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Indemonstrable, in-de-mon′stra-bl, adj. that cannot be demonstrated or proved.—n.

In mathematics, according to Euclid's treatment, the axioms alone are indemonstrable first principles, and all demonstrations are in gradation strictly subordinated to them.

Critical Reason, which realizes that deceptive fictions are not true thought, but dreams—not the result of ripe intellectual effort, but of the childish play of the imagination, seeks the roots of Morality not in the air or in the ether, but in the solid earth; not in some indemonstrable, transcendental sphere, but in an obvious need of human nature.

To Euclid’s successors this axiom had signally failed to appear self-evident, and had failed equally to appear indemonstrable.

Kant begins by distinguishing two forms which idealism can take according as it regards the existence of objects in space as false and impossible, or as doubtful and indemonstrable.