the flesh:
not merely things corporeal, belonging to the welfare of the body; or things natural for the improvement of the mind; or things civil, as riches which may be minded and sought after in a lawful way; but things sinful, the lusts, works, and sins of the flesh: which they may be said to "mind", since they judge them to be good; the bent and application of their minds are to them; their affections are set upon them; they are solicitously careful to provide for them, and savour and relish them: nor is it to be wondered at, since these are natural to them; they are opposite to God and so agreeable to them; they have no mind, thought, affection, or relish, for anything else; and it is entirely owing to mighty grace, that any mind the things of the Spirit:

but they that are after the Spirit;
not such who follow the dictates of their own spirits; or are outwardly reformed; nor all that have spiritual gifts; or profess themselves to have the grace and Spirit of God; but such who are born again, are renewed in the spirit of their minds, in whom grace is the governing principle: the work of the Spirit is begun in them, though not perfected: the Spirit himself dwells in them, and they walk after him; their minds and conversations are spiritual, though there may be a great deal of carnality in their hearts, thoughts, words, and actions, which is matter of grief unto them: these mind

the things of the Spirit;
the graces of the Spirit; spiritual blessings; the doctrines of the Gospel; spiritual sacrifices and services: these have some understanding of, can discern the difference between them and carnal things, judge and approve of them as right; have a great esteem and affection for them, and taste a sweetness in them. They have no mind naturally to these things; nor is the bias of their minds altered by themselves, nor could it; this is wholly the work of the Spirit of God; and these things are minded only because, and as they are agreeable to the spiritual part, the inward man.