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Impossible to prove or demonstrate: a seemingly valid but indemonstrable hypothesis.

in′de·mon′stra·bil′i·ty n.
in′de·mon′stra·bly adv.
References in periodicals archive ?
4) See Riccardo Strobino, "Avicenna on the Indemonstrability of Definition," Documenti e Studi sulla Tradizione Filosofica Medievale 21 (2010): 113--63; Riccardo Strobino, "Principles of Scientific Knowledge and the Psychology of (their) Intellection in Avicenna's Kitab al-Burhdn," in Raison et demonstration: Les commentaires medievaux sur les Seconds Analytiques, ed.
The exception is what MacIntosh calls 'Boyle's Modal Argument', wherein Boyle argues from the indemonstrability of God's non-existence to the possibility of God's existence to the possibility of miracles; given credible testimony to the actuality of miracles, it is possible to infer God's existence.
152) The understanding of indemonstrable principles by the new natural law theorists does not include any positive explanation, such as that provided by the process of induction, but only the negative assertion of indemonstrability.