‘Allāmah Ibn Qayyim does not introduce the objections on the use of oaths by the Qur’ān before explaining them. He positively explains the oaths of the Qur’ān. While doing so he points towards facts which remove the germs of confusion and explain away objections on the Qur’ānic oaths. His response, I believe, is relatively strong. However, he too, like Rāzī, fails to follow a single explanation and oscillates between two parallel approaches. While commenting on the sūrahs which contain any particular oath he jumps from one view to another.
What follows is a summary of his response along with my comments on it.
It is important to appreciate that Ibn Qayyim adopts inductive approach. He starts with mentioning that oaths are basically taken only by God, His attributes and His signs. He writes:
He, the glorious one, swears by certain things to establish some points. He usually swears either by His own name, which has peculiar attributes, or by His signs. Thus, by swearing by some of His creatures He has taught us these things are His great signs.
After presenting some examples he continues:
It needs to be appreciated that the Almighty swears to establish fundamental beliefs which men must acknowledge. He swears to affirm that God is one (tawḥīd); that the Qur’ān is true; that the Prophet (sws) is truthful; that final retribution is sure to come; that warnings in this regard are not empty threats. Sometimes He swears to affirm the status of men.
According to Ibn Qayyim, the Qur’ānic oaths are limited to three matters of great religious import. These three issues then converge into a single one: the attributes of God, as we shall soon see. After this introduction, he does not feel a need to investigate the jawāb al-qasam (complement of oath) for he has already identified the thing sworn of, i.e. belief in unicity of God, prophethood, and the Last Day. The oaths themselves prove these beliefs. While treating the oaths in the beginning of the Sūrah al-‘Ᾱdiyāt (Q. 100) and Sūrah al-‘Aṣr (Q. 103) he writes:
The complement of the oath has been left unstated because what is being affirmed by the oaths is already understood (i.e. tawḥīd, Prophethood, and the Last Judgment). Each among these three entails the others (they are mutalāzimah). Thus when the veracity of the Messenger is established, the Qur’ān and the Last Judgment stand proven. When it is established that the Qur’ān is true, the Messenger’s claim to be a divine Prophet and all the claims of the Book, including the power of God (to resurrect), are ratified. Therefore, the complement of oath is sometimes left unstated. It is taken for granted. In this case, the intention of the author is not to mention what is sworn of. Rather the only purpose of swearing the oath is to produce ta‘ẓīm(glorification, exaltation) of the muqsam bihī and to teach that it is a thing by which one may swear an oath.
These things, according to him, lead to His sublime attributes. This is clear from his treatment of the oaths occurring in the start of Sūrah al-Burūj (Q. 85) where he says: “All these things are signs of His power which evidence His unicity.”
Following this, he says:
The best explanation is that this oath does not need any complement because in this case the only intention is to highlight the muqsam bihī and to make it clear that it is among the great signs of God.
Similarly while dealing with the oaths occurring in the beginning of Sūrah al-Ṭalāq (Q. 65) he writes:
The Almighty has sworn by the heavens and the shining stars, each of which is one of the signs that affirm His unicity.
Then while treating the oaths occurring in the middle of the same Sūrah he says:
God has sworn by the heavens which showers rains and by the earth which in turn produces vegetations. All these things are the signs of God that prove His providence.
He has repeated the same thing while treating the oaths occurring in the end of Sūrah al-Inshiqāq (Q. 84). He writes:
These (i.e. twilight, night and moon) and other similar things constitute signs which evidence God’s providence. They call us to appreciate His perfect attributes. 
While dealing with the complement of these oaths, he says:
It is possible that the complement of this oath is left unstated.
This oath does not require a complement for, according to him, that is already understood in defined form.
The above discussion helps us see the difference between the view of Rāzī, who offers different contradictory responses, and that of Ibn Qayyim, who adopts a single method to explain all the Qur’ānic oaths. The method of Ibn Qayyim, I believe, is relatively sounder.
Now I wish to explain the basic function behind Ibn Qayyim’s method. He draws on two bases.
First, God Almighty has sworn by Himself and also by His signs. Swearing by created things is nothing but another form of swearing by God. For these things are His creatures. They are signs of His providence.
He has thus intended to explain away the third objection mentioned above which rests on the claim that swearing an oath by ordinary things, which are obviously creatures of God, means raising them above the Creator Himself. However, the question has remained unanswered. The oaths evidently concern the creatures and not the Creator. The fact that they are His signs and lead us to His attributes does not, after all, change their status of being a muqsam bihī.
Consider his statement where he says that the complement of oath is sometimes left unstated, for it is taken for granted. In such cases, he holds, the intention of the oath-taker is not to mention what is sworn of (muqsam ‘alayhi). Rather the only purpose of the statement is to produce ta‘ẓīm (glorification, exaltation) of the muqsam bihī. It also teaches us that one can swear by the stated muqsam bihī. The above clearly proves that God has sworn by other than Himself with an intention to attach glory to them. The crux of his statement, therefore, would again be that God has sworn by these things considering their glory and exaltedness. I believe there is nothing wrong with the idea that God attaches dignity and honor to some of His creations. Nor do I object to the belief that some of His creatures are glorious and exalted. Many small things are great and many insignificant things are noble when seen from different perspectives. What needs to be explained is that the status of created things has been raised to the point that the Almighty should swear an oath by them.
Second, all the oaths evidence the fact mentioned in the muqsam ‘alayhi. By this thesis he has intended to explain away the second objection. Rāzī too, as we saw, endeavored to do so when he mentioned this point among others. However he (Rāzī) never relied on this explanation consistently. As for Ibn Qayyim he fully relied on this basis. He explains most of the Qur’ānic oaths in a way that shows that the muqsam bihī evidences the muqsam ‘alayhi. When, however, in some instances, he found it difficult to relate the muqsam ‘alayhi and muqsam bihī he declared the former as left unstated. In such cases, he considered the oaths as evidencing the attributes of God among other points as I have mentioned earlier.
Despite the weakness of his response and his occasional remarks that the oaths have been brought in order to glorify the muqsam bihī, he has been right and proficient or at least, one can say, he has been proficient in more than one place during the entire discussion.