Problem, πρόβλημα from προβάλλοto project, to propose. Hence problem means besides something projecting or standing out, something put forth or proposed, sometimes something to be done in practical life, as when Orestes, in the Electra of Euripides, calls the awful task set before him a problem. (1)
In mathematical science, a problem is in like manner something to be done, the formation, for example, of an equilateral triangle, as distinguished from a theorem or speculative truth, such as that the angles at the base of an isosceles triangle are equal. With Aristotle, problem means question. A problem with him is something which may be true, but has to be proved. This sense remains in the adjective problematical, requiring to be made out, or proved.
As quœstio is the Latin equivalent to problem, so questionable would seem to be synonymous with problematical. In our general use, however, the former implies something unfavourable, a tendency to reject that to which the term is applied. Questionable taste and questionable morality all but mean bad taste and bad morality. Problematic, on the other hand, merely signifies that the point before us needs proof, without at all denoting the likelihood of its failing of such proof.
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(1) EURIP. Electra, 989.