Please define and explain vicious circle (daur) and infinite regression of causes (tasalsul)?

Please tell me what is circle and infinite regression of causes?
Concise answer
A vicious circle is a situation in which an attempt to resolve one problem creates new problems that lead back to the original situation. It is also a fallacy in reasoning in which the premise is used to prove the conclusion, and the conclusion used to prove the premise For example, “A” depends on “B” and “B” depends on “A”. The conclusion is that “A” depends on “A”. It is the circularity in argument or proof.
There is no difference among scholars regarding the invalidity of a circular argument because it amounts to something preceding itself.  Hence, if “A” depends on “B” and “B” depends on “A”, then in order that “A” may come into being “B” must have been existent and “A” must have been non-existent. However, since “B” depends for its existence on “A”, then it means that “A” must be existent in the same time and moment. The conclusion is that “A” must be existent and non-existent at one and the same time. There can be no doubt in the human mind that existence and non-existence are two complete opposites and there is no middle position. Two diametrically opposed characteristics cannot exist together.
The word tasalsul (regress) is derived from the word silsila (sequence, series, range), with the root meaning of chain and which in philosophical parlance means infinite regress, or endless chain. Therefore, tasalsul means an endless chain. Philosophers thus liken the ordered system of causes and effects to a chain whose links interlock in sequence.
The infinite regress is void because the effect which is essentially dependent and needy is possible. Hence, when we assume that such beings exist endlessly, it would mean that there is an endless chain of dependent beings whose links interlock in sequence without there being an independent existent to support them. This is absolutely impossible.
 
Detailed Answer
A vicious circle is an expression used in logic and philosophy. It is also used extensively in jurisprudence and legal theories. A vicious circle is a situation in which an attempt to resolve one problem creates new problems that lead back to the original situation. It is also a fallacy in reasoning in which the premise is used to prove the conclusion, and the conclusion used to prove the premise.  For example, “A” depends on “B” and “B” depends on “A”. The conclusion is that “A” depends on “A”. It is the circularity in argument or proof.
There is no difference among scholars regarding the invalidity of a circular argument because it means something preceding itself.  Hence, if “A” depends on “B” and “B” depends on “A”, then in order that “A” may come into being “B” must have been existent and “A” must have been non-existent. However, since “B” depends for its existence on “A”, then it means that “A” must be existent in the same time and moment. The conclusion is that “A” must be existent and non-existent at one and the same time. There can be no doubt in the human mind that existence and non-existence are two complete opposites and there is no middle position. Two diametrically opposed characteristics cannot exist together.
Types of Circle
There are two types of circle (or cycle):
1. Explicit cycle (daur musarrah), 2. Implicit cycle (daur mudhmar).
The explicit cycle is where the cycle is without mediation like the example mentioned above. A circle which contains middle ring or rings is referred to as implicit cycle. For example, “A” depends on “B” and “B” depends on “C” and “C” depends on “D” and “D” depends on “A”. This is called implicit cycle.
Definition of Regress (tasalsul)
Tasalsul literally means the flowing of water or anything whose existence depends on the existence of another entity. Tasalsul in philosophical parlance means infinite regress, or endless chain. Hence, tasalsul means an endless chain (of causes). Philosophers thus liken the ordered system of causes and effects to a chain whose links interlock in sequence.
Types of Regress
There are different types of infinite regress:
A) Regress in mentally posited things which are on the basis of the considerations of the considerer. This type of regress is called ‘yaqefi’ (stoppable) which is terminated when the considerer stops considering it.  This kind of tasalsul has not been considered as invalid because it is not, in reality, a regress because an individual can continue his imaginations and fancying  as far as he can.
B) Regress in mortal matters. This kind of regress is also not invalid because its implementation becomes existent and non-existent gradually and they will not be gathered in existence. The temporal events take place each in its respective time and place.
C) Infinite regression of causes and effects which means that every stage is the immediate cause as well as the effect of the cause before it. This kind of regress is void and impossible. This kind of tasalsul has been defined in Kashful Murad as such:
و هو وجود علل و معلولات فی سلسلة واحدة غیر متناهیة.
That is the existence of causes and effects in a single endless chain.[1]
Why is infinite regress invalid?
The infinite regress is void for the simple reason that the effect which is essentially dependent and needy is contingent. That is to say, a contingent being is a dependent and needy being. Hence, when we assume that such beings exist endlessly, it would mean that there is an endless chain of dependent beings whose links interlock in sequence without there being an independent existent to support them. This is absolutely impossible.[2]
Philosophers have presented their arguments on the impossibility of tasalsul[3] that are briefly mentioned as under:
In his proof which is known as Asad and Akhzar, Farabi argues as under:
If we assume a chain of beings each of whose ring is dependent on another in a way such that insofar as the ring before it has not come into being the ring which is dependent on and connected to it does not come into being, it would then mean, by extension, that the whole chain would be dependent on another being because all the rings in the chain are supposed to have the same feature. Inevitably, we must assume that there is a being at the top of end of this chain who is not dependent on anything, who is self-sufficient and self-dependent and whose existence and non-existence amount to existence and non-existence of the rings in the chain. So such a chain cannot be endless and there must be a beginning. In other words, infinite regression of causes is impossible.
Mulla Sadra, the founder of Transcendental Philosophy, explains how an infinite regression of causes is impossible. In his Transcendent Philosophy, he presents the following argument: Based on the principiality of existence [isalat al-wujud] and dependence of the effect on its creating cause, the relationship of every effect in respect of its cause is pure dependence and connection because the effect has no form of independence of its own. If the relationship of a present cause is supposed in connection with a higher cause, it will have the same position as that of an effect to its cause. If we consider a chain of causes and effects in which a causes is the effect of another cause, they will not be but a chain of rings whose links interlock in sequence.  Obviously, a dependent being does not and will not come into being without an independent being to which it is connected. Therefore, beyond this chain of connections and dependence there must be an independent being that causes dependent beings to come into existence. Hence, we cannot consider this chain without a beginning and an absolutely independent being.[4]
Having said that, it has now become clear that we are in need of a being which is not the effect of another cause and is not dependent on another being either. It should be absolutely independent and that is what we call ‘God’ and the philosophers call Him ‘the Necessary Being’.
For further information about the chain of infinite regression of causes, you can refer to index: The Impossibility of Infinite Regression of Causes and Proof of God’s Existence, question 2223 (site: 2367).
 
[1] Allamah Hilli, Kashful Murad fi Sharh Tajrid al-E’tiqad, research by Hasan Zadeh Amuli, Hasan, p. 117, Qom, Islamic Publications Institute, 1407 A.H.
[2] Wilayee Isa, Farhang Tashrihi Istelahaat Usul, Tehran, Nay Publication, first edition, 1374.
[3] Some arguments have been presented by philosophers.
[4]  The difference between these two arguments is that the first argument applies to al real causes, causes which must necessarily be with the effect but the second argument is particular to creating or existence-giving causes and it is applicable to perfect causes as well because they include existence-giving causes.  Vide: Philosophical Instructions, vol.2, p. 81-82.