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M Azingrace said:
Reconciling God's call to evangelize with the Calivinistic doctrines of total depravity and unconditional election.

I am not sure whether I understand you correctly but it seems to me that your problem is that why should we evangelize if there is something like unconditional election. Tom said that God uses means to bring the elect to Christ and I think it is just that. Take for example the case of Lydia in Acts 16:11 - 15. God has wonderfully lead Paul to Philippi to preach the Gospel there. And there were a group of women there. We read that "The Lord opened her heart to pay attention to what was said by Paul". And also in Romans 10:14 we read:"But how are they to call on him in whom they have not believed? And how are they to believe in him of whom they have never heard? And how are they to hear without someone preaching?".

Then there is also Acts 18:9,10: "And the Lord said to Paul one night in a vision, "Do not be afraid but go on speaking and do not be silent, for I am with you, and no one will attack you to harm you, for I have many in this city who are my people."

I would say that it is clear that God sends preachers so that the elect will hear the Gospel and He will open their hearts to the Gospel message. See also the The Canons of Dordt Articles 8 - 15 of the Third and Fourth Head of the Doctrine.

Johan