insupportable

That cannot be tolerated or endured.

My Lord you do me moſt inſupportable vexation.

The Captain, at Mr. Allworthy’s Inſtance, was outwardly, as we have ſaid, reconciled to his Brother, yet the ſame Rancour remained in his Heart; and he found ſo many Opportunities of giving him private Hints of this, that the Houſe at laſt grew inſupportable to the poor Doctor; and he choſe rather to ſubmit to any Inconveniencies which he might encounter in the World, than longer to bear theſe cruel and ungrateful Inſults, from a Brother for whom he had done ſo much.

That cannot be supported; that cannot be demonstrated or proved. (of a statement, claim, argument, etc.)

[…] the energy debate is in danger of being corrupted by misstatements small and large. Among these is the insupportable proposition that the California energy crisis can somehow be relieved by drilling in the Arctic refuge — an idea Ms. Norton echoed when she said that new drilling would “resolve some of the problems we’ve been having lately.”

This is a critical error, which undermines the report and leads the advisory group to make a series of contradictory and insupportable recommendations.