Is the division and categorisation of knowledge a good innovation (bid‘ah hasanah)?
Question

can the development of fiqh sciences and the various categorisations of fiqh be considered as Bidah Hasanah, likewise with classification of ahadith being daeef, hasan, saheeh etc, can these various categorisations be considered as 'good bid'ah'?
Praise be to Allah.Firstly:
The division of knowledge into various categories and branches, and the development of ways of approaching and studying knowledge, are all based on intellectual processes that developed over time with the increase of knowledge and reaching a high level of mastering this knowledge. Knowledge is something that has been accumulating throughout human history.
The process of compiling the Mus-haf during the era of the Rightly Guided Caliphs, then the compilation of the Prophet’s Sunnah in comprehensive volumes at the time of ‘Umar ibn ‘Abd al-‘Azeez (may Allah have mercy on him – d. 101 AH) was the first stage of building Islamic knowledge and categorising that knowledge in books arranged by chapters on various topics. In fact, in the first documents that were written during the Prophet’s time and the era of the Sahaabah and Taabi‘een, we see the beginnings of the categorisation of fiqhi books into various subject areas and chapter headings. One of the most famous of these documents is the constitution document that the Prophet (blessings and peace of Allah be upon him) instructed should be written between him and the Jews of Madinah and the Muhaajireen and Ansaar, and the document on zakaah that was kept with Abu Bakr as-Siddeeq (may Allah be pleased with him). Whoever would like to know more about that can refer to the book Tareekh Tadween as-Sunnah by Dr Haakim al-Mutayri.
Adh-Dhahabi mentioned a generation of scholars, beginning with Mak-hool (d. 113 AH) and az-Zuhri (d. 124 AH), and ending with Rabee‘ah ibn ‘Abd ar-Rahmaan (d. 136 AH). They were the students of the Sahaabah and he said of them: The elders began to compile books of Sunan and write about various issues and about the Arabic language. Compilation of books – in the precise sense – began at the end of the first century AH.
It was based on a general principle called al-masaalih al-mursalah that the fuqaha’ adopted, which dealt with every new practice that could serve an interest and that the ummah might need, but there were no instructions concerning it in the shar‘i texts. This principle was one of the most important means that gave Islamic sharee‘ah flexibility, and it was one of the most important fiqhi principles that has been needed throughout the ages.
Imam ash-Shaatibi (may Allah have mercy on him) said – after giving some examples of al-masaalih al-mursalah and mentioning how some people confused it with innovation –:
All that has been mentioned comes under the heading of al-masaalih al-mursalah, not under the heading of newly invented matters (bid‘ah). This principle of al-masaalih al-mursalah was followed by the early generations and they acted in accordance with it, as did those who came after them. It is one of the fiqhi principles that are well-established among the scholars of usool; even though they may differ concerning it, that does not undermine our argument here.
With regard to the compilation of the Mus-haf and limiting the people to that one standard text, in reality that also comes under this category. So the Companions of the Messenger of Allah (blessings and peace of Allah be upon him) did the right thing, because there was a justification for this action, which was the command to convey the teachings of Islam. Just as conveying is not restricted to a specific manner, because it is a principle, so it may be achieved by many possible means, such as memorising, teaching, writing it down and so on, by the same token protecting it from distortion and alteration is not limited to one way in exclusion of others, provided that the method used does not undermine the aim of conveying it in a proper manner, such as writing the Mus-haf in a book for the purpose of preserving it. Therefore there was consensus on this matter among the righteous early generations.
With regard to writing down knowledge other than the Mus-haf, the matter is clearer and more lenient. The principle of writing down knowledge is proven in the Sunnah. In as-Saheeh it is narrated that the Prophet (blessings and peace of Allah be upon him) said: “Write it down for Abu Shah.” The biographers stated that the Messenger of Allah (blessings and peace of Allah be upon him) had scribes who would write down for him the revelation and other things… Moreover, writing comes under the heading of that without which fulfilling an obligation cannot be done, if a person has a poor memory and there is the fear of knowledge disappearing. The earlier generations only regarded it as disliked to write down knowledge for a different reason, not because it was an innovation. Anyone who calls the writing of knowledge in books an innovation is either exaggerating or he is not using the word innovation in the right context. So it is not valid to quote these things as evidence for it being acceptable to introduce innovations.
If there is a dispute concerning the principle of al-masaalih al-mursalah, and adopting this principle is not sound according to some scholars of usool, then the argument against them is the consensus of the Sahaabah, who agreed to write the Qur’an in the Mus-haf and make it a reference point. If that principle is applied in one case, then it may be applied in other cases, and then there will be no difference between the disputing parties, except with regard to some minor details.
End quote from al-I‘tisaam (1/316-319).
