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*Tasalsul* is the belief that the present moment is preceded by an infinite number of past events. In proving the existence of God, Imam Al-Ghazali offers three arguments for the impossibility of this belief in his *Al-Iqtisad Fi Al-I’tiqad*:

All of the Philosophers agree that the bodies of the world are inseparable from events, and yet they claim that the world is beginningless. So if it is said: “you claim that whatever is inseparable from events, is itself emergent. What is your proof for this?” We say: if the world were beginningless, while being inseparable from events, then this would mean that an infinite number of past events occurred, entailing that the number of orbits each celestial body completed be infinite^{[1]}. This is impossible, because whatever entails an impossibility is itself impossible, and we will now show that three impossibilities follow from this belief.
It is impossible for an infinite number of completed orbits to be neither even nor odd, or both even and odd. An even number is one that is divisible by two, like ten for example. Whereas an odd number is one that is not-divisible by two, like nine. And any amount is composed of a multiplicity of singulars, such that this amount is either divisible by two, or not. Therefore, it is impossible for an amount to be neither divisible nor not-divisible by two, and it is impossible for an amount to be both divisible and not-divisible by two. It is impossible for an infinite number of completed orbits to be even, since an even number is so because it lacks one, such that if this one were added to it, it turns odd. But how can an infinite amount lack anything? It is also impossible for this amount to be odd, because an odd number becomes even by adding one to it, so it can only remain odd as long as it lacks this one. But then again, how can an infinite amount be lacking in anything?
To make matters clearer: they [the Philosophers] claim that Saturn completes one orbit [around the Earth] every thirty years, while the Sun completes one orbit every year. So the number of orbits that Saturn completes annually, is a thirtieth of the Sun’s. But if one proposes that Saturn has been orbiting since eternity past, then the number of its orbits would have been infinite, even though this amount is also less than the orbits of the Sun. After all, a thirtieth of an amount is obviously less than the full amount. Similarly, the moon completes twelve orbits every year, which means that the Sun completes twelfth as many orbits as the moon. Each amount is said to be infinite, while each is less than the other, and this is a clear impossibility. |

– Al-Ghazali, *Al-Iqtisad Fi Al-I’tiqad*, page 28

[1] The Philosophers maintained that the celestial bodies have been orbiting the earth since eternity past. So the Imam argues that if the world were beginningless, then this would mean that the number of orbits each celestial body completed, would have been infinite.

salam,

if by ‘concluded’, you mean ‘passed’, elapsed’, etc., then all you’re saying is:

‘before this moment/event, an infinite number of moments/events’ passed or elapsed’

and, i said, this means:

‘for every in the past you care to choose, there’s one before it, without end’

and i don’t see a problem here. but if by ‘concluded’ you mean something else, i don’t understand it.

‘[…] how can addition be performed on a non-number?’ – you’re adding elements or members to a set or aggregate (jumla) i.e., the set of past infinite events. and there’s no problem with that.

regarding the third objection, most of what you said is beside the point (and contentious in any case). however numbers exist, my main claim is that Ghazali’s claim that ‘infinities don’t stand in a larger than/smaller than relation’ is false; for the real numbers are greater than the naturals, even though both are infinite.

as for this: ” Rather, that whenever you mention a natural number to some person, this person can give you a natural number greater than the one you mentioned. However, no matter the number of naturals this person lists for you, he will never be able to finish listing an infinite number of them” – it shows that you don’t understand the point at issue. i suggest you go and learn Cantor’s proof for why the real are greater than the naturals, even though both are infinite. it’s called ‘the diagonal argument’.

Wa ‘alaykum Al-Salam,

“if by ‘concluded’ you mean something else, i don’t understand it.”

Concluded as in came to an end, since the past is the series of events which leads up to and then ends with the present moment. And if the past were infinite it would never come to an end, since an infinity is endless. Thus, if the past were infinite, then an endlessness would have come to an end, and therein lies the absurdity.

“you’re adding elements or members to a set or aggregate (jumla) i.e., the set of past infinite events. and there’s no problem with that.”

The problem is that you’re treating infinity as a quantity when you claim that an infinite number of events elapsed, but then you argue that infinity is not a quantity when Al-Ghazali shows that the existence of an infinite quantity is absurd.

“However numbers exist, my main claim is that Ghazali’s claim that ‘infinities don’t stand in a larger than/smaller than relation’ is false; for the real numbers are greater than the naturals, even though both are infinite.”

Numbers don’t exist. They are abstract objects whose infinitude is a mere potentiality as has already been explained. e.g. whenever you give someone a natural, he is able to give you a greater one. However, at any given step of this counting process, the set of counted numbers will always be finite. Cantor’s arguments do not impact this fact, and there is nothing contentious about it.

I highly recommend the entirety of this presentation (although you can skip to minute 48 for a discussion on Dedekind’s and Cantor’s theories specifically), perhaps it will help make the above clearer to you:

salam,

the three objections Ghazali raises are weak, based on misunderstandings of the positions of the hukama’.

what we mean when we say that the past is infinite is that:

for any past event you care to choose, there’s a event before it, without end.

this disarms the first objection; for all i mean when i say ‘an infinity of past events have ‘occurred’ is that ‘every past event (you want) is preceded by some other event’, ad infinitum’. nothing absurd about that.

as for the second objection, it fails because it treats what is infinite as an actual number.

as for the third objection, the claim there is just false – one infinite can be greater/lesser than another. example: the set of natural numbers (infinite) is less than set of real numbers (also infinite).

Wa ‘Alaykum Al-Salam,

“for any past event you care to choose, there’s an event before it, without end.”

Meaning: this chosen event is preceded by an infinite number of other events. Such that this infinite series of preceding events concluded, before this chosen event emerged into existence. And this is absurd because an infinite cannot be concluded, since it is endless by definition.

I don’t see how your rephrasing is an answer to the first objection.

“as for the second objection, it fails because it treats what is infinite as an actual number.”

If you accept that infinity is not a number, then you can be asked: new events are being added to the series of past events as time progresses, so if this series of past events were infinite, and infinity is not a number, how can addition be performed on a non-number?

“as for the third objection, the claim there is just false – one infinite can be greater/lesser than another. example: the set of natural numbers (infinite) is less than set of real numbers (also infinite).”

In of themselves, numbers are abstract objects that don’t exist in the real world. Therefore, when one claims that the set of natural numbers is infinite, the claim isn’t that there is an actual infinite number of existents. Rather, that whenever you mention a natural number to some person, this person can give you a natural number greater than the one you mentioned. However, no matter the number of naturals this person lists for you, he will never be able to finish listing an infinite number of them (for the reasons mentioned above).