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Even if the meaning is to some extent clear from "How Aql is different from Qiyas?" but a clear example or two to make clear how this source of fiqh is applied would be very helpful to understand it and this is the goal of this question.

I'm honestly assuming according the only given example that it is more or less part of what sunni scholars may call maslaha or istihsaan or covered in the fiqh rules...

For example:

  • The basic fiqh rule الضرورات تبيح المحضورات "the (forced) necessities allow the (application of) unlawful (things/acts)" based on (2:173) would already cover a solution for that example issue!
  • Assuming this fiqh rule doesn't exist, the hanfis might solve the issue by their osol like trickery and istihssan, the malikis by istihissan and maslaha al mursala and their maqasid considerations, the hanbali also via the maslaha mursala only the shafi'i and dhahiri seem not to have a direct solution in their osol, but that doesn't mean that they wouldn't have one!
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    While having absolutely no reference for this, I have the impression that qiyas is a somewhat formal style of using an existing rule and applying it to cases that don't formally fulfill the requirements of the rule, but are "close enough" or can be argued on accepted principles that they should have the same ruling, or at least as strict or lenient a ruling. Aql on the other hand seems significantly more indipendent to me and work from less precise principles. – G. Bach Sep 14 '16 at 12:04
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    @medi Did you read this answer? Does it not help anything? – Honey Jan 18 '17 at 17:18
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    @Honey I've linked that answer already as it doesn't seem to me a satisfactory explanation the single example might be covered by more than one asl of the osol of sunni madhabs! – Medi1Saif Jan 19 '17 at 6:52
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    1. I saw your link before, I just wanted your comment on that answer 2. What do you mean by: "the single example might be covered by more than one asl of the osol of sunni madhabs" – Honey Jan 19 '17 at 10:37
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    @Honey the example of a dying person where one needs to steel a car to save a life! – Medi1Saif Jan 19 '17 at 10:41
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From the Oxford Dictionary of Islam:

Aql - intelligence. In Islamic theology, natural human knowledge. In philosophy, the intellect. In Neoplatonic speculation, Allah's first creation. In Ismaili thought, the intellect as divine emanation. In jurisprudence, reason as a source for shariah. For modern Islamic reformers, aql as rationality is an integral part of Islam.

Whilst the dictionary al-Mu'jam al-Wasit published by the Arabic Language Academy in Cairo defines reason as what corresponds to the natural instincts, what enables thought and reasoning, what distinguishes the beautiful from the repulsive and good from evil.

In the Shirazi school of Illuminationism, founded by Suhrawardi, It is also understood as the spiritual light by which the self perceives the necessary and theoretical disciplines.

This emphasises what the Sixth Imam, Ja'far al-Sadiq, has written:

'The aql is that through which Allah is worshipped and heaven attained'.

Whilst the Seventh Imam, Ja'far al-Khazim has said,

Allah has two proofs upon the people: the first is the outer and the other is the inner. The outer proofs are the Messengers, Prophets and the Imams. Whilst the Inner is the Aql.

This is emphasised in the Qu'ran itself:

3:118, We have clarified the signs for you, if you only use your intellects.

Here, the term 'to use your intellect' has been used to translate ta 'qiluna, which is a verbal form of the triliteral root - ayn, qaf, lam and which is easily seen to be related to aql.

According to Dar al-Ifta al-Misriyyah, a religious ministry of Egypt and affiliated to the Ministry of Justice, aql can be usefully understood with its relationship with its opposite,naql. This is the

knowledge that emerges from divine revelation or a prophetic source ... [it] is inherited through the generations, being transmitted by one to another. It cannot be attained through empirical observation, experience or theoretical reasoning or deduction.

It's worth noting that the empirical sciences, that is what is generally understood as science today, generally underline their approach as outside of tradition and authority. They mean by this outside of the religious tradition and authority. That is aql rather than naql. However, it should also be pointed out that science just as equally relies on authority and tradition - after all, this is one of the functions of universities: to conserve what is known, as well as to uphold it. And this means also the standards by which this form of knowledge is understood and appraised. Moreover, although the terms are said to be 'opposed', it might be better to say that they complement each other, or even perhaps, that one transcends the other. The real relationship, at least to my mind, between aql and naql is actually quite profound and mysterious.

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  • Thanks for your research effort. But except with the quotations of the two imams there's not much I'd regard as new information. Beside Dar al-Ifta al-Masriyyah is certainly nto an authority on shi'a fiqh. The terms they use are certainly in usage among sunni scholars. – Medi1Saif Aug 26 at 15:08
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This is my personal understanding of the issue. A more complete and sound answer can be found here (you should probably use translators if you cannot read in Persian/Farsi)

First of all, in the common Shiʻite view of the Shia scholars, Aql is not only a source of Fiqh, but it is the only way we have when we are at a point to accept/reject Islam before to become a Muslim/Kafir. (Note This Aql is not something more related to the brain, like is thinking and logic, but it is more related to heart, although this fact is largely ignored some times)

Next, about Aql as a source of Fiqh. A simple example is that if something is obligatory in Islam, preparing the conditions to be able to behave according to that obligation is also obligatory, intellectually. For example, I know that I must get up early in the morning for the morning prayer, and I know that if I go to sleep late in the night, then it will be certain that I will miss my prayer. So intellectually, it is forbidden for me to sleep so lately. This is not that simple though in the words of scholars, as it has many problems involved that needs consideration, so for a more thorough answer you should read books, or ask due scholars, I'm not the one that can help.

