The types of Kufr (disbelief) according to Ibn Al-Qayyim
3-1-2018 | IslamWeb
Question:
In order for a Kaafir (disbeliever) to be punished for their disbelief, do they have to hear about Islam and think that it is true, or do they simply have to hear about Islam and reject it, regardless of whether they believe it to be true or not? Please do not refer me to an existing fatwa.
Answer:
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad 
is His slave and Messenger.
If a non-Muslim hears about Islam and was informed about the Prophet then the evidence is established against him and he is obliged to yield and embrace the religion of Allah. This is because if he looked into it, even in the least way, he will discover the truthfulness of the religion and will find out clearly, without any confusion, that the Prophet is truthful.
If he disbelieves after the evidence has been established against him and after he has become aware of the prophecy of Muhammad then he will abide in Hellfire eternally.
Allah says (what means): {…that I may warn you thereby and whomever it reaches.} [Quran 6:19]
So whoever the Quran has reached, he is warned by it. Allah also says (what means): {But whoever disbelieves in it from the [various] factions - the Fire is his promised destination.} [Quran 11:17]
For more benefit, please refer to fatwa 90888.
It is not necessary for establishing Kufr (disbelief) that the non-Muslim believes that Islam is true and then disbelieves in it again; rather, this is one kind of Kufr which is called Kufr Juhood (disbelief due to rejection of the truth). There are other types of Kufr, such as Kufr I'raadh (turning away from the truth, neither rejecting nor accepting it), Kufr Shakk (disbelief due to doubt), and others.
Ibn Al-Qayyim clarified the types of Kufr in detail, saying:
"And as for the Major Kufr (Kufr Akbar), then it is of five types: Kufr Taktheeb (disbelief due to rejection); Kufr Istikbaar (disbelief due to arrogance and pride whilst one acknowledges the truth); Kufr I’raadh (disbelief due to turning away/ignoring); Kufr Shakk (disbelief due to doubt); and Kufr Nifaaq (disbelief due to hypocrisy).
1. Kufr Taktheeb (rejection): it is to believe that the Messengers are not truthful, and this type is not very common amongst the disbelievers because Allah supported His Messengers and granted them of proofs and signs to establish their truthfulness what would be sufficient to establish decisive proof, and (by which) any excuse would be invalid. Allah, the Most High, said about Pharaoh and his people: {And they rejected them, while their [inner] selves were convinced thereof, out of injustice and haughtiness.} [Quran 27:14] Allah said to His Prophet (what means): {And indeed, they do not call you untruthful, but it is the verses of Allah that the wrongdoers reject.} [Quran 6:33] If this type of Kufr is also called Kufr Taktheeb, then it is correct, as it is rejecting with the tongue.
2. Kufr Istikbaar (arrogance and pride): it is like the Kufr of Iblees (Satan), for he did not deny the command of Allah, and he did not face it with rejection, but he responded to it with arrogance and pride. From this comes the disbelief of the one who knows the truthfulness of the Messenger and that he has come with the truth from Allah but does not comply with it due to arrogance and pride. This mainly is the Kufr of the enemies of the Messengers, as Allah, the Exalted, quotes from Pharaoh and his people: {They said, "Should we believe two men like ourselves while their people are for us in servitude?"} [Quran 23:47] and the saying of the various nations to their Messengers: {They said, "You are not but men like us"} [Quran 14:10]; and Allah’s saying: {Thamud denied [their Prophet] by reason of their transgression.} [Quran 91:11] This is the Kufr of the Jews, as Allah says: {but [then] when there came to them that which they recognized, they disbelieved in it} [Quran 2:89], and: {Those to whom We gave the Scripture know him as they know their own sons.} [Quran 2:146] This is also the Kufr of Abu Taalib, who believed in the Messenger and did not have doubt in his truthfulness, but fanaticism overtook him, as well as the glorification of his forefathers, and that he should not leave their religion and testify to their disbelief.
3. Kufr of I’raadh (turning away/ignoring): it is to turn away with one’s hearing and one’s heart from the Messenger, neither believing in him nor rejecting him, neither allying with him nor showing enmity towards him, and not paying attention to that which he came with at all. This is like what a man from Banu Abd Yaaleel said to the Prophet "By Allah, I will say a word to you: If you are truthful, then you are too great in my eyes that I should reply to you, and if you are lying, then you are more despicable than that I should (even) talk to you."
4. Kufr of Shakk (doubt): it is when one is not certain of the Messenger’s truthfulness and one does not disbelieve in him but has doubts about him. This doubt of his will not continue unless he deliberately turns away from looking into the signs related to the truthfulness of the Messenger in general, such that he does not hear them and does not turn to them. If he was to turn to them and look into them, then nothing of his doubt would remain with him, since those signs necessitate truthfulness, especially in the totality of them, as they indicate the truth just as the sun indicates daytime.
5. Kufr Nifaaq (hypocrisy): it is when a person shows belief with his tongue while rejection is hidden in his heart, and this is the major hypocrisy, and an explanation of its types will come later."
Allah knows best.