Secondly: 
With regard to calling this a good innovation (bid‘ah hasanah), that is subject to further discussion and it may be one of two things:
The first possibility is that what is meant by innovation here is innovation in the technical shar‘i sense which is criticised in the Qur’an and Sunnah, especially in the words of the Prophet (blessings and peace of Allah be upon him): “Every innovation is a going astray.” Narrated by Muslim (867). So it is not valid to call it a good innovation, because describing it as good is contrary to the criticism that is proven on the basis of shar‘i evidence.
This is what is implied by the view of those who rejected the division of innovation into bad and good, as Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
If anyone thinks that this is an innovation and that it is good, he is wrong on two counts:
Either it is not an innovation, but he thinks that it is, such as if he were to say: The categorisation of the Sunnah into different subject areas is an innovation, but it is a good innovation; or if he were to say: The building of schools is an innovation, but it is a good innovation – and so on.
We say: You are mistaken by calling that an innovation, because the one who does that does not intend to draw closer to Allah by means of the mere action itself; rather he seeks to draw closer to Allah because it is a means of achieving something that is prescribed in Islam. So the categorisation of books, for example, is a means of making the Sunnah and knowledge more accessible. The aim, first and last, is the Sunnah and making it accessible to people, and this categorisation is a means of making it more accessible to them. So it is not an innovation in the technical shar‘i sense, because if you were to ask the author: Is this categorisation of the book into chapters and sections is a means by which you draw closer to Allah, so that you think that the one who differs with you in that is going against sharee‘ah? Or are you drawing closer to Allah, may He be exalted, because it is a means of achieving a shar‘i goal, which is making the Sunnah more accessible to the ummah? He will say: My aim is the latter, not the former.
Based on that, we say: the compilation of books is not an innovation in the technical shar‘i sense.
Likewise, the building of schools for students was not something that was done at the time of the Messenger (blessings and peace of Allah be upon him), but it is a means of achieving one of the aims of sharee‘ah, which is helping the students so that he can devote his time to seeking knowledge. It is not an act of worship in and of itself, but it is a means.
Hence you will find that people differ with regard to the building of schools: some of them build them in one way, and some build them in another way, and neither group thinks that the other is following innovation just because they did it in a way different from the other school, because each of them believes that it is a means and is not sought in and of itself. Therefore this is not an innovation; rather it is a means of doing something that is prescribed in Islam.
End quote from Fataawa Noor ‘ala ad-Darb (4/2)
He (may Allah have mercy on him) also said:
These things, if the doer does them as a means of drawing closer to Allah and as an act of worship, then they constitute innovation and misguidance, but if they are a means of achieving something that is prescribed in Islam, such as categorising knowledge, printing books, and the like, then they are Islamically acceptable.
End quote from Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen (17/380)
The second possibility is that what is meant by saying that it is a good innovation is by way of calling newly-introduced practices an innovation in the general linguistic sense of the word. There is nothing wrong with that, as ‘Umar ibn al-Khattaab (may Allah be pleased with him) said, “What a good innovation this is.” Narrated by al-Bukhaari (2010). And many of the fuqaha’ and scholars – such as ash-Shaafa‘i, al-‘Izz ibn ‘Abd as-Salaam, an-Nawawi and others – divided innovations into good and bad. Hence al-Haafiz ibn Rajab (may Allah have mercy on him) said: Whenever any of the early generations described some innovations as good, that referred to innovations in the linguistic sense, not in the shar‘i sense.
End quote from Jaami‘ al-‘Uloom wa’l-Hikam (2/128)
Once we understand the above, it becomes clear that the difference is in vocabulary.
Abu Shaamah al-Maqdisi (may Allah have mercy on him) said: Another thing that is regarded as a good innovation is the compilation of books in all beneficial branches of Islamic knowledge, of various kinds, working out fundamentals and rules, dividing knowledge into main categories, discussing them and teaching them, developing minor categories and assuming different scenarios that never happened before, and coming up with answers to these different scenarios, explaining the Holy Qur’an and Prophetic reports, critically examining isnaad (chain of narration of hadiths) and matn (text of hadith), studying the literature of the Arabs, both prose and poetry, writing down all of that, and basing many branches of knowledge on it, such as grammar, meanings of vocabulary, literature and poetic rhythms. All of that, and whatever is like it, is clearly something good and useful, that helps one to understand the rulings enjoined by Allah, may He be exalted, and to understand the meanings of His Book and the Sunnah of the Messenger of Allah (blessings and peace of Allah be upon him). All of that is enjoined, and there are no shar‘i reservations about that.
End quote from al-Baa‘ith (p. 24)
For more information, please see the following fatwas: 205, 864, and  10262 .
And Allah knows best.