The Kalaam Cosmological Argument

The Kalam Cosmological Argument
[from http://www.philosophyofreligion.info]

The temporal, kalam cosmological argument, dates back to medieval Muslim philosophers such as al-Kindi and al-Ghazali. It has recently been restored to popularity by William Lane Craig. Like all cosmological arguments, the kalam cosmological argument is an argument from the existence of the world or universe to the existence of God. The existence of the universe, such arguments claim, stands in need of explanation. The only adequate explanation, the arguments suggest, is that it was created by God.

What distinguishes the kalam cosmological argument from other forms of cosmological argument is that it rests on the idea that the universe has a beginning in time. Modal forms of the cosmological argument are consistent with the universe having an infinite past. According to the kalam cosmological argument, however, it is precisely because the universe is thought to have a beginning in time that its existence is thought to stand in need of explanation.

This argument has the following logical structure:
The Kalam Cosmological Argument

(1) Everything that has a beginning of its existence has a cause of its existence.
(2) The universe has a beginning of its existence.Therefore:
(3) The universe has a cause of its existence.
(4) If the universe has a cause of its existence then that cause is God.Therefore:
(5) God exists.

The first premise of the argument is the claim that everything that begins to exist has a cause of its existence. In order to infer from this that the universe has a cause of its existence the proponent of the kalam cosmological argument must prove that the past is finite, that the universe began to exist at a certain point in time.

The crucial premise of the kalam cosmological argument, then, is the second: “The universe has a beginning of its existence”. How do we know that the universe has a beginning of its existence? Might not the universe stretch back in time into infinity, always having existed? The proponent of the kalam cosmological argument must show that this cannot be the case if his argument is to be successful.

Advocates of the kalam cosmological argument claim that it is impossible that the universe has an infinite past. In support of this claim, modern advocates of the argument often appeal to modern science, specifically to the Big Bang theory. Modern science, they say, has established that the universe began with the Big Bang.

Traditionally, however, it is mathematics that has been used by proponents of the kalam argument in order to establish that the past is finite. There are a number of ways of doing this; I’ll outline three mathematical arguments for the finitude of the past.

Maths and the Finitude of the Past


The kalam cosmological argument rests on the idea that the universe has a beginning; its second premise states as much. Advocates of the argument offer two kinds of argument in favour of this claim: scientific and mathematical. Here three mathematical arguments for the finitude of the past will be outlined.

The first argument draws on the idea that actual infinites cannot exist, the second on the idea that actual infinites cannot be created by successive addition, and the third on the idea that actual infinites cannot be traversed.

If any of these arguments is successful, then the second premise of the kalam arguments will have been proven.

The Impossibility of an Actual Infinite

The first mathematical argument for the claim that the universe has a beginning draws on the idea that the existence of an infinite number of anything leads to logical contradictions. If the universe did not have a beginning, then the past would be infinite, i.e. there would be an infinite number of past times. There cannot, however, be an infinite number of anything, and so the past cannot be infinite, and so the universe must have had a beginning.
Why think that there cannot be an infinite number of anything? There are two types of infinites, potential infinites and actual infinites. Potential infinites are purely conceptual, and clearly both can and do exist. Mathematicians employ the concept of infinity to solve equations. We can imagine things being infinite. Actual infinites, though, arguably, cannot exist. For an actual infinite to exist it is not sufficient that we can imagine an infinite number of things; for an actual infinite to exist there must be an infinite number of things. This, however, leads to certain logical problems.

The most famous problem that arises from the existence of an actual infinite is the Hilbert’s Hotel paradox. Hilbert’s Hotel is a (hypothetical) hotel with an infinite number of rooms, each of which is occupied by a guest. As there are an infinite number of rooms and an infinite number of guests, every room is occupied; the hotel cannot accommodate another guest. However, if a new guest arrives, then it is possible to free up a room for them by moving the guest in room number 1 to room number 2, and the guest in room number 2 to room number 3, and so on. As for every room n there is a room n + 1, every guest can be moved into a different room, thus leaving room number 1 vacant. The new guest, then, can be accommodated after all. This is clearly paradoxical; it is not possible that a hotel both can and cannot accommodate a new guest. Hilbert’s Hotel, therefore, is not possible.

A similar paradox arises if the past is infinite. If there exists an infinite past, then if we were to assign a number to each past moment then every real number (i.e. every positive integer) would be assigned to some moment. There would therefore be no unassigned number to be assigned to the present moment as it passes into the past. However, by reassigning the numbers such that moment number one becomes moment number two, and moment number two becomes moment number three, and so on, we could free up moment number one to be assigned to the present. If the past is infinite, therefore, then there both is and is not a free number to be assigned to the present as it passes into the past.

That such a paradox results from the assumption that the past is infinite, it is claimed, demonstrates that it is not possible that that assumption is correct. The past, it seems, cannot be infinite, because it is not possible that there be an infinite number of past moments. If the past cannot be infinite, then the universe must have a beginning. This is the first mathematical argument for the second premise of the kalam cosmological argument.

The Impossibility of an Actual Infinite created by Successive Addition

The second mathematical argument for the claim that the universe has a beginning draws on the idea that an actual infinite cannot be created by successive addition. If one begins with a number, and repeatedly adds one to it, one will never arrive at infinity. If one has a heap of sand, and repeatedly adds more sand to it, the heap will never become infinitely large. Taking something finite and repeatedly adding finite quantities to it will never make it infinite. Actual infinites cannot be created by successive addition.

