I have to disagree here in the same way that Oliver Wendell Holmes would go into his office every day and tell his clerk to take a side of an issue, and Holmes would take the other side and win every time.
While I understand the critique of pure reason, experience, as you say, reason, and eloquence can render a fair argument.
And just as Rebecca Solnit thought she was being brilliant when she condemned a man at a party for arguing with her unknowingly about a book she had written, all this sh&t about what you can and cannot do is just that. You can solve a problem in your head.
And, it has been said by George Lakoff Einstein’s famous equation E MC2 came to him in a dream.
Science and truth is no more than metaphors derived by the human brain, which sees reality in a particular way. Ask the grasshopper about reality and I bet you’d get a whole other take.