Man does not have two natures that are independent of each other. hummm . . . I believe scripture even makes references to two natures - and that these two natures war one against the other.
There is an 'old nature' - That which is born of the flesh is flesh. John 3:6a - Concerning the 'Flesh' we are told it 'cannot please God.' (Romans 8:8); it 'profiteth nothing:' (John 6:63); there is in it 'no good thing:' (Rom. 7:18). or the 'Natural Man' - The 'natural man' receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he get to know them because they are spiritually discerned' (1 Co. 2:14). This portion of scripture stands in correspondence with verse 8 which tells us that 'none of the princes of this world knew the wisdom of God', i.e. the mystery - for it was "hidden" in God (Eph. 3:9) and even now it is "revealed" (1 Cor. 2:10), the natural man cannot get to know it because it is only discerned by the spirit, or the new nature within us, created by the holy Spirit. The 'old nature is in contrast to the 'new nature' - That which is born of the Spirit is spirit. John 3:6b -born or begotten of the holy Spirit. This new nature is called the 'Divine Nature' (2 Peter 1:4). This new nature [spirit] does not change the old nature [flesh] - that's why we are told to renew our minds - to cast down imaginations - to keep our body in subjection.
The 'Old Man' - The 'old man' "is corrupt according to the deceitful lusts" (Eph. 4:22). These desires or lusts are in all things contrary to God, contrary to His Spirit, and His Word; and to the new nature, the spirit. In contrast to the 'old man' is the 'new man' - Therefore if any man be in Christ, he is a new creatrue: old things are passed away; behold, all things are become new. And all things are of God.. (2 Co. 5:17,18a) - i.e. in that which was created in us; Spirit. We are to 'put on the new man, which after God is created in righteousness and true holiness'. (Eph. 4:24; Col. 3:10) and this is also done by the renewing of our minds - being not conformed to this world but being transformed by the renewing of our minds (Romans 12)
The 'Outward Man' - that which is seen and that which actually perishes (2 Cor. 4:16) and this is 'day by day'. As long as we are in the flesh we die daily. In contrast to the 'outward man' is the 'inward man' which is renewed day by day (Rom. 7:22; 2 Co. 4:16; Eph. 3:16) Those that are born again are constantly being nourished and established day by day with grace and strength by the holy Spirit; so that Christ dwells in the heart by faith and we are filled with all the fulness of God (Eph. 5:19). The inward man delights in the law of God (Rom. 7:22) while the outward man is 'not subject to the law of God' (Rom. 8:7)
The 'Heart', i.e. the natural heart which is "deceitful above all things and desperately wicked" (Jer. 17:9) "Out of the heart proceed evil thoughts, murders, adulteries, fornications, thefts, false witness, blasphemies." (Matt. 15:19) The 'Carnal Mind' - The 'carnal mind' means 'the mind of the flesh' (Rom. 8:7); this mind of the flesh is 'enmity against God.' 'Not subject to the law of God, neither indeed can be', and 'cannot please God'. In contrast to this we have 'the mind'; i.e. in the new nature. It is used in contrast with "flesh" (as "spirit" is), because it refers to that which is inward and invisible. This "mind" serves the law of God (Rom. 7:25) and delights in it (5:22). "the law of the mind" is put for 'the law of God' in Rom. 7:23.
'Sin' - One thing that needs to be distinguished is sin and sins. Sin is the root - sins are the fruit; i.e. the outcome of the old nature. From Romans 5:12 to 8:39 it is "Sin" that is dealt with: the old nature. Although the sinner is justified in Christ, he still feels the working of the old nature, and experiences the conflict between that and the new nature. (Romans 7) It would do anyone good to look up all the verses and maybe do a word study on the differences between our old nature and our new nature - how our walk in the spirit is an actual battle and that the flesh and the spirit are contrary the one to the other. Galatians 5:17 For the flesh lusteth against the Spirit and the Spirit against the flesh: and these are contrary the one to the other; so that ye cannot do the things ye would. We need to renew our minds daily so that we can be led by the spirit, the new creature, the new man created in us via the new birth - given by the holy Spirit - washed in spiritual water; i.e. living water given by our Lord Jesus Christ through faith in him.