The phrase "blindly for" is grammatically correct and can be used in written English.
It is most commonly used to show something done without thought or consideration. Example: She voted blindly for her party without understanding their policies.
"I'll book one," I mumbled, head down, aiming blindly for the door.
Everyone wants to be clever — it's hard to give up that side and go blindly for stupidity.
If she had simply abandoned the stage, there could have been dangerous panic as everyone galloped blindly for the exits.
As soon as I saw the dancers, I felt it was the right atmosphere, to go blindly for your abilities.
Ergonomics criteria, while serving as the basis for this science, cannot be applied blindly for they do not ensure comfortable automobile seats.
If we fail to get some clarity and honesty to this question from either Brown, Cameron or Clegg, why should we vote blindly for a dishonest candidate?
"We're willing to take a look at both sides of the fence," he said, "instead of voting blindly for the Democratic Party".
When I visited my boyfriend in the hospital after his chemotherapy had started, he scuffed his white-socked feet along the floor, searching blindly for his slippers.
People were beginning to realize that this was not a bizarre setup; Notaro was telling the truth and groping blindly for a way to make it funny.
He jumps from the tower, landing in thorns that pierce his eyes, and wanders blindly for years, eating grass and roots.
This technique, I later discovered, is a classic intro-to-art exercise called "blind contour drawing". Freshmen at art school are forced to draw blindly for hours.
