Does Faith Increase?

Does faith increase? What do iman-i tahqiqi and iman-i taqlidi mean?

“They only are the (true) believers whose hearts feel fear when Allah is mentioned, and when His revelations are recited unto them, and who trust in their Lord;” (Surah-al Anfal, 2)
“He it is Who sent down peace of reassurance into the hearts of the believers that they might add faith unto their faith. Allah's are the hosts of the heavens and the earth, and Allah is ever Knower, Wise - (Surah-al Fath, 4)
Scholars have different opinions about the issue of increase and decrease in faith. Those scholars who consider faith to be a whole of belief, acknowledgement and deeds conclude two points from the aforementioned ayahs:
1. The expression “they increase their faith” in the 2nd verse of Surat-u Anfal indicates that faith is available for increasing. If ever faith were to consist of just knowing and acknowledging and declaring, it wouldn’t be available for increasing.
2. Those who believe that faith is the total of three pillars (belief, acknowledgement and deeds) say that the ayah declares quite clearly and obviously that faith can increase. They conclude that since “acknowledging” is not a changeable concept, it means that change in the strength of faith results from the change in deeds.
Narrated Abu Hurayrah;
“Faith has over seventy branches or over sixty branches, the most excellent of which is the declaration that there is no God but Allah and the humblest of which is the removal of what is injurious from the path; and modesty is a branch of faith.” (Muslim)
These proofs are enough to explain that the degree of faith may change. Allah knows the best. (Fahruddin al-Razi, Al Tafsir-al Kabir)

The most important issue about faith is to convert it into a verified belief from the imitative level

There are two types of faith. One type is imitative (Taqlidi) while the other is verified (tahqiqi).
Imitative faith (iman-i taqlidi) is the faith which a person has just through the people around him without any proofs.
Since a person having imitative belief doesn’t have any investigation and Islamic studies to acquire certain knowledge about faith he just believes in the way that he observes in the people around him. This kind of belief is weak and shakeable in the face of doubts and misgivings of disbelief, because it doesn’t stand on any proofs and knowledge.
However, tahqiqi iman which is the “certain, verified faith” means believing in Allah (swt) as strong as seeing Him. This kind of belief is obtained as a result of acquiring certain knowledge of all the questions related to belief through close investigation and Islamic studies. Since “verified belief” has the answers of all questions of doubt and disbelief, it is too strong, firm and unshakable.
Ulama (scholars) are in consensus that even though it is valid to have an imitative faith, it is fard for very Muslim to raise their faith to the ‘certain, verified belief’ from imitative level. (Aliyy-ul Qari, Commentary of Fiqh-i Akbar)