what does it mean an idea or belief having no logical reason
Logical means the princibles of reason. If something is Logical, it means it is the smart thing to do.
reason means logical thinking.
Probability
The phrase "rhyme and reason" refers to having a logical basis or justification for something, in addition to being ordered or structured. It suggests that there is a understandable relationship or coherence between different elements.
Superstitious
Reason as a verb means: to think or argue in a logical manner to form conclusions, judgments, or inferences from facts or premises. We use our minds to think and reason.
logical means which has strong meanings.
I suggest slightly different wording of the question: What is the term for a logical way to find answers to questions? Investigation (or as a verb: to investigate) Reasoning (to reason)
No reason means no way to explain things. No rhyme means, nothing rhymes. Bahaha, I am reading The Phantom Tollbooth, too. (:
Superstition means a belief or notion not based on reason or knowledge, or on an actual connection to a logical or scientific phenomenon. Superstitions are commonly used to explain occurrences that may be random chance, or that have some undiscovered logical explanation. They would include such ancient folklore as breaking a mirror, or black cats, and such modern examples as sports fans wearing "lucky socks" to a game.
Confident means having a belief or feeling that you can do something well or succeed at something; showing that you have confidence; sure of your abilities, correctness, successfulness
The meaning of the idiomatic expression, without rhyme and reason, means that someone is said or done without a purpose. Meaning that there is logical explanation for or understandable reason for the way something is done.