Cryptic crossword clue
Well-founded desert isle with lake 8

The most common and most likely answer to this crossword clue is the 8 letter word RATIONAL

I've seen this crossword clue in The Daily Telegraph
R
A
T
I
O
N
A
L


Buddy explains!

The straight part
We know that "Well-founded" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case well-founded = rational.
The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

What does RATIONAL mean?

RATIONAL noun
  1. A rational number: a number that can be expressed as the quotient of two integers.
RATIONAL adjective
  1. Capable of reasoning.
  2. Logically sound; not contradictory or otherwise absurd.
  3. (of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
  4. Of a number, capable of being expressed as the ratio of two integers.
  5. Of an algebraic expression, capable of being expressed as the ratio of two polynomials.
  6. Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae.
  7. Expressing a physical object.
RATIONAL noun
  1. The breastplate worn by Israelite high priests.

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