It is the proclamation of the Gospel, not argumentation, that transforms minds. See Give Them the Gospel.

Revelation from God is the only way to escape from error.  Logic collapses if it is not based on God's revelation.  Every thought needs a foundation.  If the foundation is another thought, then that thought needs a foundation.  Jesus Christ is the foundation of all thoughts except those that are error.  The person who tries to escape from Jesus Christ's revelation will find themselves in circular reasoning, openly claiming that their made up assumptions are valid, or else admitting that all their thoughts are coming from evil spirits (though they may think that those evil spirits are aliens, spirit guides, gods, or something else.

So, how can we know that God exists?

Here is some circular reasoning:

1. Is there a God?  Yes.
2. How do you know?  Because the Bible says so.
3. How do you know the Bible is accurate?  Because it was inspired by God. (This is true, but it is not the reason that we know.)

Here is some more circular reasoning:

1. Is there a God?  No.  
2. How do you know?  Because evolution says so.  
3. How do you know that evolution is correct?  Because the similarity in anatomy of various creatures is clear evidence of evolution.
4. Why do you think this is clear evidence for evolution?  Because the fish's forelimb and a human's forelimb show a common ancestry.

This is NOT circular reasoning:

1. Is there a God?  Yes.
2. How do you know?  Because I have met with the Almighty Creator God and He leads me moment by moment.  He has also revealed to me that the Bible is His Word without error, and He speaks to me through His written Word.

This is NOT circular reasoning:

1. How do you know the Bible is accurate?  Because the Almighty, Creator, God has personally told me this.
2. How did God show you?  He revealed it to me using the Bible.

God does reveal.  So does Satan.  God reveals through the Bible.  When any person reads the Bible, God does speak to that person.  God reveals through His creation.  When any person observes creation, including all scientists [that is what scientists do; they observe creation], God speaks to them through creation.  God can also speak in many other ways.  Mostly, He speaks through His people, those who are following Christ.  The integration between the spiritual realm and the material realm is very complete, so we sometimes think that thoughts are just coming to us through naturalistic forces in our brains.  That is not the case.  There is a spirit behind every thought, every word, and every action.  Satan also reveals, but his revelations are always lies.  They have enough truth to be convincing, but they come to the wrong conclusions.  Satan speaks through is slaves, whoever will carry his messages.  Satan also speaks through creation and through the Bible.  That is why two people can look at the same creation or read the same Bible and come to very different conclusions.  (some caveats about hearing God's Voice)
 
The scoffer will wave his or her wand and claim that these revelations are just imagination.  Reality can always be explained away with a good lie.  For a scoffer to discern such a thing would require the spiritual gift of discernment of spirits.  The scoffer is arguing against revelation while claiming to possess knowledge that could only be gained by revelation.  This is what is known as a self-refuting argument.  If the scoffer wins the argument, they have lost the argument.  

The scoffer will wave a wand and say "personal testimonies, changed lives, and miracles, well they exist in all religions."  Wait a minute.  We are speaking of eye-witness accounts.  Eye witness accounts also exists in courts of law, science labs, news reports, and many other places.  The scoffer is being irrational by trying to imply that because these things exist in more than one place, they are not valid.  Now, if God had assigned to Christians the task of converting others to follow Christ, then it might be a problem to us when a scoffer rejects our testimony.  The fact is that the testimony of Jesus Christ is the Spirit of Prophecy.  In other words, when you tell what happened to you, it is the flow of the Anointing of the Holy Spirit Who is speaking through you, and it is not your fleshly nature speaking.  When they reject you, they are rejecting Christ, and when they reject Christ, they are rejecting God.  Their condemnation is just.  However, there will be some who receive your testimony.  They are not accepting you.  They are accepting Christ and the Father.

The scoffer does not realize how reality works.  There is a spiritual side of life.  The scoffer is blind to this.  The scoffer has been ignoring God's voice so long that the scoffer cannot hear the voice of God as the Holy Spirit flows through you an attempts to minister to the scoffer.  The scoffer doesn't realize that God has done His part, but the scoffer has failed to respond.  This is the sin against the Holy Spirit.  It is failure to cooperate with the Holy Spirit.  The reason this sin is unforgivable is because it makes it impossible for the Holy Spirit to help the scoffer.