"...he has given us his very great and precious promises," verse 4a (RSV)
"Through these" : to what is "these" referring ?
Looking at the preceding verse it must be through a) "our knowledge of Him" who has called us by a calling which he has effectuated by b) "his own glory" and c) "excellence" (hence the plural "through these").
Picking up on this idea of God's glory and excellence which is explicitly stated or implied in Romans 1 as being the attributes of God's revelation of Himself in the Creation, we further conclude that this God is a God who a) calls and b) makes promises.
Perhaps nature does not teach us this about the God who stands behind it or perhaps man has become too blind and dull to perceive it since the Fall.
So now man needs in addition to natural revelation the special revelation of the Bible - a dual form of revelation technically referred to as duplex cognitio dei.
This fits very well with Peter's argument since he goes on to dwell on this point in verses 16 to 21 of the same chapter .
Peter mentions his experience of Jesus' transfiguration for epistemological reasons. However, Jesus himself speaks of his crucifixion and death as a demonstration of God's glory and as being glorified (see John 13:30-32 .)
I might perhaps have more to say on this in a future post, God willing.