Sarkinos: as Rom. 7.14; Heb. 7.16; 2Cor. 3.3. This word is said to mean properly the material -- the composition of a thing. 'Carnal,' twice in verse 3, is sarkinos, a form used, in some places, to express either material or physical or moral ideas. It occurs also in Rom. 15.27; 1Cor. 9.11; 2Cor. 1.12; 10.4; 1Pet. 2.11. This last passage, 'fleshly lusts,' shows how the material and moral thoughts run into one another.
The addition of the article gives the right sense: 'saved by fire' may mean that the fire was a means of safety, whereas 'through the fire' is in spite of it, or going through the danger and difficulty of it. Dia has two distinct uses as 'through' in English: see 1Pet. 3.20 for the other sense.