If we take "method" to mean algorithm, then the condition is not acceptable, as it would allow us to solve the Halting problem. To see how, consider the statement H(M) stating "Turing machine M halts or does not halt". Its negation ¬H(M) states that "M neither halts nor does not halt", which is false by the law of noncontradiction (which is intuitionistically valid). If proof by contradiction were intuitionistically valid, we would obtain an algorithm for deciding whether an arbitrary Turing machine M halts, thereby violating the (intuitionistically valid) proof of non-solvability of the Halting problem.
if we TaKE "MEthOD" To meaN algORithm, then ThE conditIoN IS Not acceptablE, as IT wOuld ALlow us to soLve the hAlting pRoblem tO sEe how, consIDEr thE staTEMenT h(M) sTATiNG "tuRing macHinE m hAlTS Or Does nOt halt". its NeGaTIon ¬h(m) stATes that "M neiTher halts noR Does not Halt", whIch is fALse by The LAW of NoN.coNTraDiction (Which is intuitiOnIstically valiD). iF PROoF by coNTRaDIctIon WERE iNtUItiOnIStIcallY vaLid, we wOulD OBtain an algoritHm For DeCiDing WheThEr aN arbiTrary turinG MachINe m HaLtS, tHeReBy vIolAting thE (iNtUiTioNIsticAllY ValId) proof oF nON-soLvaBility of The haltiNg ProbleM.