We read that Ibn Hajr (in his responce to Ibn Salah) said that the total amount of authentic hadiths, according to Ibn Qattan, Ibn Mahdi, Ahmad, and others is 4400 (or so) in number, and Ibn Rajab attributed (aproximately) 4000 to the count of Abu Daawud. Our question is: Do these reports only include what has been narrated from the Prophet, sallallaahu 'alayhi wa sallam, and do they exclude what is "Hasan Li Ghayrihi"? Also, is it true that Al-Jam‘ bayna As-Saheehayn of Al-Humaydi and Al-Jaami’ As-Saheeh mima laysa fi As-Saheehayn of Muqbil include all (or most) of that? May Allaah bless you.

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.

The scholars of Hadeeth made various statements about the number of the authentic ahaadeeth from the Prophet and there is a great difference between these numbers.

Some mentioned that they are nearly four thousand ahaadeeth – as you mentioned – and Ibn Hajar interpreted this to mean the ahaadeeth about the rulings only, without the ahaadeeth about the virtues, Al-Maghaazi (the Prophet's battles), and the like. However, some scholars mentioned that what is meant is the totality of the ahaadeeth, such as the statement of Abdur-Razzaaq, “I say what Yahya ibn Sa‘eed said, that the Musnad ahaadeeth are 4400; 1200 about the Sunan; 800 about what is lawful and what is unlawful, and 2400 about virtues, etiquette, and advice.”

Their statements can also be understood to mean the principal texts of the authentic ahaadeeth and not their branches, or the ahaadeeth that are agreed upon to be authentic, for example.

There are other statements which say that the authentic ahaadeeth number in the thousands!

For example, in his book Al-Madkhal, Al-Haakim quoted Imaam Ahmed as saying, “The ahaadeeth that are authentic are more than seven hundred thousand.”

Also, Al-Bukhaari said, “I memorize 100,000 authentic ahaadeeth.” Others mentioned similar numbers.

Ibn Hajar and Az-Zarkashi and others interpreted this to mean that these numbers include the different chains of narrators for each hadeeth text, and that this count is not restricted to the ahaadeeth attributed to the Prophet ; rather, it includes the statements of the Companions and the statements of the Taabi’is (generation following that of the Companions).

Other numbers, such as: 900; 8,000; 10,000; 12,000; 14,000; and 70,000 were also mentioned.

The statements of the scholars in this matter were stated in Ibn Hajar's book An-Nukat ‘ala Kitaab Ibn As-Salaah and Az-Zarkashi's book An-Nukat ‘ala Kitaab Ibn As-Salaah.

In any case, all what is mentioned is an approximate estimation. It is very difficult or nearly impossible to determine the number of authentic ahaadeeth exactly.

In addition to that, classifying a hadeeth as Saheeh (authentic) or Dha‘eef (weak) is a relative matter, as a hadeeth may be classified as Saheeh by some scholars while the same hadeeth is classified as Dha‘eef by others. Moreover, determining the number of Saheeh ahaadeeth does not lead to a great effect in principle.

As regards the issue of the Hasan (good) hadeeth being included in the Saheeh hadeeth, then we have not come across any statement of the scholars on this issue, nor any statement of the Hadeeth interpreters among the late scholars; nevertheless, this is something probable. Saheeh could mean the general ahaadeeth that are accepted and which are not rejected, so the two categories of Hasan (the Hasan Lithaatih, i.e. the good by itself and the Hasan Lighayrih, i.e. the good due to external factors, such as another hadeeth with stronger chains of narration corroborating it) are included in it, especially given that some scholars,  such as Al-Haakim, only divide the ahaadeeth in Saheeh and Dha‘eef.

The Saheeh hadeeth could mean the very Saheeh with its known conditions in the terminology of hadeeth.

As regards the book Al-Jam‘ bayn-as-Saheehayn by Al-Humaydi; then this is a book that is specialized in collecting the ahaadeeth of Saheeh Al-Bukhaari and Saheeh Muslim only, and he may state some wordings that are not among the Saheehayn  within the context of mentioning the ahaadeeth without drawing attention to this fact – the scholars criticized him for this. It is certain that the book did not encompass the totality of the Saheeh ahaadeeth.

Concerning the book Al-Jaami’ As-Saheeh mimma laysa fi As-Saheehayn, then that is about the Saheeh ahaadeeth that are not reported by Al-Bukhaari and Muslim in their Saheeh, so the book neither encompassed all the Saheeh ahaadeeth, nor their majority.

Allah knows best.