The invalidity of circular series can be proven in this manner. There can be two or more elements in the circle of causation. If there are only two elements A and B, we may represent the causal relationship by writing A ↔B. If there are more than two elements, for instance A, B, C and D, we may represent the causal relationship in this way: A → B →C→ D . In this case, A is the cause of B, B is the cause of C, C is the cause of D, and D is again the cause of A. Both the cases are, however, invalid, since it entails that A should be existent and nonexistent at the same time: it should exist to create B and not exist to be created by B. This is self‑contradictory and stands refuted. Also, the circle with more than two elements implies a succession of several effects without a cause, which is also seen to be invalid.
As to the infinite series, there are many reasons for considering it invalid. We shall discuss two of them here.
a) If we consider a chain of causes and effects whose last link is an effect which has not yet become a cause of another thing‑for example, a slight movement of the hand, which we consider as an effect of preceding causes, but it is not yet a cause for another effect‑we shall see that every preceding link of this chain, which precedes this last effect, must at the same time be a cause for its next link and an effect for its previous link, and so on. Thus, every link of this chain is at the same time a cause and an effect, and we know that if a link in the chain is the cause of its succeeding link that does not excuse it from the need of a cause preceding it. Therefore, every link in the series is an effect dependent on a cause.
Now supposing that this chain is infinite and there is no First Cause, it implies an infinite number of middles with no sides,5 which is of course impossible. For example, in the chain A→ B→ C→ D→ E→∞ we take A to be the last effect (the slight motion of the hand which has not yet become a cause for another thing). 6
The link B (the muscles, in our example) is the cause for A and is also the effect of C or the effect of nerves). Link C is the effect of D (the effect of will, in our example). Thus every one of the links of the chain is both a cause and an effect at the same time. As has been argued, though every link is the cause for the following link, it does not mean that it can itself dispense with a cause preceding it. Therefore, every link is necessarily an effect, too. So we may overlook the causation of all links and illustrate them thus: A→ B→ C→ D→ E→∞ ; this means that we have an endless chain of effects without coming across anything which is a cause without being an effect; as we have already shown, it is impossible.
b) We said that the existence of an effect or phenomenon is dependent, not self‑existent, or in other words, it is a contingent being or an intermediary existent. Now the supposition that there is an endless chain of contingent beings, implies an infinite chain of dependent and intermediary beings which do not depend for their existence on an independent, self‑existent being, and this is impossible.
From what we have said, we can draw this conclusion: first, that we perceive the existence of phenomenon or the contingent being either through our acquired knowledge or through introspection (`ilm huduri); i.e. we perceive the external world through acquired knowledge (`ilm husuli) and the inner states of the self through introspection (`ilm huduri); second, that every contingent being is dependent on a cause, otherwise it cannot possibly be existent; third, the chain of contingent beings and causes must inevitably originate from the First Cause, the Self‑existent Being, that is, God.
Khwajah Nasir al‑Din al‑Tusi has formulated the argument of the Necessary Being in this statement:
الوجود ان كان واجبا، فهو المطلوب والااستلزمه لاستحالة الدوروالتسلسل
Which means, if we accept the cause of all existence as the existence of the Necessary Being, we have reached the desirable conclusion; otherwise‑that is, if we do not accept the Necessary Being as the first cause‑ the existence of the Necessary Being is necessitated by the impossibility of a causal circle and a causal linear series.
As to the infinite series, there are many reasons for considering it invalid. We shall discuss two of them here.
a) If we consider a chain of causes and effects whose last link is an effect which has not yet become a cause of another thing‑for example, a slight movement of the hand, which we consider as an effect of preceding causes, but it is not yet a cause for another effect‑we shall see that every preceding link of this chain, which precedes this last effect, must at the same time be a cause for its next link and an effect for its previous link, and so on. Thus, every link of this chain is at the same time a cause and an effect, and we know that if a link in the chain is the cause of its succeeding link that does not excuse it from the need of a cause preceding it. Therefore, every link in the series is an effect dependent on a cause.
Now supposing that this chain is infinite and there is no First Cause, it implies an infinite number of middles with no sides,5 which is of course impossible. For example, in the chain A→ B→ C→ D→ E→∞ we take A to be the last effect (the slight motion of the hand which has not yet become a cause for another thing). 6
The link B (the muscles, in our example) is the cause for A and is also the effect of C or the effect of nerves). Link C is the effect of D (the effect of will, in our example). Thus every one of the links of the chain is both a cause and an effect at the same time. As has been argued, though every link is the cause for the following link, it does not mean that it can itself dispense with a cause preceding it. Therefore, every link is necessarily an effect, too. So we may overlook the causation of all links and illustrate them thus: A→ B→ C→ D→ E→∞ ; this means that we have an endless chain of effects without coming across anything which is a cause without being an effect; as we have already shown, it is impossible.
b) We said that the existence of an effect or phenomenon is dependent, not self‑existent, or in other words, it is a contingent being or an intermediary existent. Now the supposition that there is an endless chain of contingent beings, implies an infinite chain of dependent and intermediary beings which do not depend for their existence on an independent, self‑existent being, and this is impossible.
From what we have said, we can draw this conclusion: first, that we perceive the existence of phenomenon or the contingent being either through our acquired knowledge or through introspection (`ilm huduri); i.e. we perceive the external world through acquired knowledge (`ilm husuli) and the inner states of the self through introspection (`ilm huduri); second, that every contingent being is dependent on a cause, otherwise it cannot possibly be existent; third, the chain of contingent beings and causes must inevitably originate from the First Cause, the Self‑existent Being, that is, God.
Khwajah Nasir al‑Din al‑Tusi has formulated the argument of the Necessary Being in this statement:
الوجود ان كان واجبا، فهو المطلوب والااستلزمه لاستحالة الدوروالتسلسل
Which means, if we accept the cause of all existence as the existence of the Necessary Being, we have reached the desirable conclusion; otherwise‑that is, if we do not accept the Necessary Being as the first cause‑ the existence of the Necessary Being is necessitated by the impossibility of a causal circle and a causal linear series.
Notes:
6. Here `c' stands for cause and `e' for effect.