The inner "self" or the "inner man" (Rom. 7:22; Eph. 3:16; 1 Peter 3:4), the core personality of Paul and any other man survives death of body and continues to live even in a greater intensity of the presence of God. That's why Paul says that he desires his body to dissolve, which will be a condition for his being with Christ (that is to say, with a greater intensity of union with Christ, for even while in body Paul experiences Christ’s presence and in-dwelling, even joint life in him /Gal. 2:20/), but to be in body is more beneficial for those to whom he preaches Gospel (Phil. 1:23).
This makes fool of those who purport to be Christians and simultaneously claim that human personality, sometimes called also "soul", dies together with body, thus abolishing and annulling the great tradition of praying to saints (who albeit dead, must live in order to listen to our prayers and intercede for us to God); for, in fact, how Paul could consider his annihilation as better than being alive in body, unless he did not consider the death of body as his annihilation at all, but as his transmission to a greater intensity of life in and with God.
But the bodiless state is not the final one, for as Paul says, "perishable should be clad in imperishability" (1 Cor. 15:53), that is to say, the perishable body will be re-united as imperishable to the soul/bodiless personality of a deceased man and the eternal status will be that of a full personality with soul and body both clad in immortality and imperishability by grace of God.
Moreover, as Paul elsewhere says, not all humans will die and be disjuncted from their bodies, but those who will live to the Second parousia of Christ, will be taken to sky to meet Him there and be with Him eternally without experiencing death at all (1 Cor. 15:51).
Great mystery, and joyful one for that matter. Holy Apostle Paul who are with Christ now, while your body lies in Rome, pray to Him for us.