God does want humanity to use their brains and logic, or reasoning capabilities. You want biblical eveidence for this well just read the gospels and you will see Jesus asking questions of the people all the time. He encouraged them to answer on many things instead of telling them the answers...especially the pharisees when they tried to trick him with points of law.
But in the Old Testament in Isaiah God says this;
"Come now and let us reason together".
This is God saying its OK, you can use your brain, you dont have to commit intellectual suicide to be a Christian.
This piece is from;
http://www.preachersfiles.com/evangelism/000569.htm"
This is given early in the book of Isaiah (1:18), and is especially striking in that Jehovah here invites man to , as it were, sit down and think seriously with Him on matters of grave importance. The latter part of the verse focuses on the sinfulness of man, and the fact that man's scarlet, red sins can be as wool, as white as snow. Involved in this is surely the fact that if man thinks seriously about eternal and spiritual matters, the message God has provided will be of importance to him. And therein the problem of our time: Getting men to think seriously about their souls!"
Also the first and greatest command
demands the Christian to use his brain and love God not onlt from the heart,(which would be an emotional love), but with all his mind also.
Matthew 22:36–3836 ‘Teacher, which is the greatest commandment in the Law?’
37 Jesus replied: ‘
Love the Lord your God with all your heart and with all your soul and with all your mind.’38 This is the first and greatest commandment.’
Also Paul in Romans ch12 has stated;
Romans 12:1-3:
Therefore, I urge you, brothers, in view of God's mercy, to offer your bodies as living sacrifices, holy and pleasing to God -- which is your spiritual [logikos: reasonable, rational] act of worship [service]. Do not conform any longer to the pattern of this world, but be transformed by the
renewing of your mind [nous: the intellect, i.e. the mind ]. Then you will be able to test and approve [dokimazo: to test, approve, examine, discern, prove] what God's will is -- His good, pleasing and perfect will.
At twelve years old we also see Jesus in the temple, astounding the adults with his wisdom and intellect, but the text tells us that he was both 'listening and asking questions'. He was encouraging them to think, he was encouraging rational debate!
Luke Ch2.
41And his parents went every year to Jerusalem at the feast of the passover. 42And when he was twelve years old, they went up after the custom of the feast; 43and when they had fulfilled the days, as they were returning, the boy Jesus tarried behind in Jerusalem; and his parents knew it not; 44but supposing him to be in the company, they went a day’s journey; and they sought for him among their kinsfolk and acquaintance: 45and when they found him not, they returned to Jerusalem, seeking for him. 46And it came to pass, after three days they found him in the temple, sitting in the midst of the teachers, both hearing them, and asking them questions: 47and all that heard him were amazed at his understanding and his answers.