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untenable (adj) (of an argument, situation, etc.,) indefensible; unsound.
An argument is untenable if you cannot continue to maintain or support it against criticism. It is unsound. An untenable situation cannot continue for a long time. It is too weak. You are in untenable position if you cannot continue in that position.
- He found that his argument was untenable, because it was proved successfully wrong by his opponents. As he could not defend it any more, he gave up the argument.
- With very strong proofs against it, the theory was untenable. It was wrong, and could not be supported any more.