The past has been created by successive addition. The past continuously grows as one moment after another passes from the future into the present and then into the past. Every moment that is now past was once in the future, but was added to the past by the passage of time.
If actual infinites cannot be created by successive addition, and the past was created by successive addition, then the past cannot be an actual infinite. The past must be finite, and the universe must therefore have had a beginning. This is the second mathematical argument for the second premise of the kalam cosmological argument.

The Impossibility of an Actual Infinite that has been Traversed

The third mathematical argument for the claim that the universe has a beginning draws on the idea that actual infinites cannot be traversed.

If I were to set out on a journey to an infinitely distant point in space, it would not just take me a long time to get there; rather, I would never get there. No matter how long I had been walking for, a part of the journey would still remain. I would never arrive at my destination. Infinite space cannot be traversed.

Similarly, if I were to start counting to infinity, it would not just take me a long time to get there; rather, I would never get there. No matter how long I had been counting for, I would still only have counted to a finite number. It is impossible to traverse the infinite set of numbers between zero and infinity. This also applies to the past. If the past were infinite, then it would not just take a long time to the present to arrive; rather, the present would never arrive. No matter how much time had passed, we would still be working through the infinite past. It is impossible to traverse an infinite period of time.

Clearly, though, the present has arrived, the past has been traversed. The past, therefore, cannot be infinite, but must rather be finite. The universe has a beginning. This is the third mathematical argument for the second premise of the kalam cosmological argument.

Justice in Judgement

Salaams and Peace & Blessings upon us all

I had been pondering upon something for a long time. Being exposed to gossip and bad opinions and overly good opinions. I was concerned how such notions would have such strong effects upon individuals and groups, towards one another and upon themselves. In other words, I feared how me having a bad opinion of someone made me more likely to be unjust, unfair and thus neglectful of my duty towards them. Yet also, me having an overly high opinion of someone, may blind me, making me neglect myself and others too, but being unjust and unfair in this respect also.

So here I shall divulge some of my meanderings and I would ask anyone, to please give their opinions and any knowledge/wisdom they have freely. So that it may aid me in my thinking around this subject to come to some formalised conclusion on the topic.

Bismillah Hir Rahman nir Raheem.


To judge is Allah's right and only Allah is perfected and absolute in it.

Thus Shariah is the guide to judge, the Quran also meaning "Criterion" & also the life and Sunnah of Rasul(SAW) as the best example of being one who held judgement, yet fulfilled all duties and was the most just.

We do not ever have complete knowledge of anything, that is with Allah alone. Yet we must judge and naturally we will. Our first duty is thus not to forget how lacking we are to make judgements.

It would be difficult to act and interact in this world without making judgements. Judgements are like measurements and every action can be measured and should be measured. So one must judge in order to act, to decide what to do and not to do, when, how, where & why. The 'why' relates to intentions & all actions are based upon it.

Our actions are made righteous by being based on our correct belief. Now if our belief is not correct and our certainty of our belief is not 100%, then our judgements & actions are at stake. The worst scenario is having baseless judgements and actions, which with belief we should be far from.
Yet are we not making judgements in what and how to believe? Thus as already addressed our capability in judging is not perfect when based on our own devices, we are therefore in need of other than our own selves. Hence guidance must be sought and Prophecy is necessitated.

In judging people, one may make bias their actions and reactions to such an extent from such judgements so as to neglect the duties owed to people.

This is why we are meant to offer "benefit of the doubt" to others, as we can not know them like we know our own selves. Remember, even with our own selves we struggle to understand and know ourselves. How we know ourselves paints how we see others. We compare others to ourselves to know them. Thus some people who really don't like things about themselves, when they see it in others they tend to not like such others. When we see things we like in our selves, we like to see it in others and thus are attracted to such people.

Though we may know people whom we have shared a great deal in terms of experience, knowledge, tastes and opinions; these can never be exact. Though each one of us judge according to the devices we have, we are gifted with being able to richly communicate with one another, share, express, challenge and correct judgements of one another. This thus makes clear the great importance communication plays in our lives. Know that gossip is the lowest form of communication, it rather distorts and destroys communication, rather than aid its useful purposes.

So rather, I propose a solution. When we have judgements of people, to know that we are lacking, so not to take them to heart. Whenever possible, to be open and honest with each other, so that false inaccurate judgements are done away with. If that can not be done, then to have benefit of the doubt. If still, you can not directly communicate with a person and still can not give them the benefit of the doubt. Then speak to Sheikh. It may be that you are on to something and something needs to be done about that person. Or it may be that you have a disease in your own heart and it needs to be removed.

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"Yet also, me having an overly high opinion of someone, may blind me, making me neglect myself and others too, but being unjust and unfair in this respect also"
Some people get more praise than they deserve. This is fine, and certainly better than blaming. Praise is a good thing. However, when we go beyond and start to almost attribute things to them that they do not deserve, such as worship and unquestioned devotion.

For instance, why will I forgive a friend easier than a stranger or someone who I don't like?

Say for instance, I have a car to go to class/lesson, the first people I think of, will most naturally be my friends perhaps. Now surely I should be seeking who is more in need, and not forget those in more need of a lift than my friends, especially when we find certain people to be boring or even "smelly" for the journey.

It is good to have friends and have them close to you more than others. But we should not forget others who may be in more need or have more right to a thing.

This sort of thing is what I am talking about, when I fear my high opinion of someone, may blind me, making me neglect myself and others, in regards to when others are more in need or more deserving.

When in a crowd or gathering, it is good to want to spend time with your close friends, but do not neglect those who have no friends present or new people who don't know anyone. These are perhaps more in need of our company than our friends.

These are subtle things indeed and know that it is not as bad as blaming someone, to over praise someone. It is just about keeping it all in context of Justice and Duty.

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I thank you for reading this, and I look forward to your responses.