Feel, think, and believe are not interchangeable.” – George T. Arnold

”The use of feel for words like think, believe, and argue is becoming unsettlingly common. It's a cliché, and a touchy-feely one at that, reducing all cognition to sensation and emotion.” – Jack Lynch

People can feel sick or can feel the table. People DO NOT feel an opinion - they think, opine, or believe an opinion. – The Devereaux Bureau

    Bottom Line:
  • Feel
    • Sense/Perception
  • Think
    • Opinion
  • Believe
    • Conviction or principle; value

Example sentences:
The delegate said he THINKS (not feels) his bill will be approved.
The minister said she BELIEVES (not thinks or feels) there is life after death.
The applicant said she THINKS (not feels) her interview went well, and she FEELS good about her chances of getting the job.
I FEEL the wet grass between my toes.