Another example can be the fact that if doing something obligatory, does it necessarily mean that not doing that is always forbidden. For example, telling lie is forbidden, but telling the truth is not always obligatory.

Another example, which I didn't find in the link provided above, but I guess to be a proper example, is when different rules of the religion yield into a dilemma. Not all such situations are addressed in Quran and the reliable Ahadeeth, so maybe it will be a serious application of Aql in identifying what Allah expects from me to do. By the way, this is called Hikmah (a global knowledge as a whole, compared to local knowledge of the rules individually) in some Ahadeeth.

Last but not least, let me add that Aql being a source of Fiqh is both on Quran and Ahadeeth as well, though somewhat implicitly (if you conduct a study on the real meaning of Aql, you may conclude that the references in Quran and Ahadeeth are rather explicit indeed). For example see:

وَنَفْسٍ وَمَا سَوَّاهَا ﴿٧﴾ فَأَلْهَمَهَا فُجُورَهَا وَتَقْوَاهَا ﴿٨﴾ قَدْ أَفْلَحَ مَن زَكَّاهَا ﴿٩﴾ وَقَدْ خَابَ مَن دَسَّاهَا ﴿١٠﴾

By the Soul, and the proportion and order given to it; (7) And its enlightenment as to its wrong and its right;- (8) Truly he succeeds that purifies it, (9) And he fails that corrupts it! (10)

بَلِ الْإِنسَانُ عَلَىٰ نَفْسِهِ بَصِيرَةٌ ﴿١٤﴾ وَلَوْ أَلْقَىٰ مَعَاذِيرَهُ ﴿١٥﴾

Nay! man is evidence against himself, (14) Though he puts forth his excuses. (15)

There are much more things about Aql that can be said, but this much should suffice as for the beginning.

Hope that it helped. Godspeed


EDIT to answer OP's comment here, as it was not a proper fit to comment area:

@Medi1Saif, actually both yes and no. If Aql is something from my own side (like thinking apparently is), its wrong to use it to go by, since "إِنِ الْحُكْمُ إِلَّا لِلَّـهِ", that is, "the command is for none but Allah". Although even if so, one may exploit "لَا يُكَلِّفُ اللَّـهُ نَفْسًا إِلَّا وُسْعَهَا", that is, "On no soul doth Allah Place a burden greater than it can bear".

But why no, because Aql resides in Heart: "لَهُمْ قُلُوبٌ يَعْقِلُونَ بِهَا", that is, "have hearts by which to reason", while for some people "تَعْمَى الْقُلُوبُ الَّتِي فِي الصُّدُورِ", that is, "blinded are the hearts which are within the breasts".

those people who suffer disease in their heart "فِي قُلُوبِهِمْ مَرَضٌ", if they think they are using their intellect, they may go astray instead of getting survived. This is why in Shia there is a famous saying that, what ever Aql rules, is a rule of Allah, and whatever Allah rules, is something that Aql accepts (کلما امر ب العقل امر به الشرع، و کلما امر به الشرع امر به العقل). And there is a Hadeeth from Imam Hussain PBUH that go by religious rules, so that your intellect recover from its diseases and incompletenesses.

Those who can safely use their Aql, are actually those who have قلب سلیم, "إِلَّا مَنْ أَتَي اللَّهَ بِقَلْبٍ سَلِيمٍ", that is, "But only one who comes to Allah with a sound heart"

What usually people mean by Aql is different, they at most try to think logically, and sometimes they conclude the opposite of the rules of Allah, that's a place where Allah says "مَا أُوتِيتُمْ مِنَ الْعِلْمِ إِلَّا قَلِيلًا", and "ذَلِكَ مَبْلَغُهُمْ مِنَ الْعِلْمِ" and "وَ مَا يَتَّبِعُ أَكْثَرُهُمْ إِلَّا ظَنًّا إِنَّ الظَّنَّ لَا يُغْنِي مِنَ الْحَقِّ شَيْئًا".

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  • When I read this I wonder why all this "hullabaloo" about 'Aql in Shi'ism. At least if I then read this question) after reading this answer it starts looking a kind of abusive or mockery without any sense. Because people use their mind to interpret Allah's orderes no matter if they are shi'a or non-shi'a. I don't see a reason why to consider 'Aql as a kind of superiority because everybody uses it according their capacities. – Medi1Saif Aug 26 at 8:51
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    @Medi1Saif, check out the edit – owari Aug 26 at 14:46
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    Thanks for your effort. I'd like to take some time to try to read the farsi stuff (translated) when I have more time to concentrate on that. – Medi1Saif Aug 26 at 15:06

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