For though we walk in the flesh, we do not war according to the flesh:
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Ambrosiaster
AD 400
This means that although we are living in the body we act in a spiritual way. Anyone who does what is pleasing to God is acting spiritually. Commentary on Paul’s Epistles.
And again he says, "Though in the flesh, we do not war after the flesh.".
"For though we walk in the flesh, we do not war after the flesh; for the weapons of our warfare are not carnal, but mighty through God to the demolition of fortifications, demolishing thoughts, and every high thing which exalteth itself against the knowledge of Christ."
Here he goes on to alarm them also by the figure he uses, 'for,' says he, 'we are indeed encompassed with flesh; I own it, but we do not live by the flesh;' or rather, he said not even this, but for the present reserves it, for it belongs to the encomium on his life: but first discourses of the Preaching, and shows that it is not of man, nor needs aid from beneath. Wherefore he said not, 'we do not live according to the flesh,' but, we do not war according to the flesh, that is, 'we have undertaken a war and a combat; but we do not war with carnal weapons, nor by help of any human succors.'