Why cannot our good works make up all or part of our righteousness before God?
Because the righteousness which can be approved of before the judgement seat of God must be absolutely perfect and in all respects in conformity with the divine law, and also our best works in this life are all imperfect and defiled with sin.
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Do our good works earn nothing, even though God will reward them in this life and the life to come?
This reward is not of merit but of grace.
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Does this doctrine make people careless and irreverent?
No, for it is impossible that those who are implanted into Christ by a true faith should not bring forth fruits of thankfulness.