Does Ibn Taymiyyah mean by the word "impossible" (mumtani') in the instances mentioned in his books, that which is impossible and does not fall under divine power, such as combining opposites? And what prompted him to delve into such philosophies?

Entities are divided into: that which is necessarily existent (wajib al-wujud), that which is possibly existent (mumkin al-wujud), and that which is impossibly existent (mumtani' al-wujud). Divine power relates only to possibilities, because the existence of the necessarily existent and the non-existence of the impossibly existent are entailed by their very essences. Sheikh al-Islam Ibn Taymiyyah used the terminology of the mutakallimun (speculative theologians) and philosophers to refute them and demonstrate the corruption of their method, showing that the method of the Salaf (pious predecessors) is sounder, more knowledgeable, and wiser. He clarified that the impossible can be so either in itself or due to something else. An example of this is his refutation of the Jahmiyyah and Mu'tazilah regarding their assertion of the impossibility of the Lord's action and speech in eternity.