WordNet sense 1 (without a basis in reason or fact):

baseless, groundless, idle, unfounded, wild

WordNet sense 2 (not sustained or maintained by nonmaterial aid):

unsupported

WordNet sense 3 (lacking justification or authorization):

undue, unjustified

WordNet sense 4 (not reasonable; not showing good judgment):

unreasonable

WordNet sense 5 (incapable of being justified or explained):

indefensible, insupportable, unjustifiable, unwarrantable

WordNet sense 6 (without excuse or justification):

inexcusable