Albert Barnes on 2 Peter 3:1

This second epistle, beloved, I now write unto you. This expression proves that he had written a former epistle, and that it was addressed to the same persons as this. Comp. Intro. & 3.

In both which I stir up your pure minds, etc. That is, the main object of both epistles is the same--to call to your remembrance important truths which you have before heard, but which you are in danger of forgetting, or from which you are in danger of being turned away by prevailing errors. Comp. 2Pet 3:12, seq. The word rendered pure, ειλικρινης occurs only here and in Php 1:10, where it is rendered sincere. The word properly refers to that which may be judged of in sunshine; then it means clear, manifest; and then sincere, pure--as that in which there is no obscurity. The idea here perhaps is, that their minds were open, frank, candid, sincere, rather than that they were pure. The apostle regarded them as disposed to see the truth, and yet as liable to be led astray by the plausible errors of others. Such minds need to have truths often brought fresh to their remembrance, though they are truths with which they had before been familiar.

(*) "remembrance" "reminding"