This is an episode from the series hosted by Morgan Freeman entitled “Through
the Wormhole”. Focusing on the finitude/infinitude of the universe, it explores various scientists’ work in trying to determine whether there is, in fact, an edge.
An absolutely amazing show.
Straight up, I love port.
I must admit, I am going through a bit of an existential crisis at the moment: I have finished classes; I have handed in all papers and assignments, including my thesis; I have 4 exams between me and freedom. A week from Saturday, I will be sitting outside, consuming gratuitous amounts of wine, and reading ALL the Sherlock, because I will be done.
That being said, tomorrow is my thesis defence. I will be the first to say that I was damn scared about having to do this. The question period at the last presentation I found to be quite difficult. However, we persevere.
And so, tomorrow afternoon around 4pm, my ten long months of work will all come to an end. I will give my presentation, answer any question, and then there will be a moment of blinding clarity in which we understand the universe. Don’t worry, this will pass; and then we will move on with our lives.
I doubt I will be this classy, though.
In times like these, I find myself turning to others for inspiration and the courage to believe in myself, to have confidence that, damn it, I know what I am talking about! One of mu staple sources of inspiration is G.K. Chesterton. His writing and his wisdom represents everything I want to be. Take, for example, this gem: “Fairy tales are more than true; not because they tell us that dragons exist, but because they tell us that dragons can be beaten.” Not only is it true and wonderfully relevant to my current situation, but its awesome!
I guess the message I am trying to communicate is that I have overcome a lot this year,
Come at me, bro.
and I am proud. I am proud that I fell sometimes and had the courage to pick myself up and keep going. I am proud that I didn’t always understand things because it forced me to study more deeply and thoroughly my material. I am proud that this year was not easy and that I DID IT.
By the grace of God, I did it.
Pretty nifty stuff! Click below!
Minimalist posters explain complex philosophical concepts with basic shapes.
I spent the day with a friend and after we had done homework and gone shopping, we decided to do our nails. Here is a picture of mine.
Bam. Space Nails.
I should really take pictures as I make things, but I only thought to blog about this when
the cake was in the oven. Ah well.
Preheat oven to 350; grease and flour a cake pan or muffin tins.
1. Start with one white cake mix. Follow the instructions to make the batter. Alternatively, make a white cake from scratch.
2. Separate equal amounts of the batter into 5-7 different small bowls.
3. Add food colouring to each of the bowls, mixing as many different colours as you like! I usually use the neon food colouring because I like the bright colours it gives the cake.
4. If you are using a regular circular pan, pour the batter from each of the bowls, one at a time, into the middle of the pan. You should be pouring over every previous colour when you put a new one in. Do not spread it around the pan; let the batter work its way to the edges.
If you are using a bundt pan, pour the batter from each bowl in layers around the pan.
If you are making cupcakes, use about 3 spoonfuls of batter, each of a different colour, per cupcake. When the tins are full, marble the colours together, but not too much or the rainbow effect will not take. (If you are going for the surprise effect, use cupcake papers to hide the rainbow!)
Bake according to time on box. Let cool. Ice with white icing so that feasters are surprised when you cut into it. ENJOY!
Recently, my roommate had a dinner party for which I made Rainbow Cake! We covered it in white icing so that the rainbow part of it would be a surprise and people loved it!
I brought the cupcakes in to school and they were a huge hit! I am so glad everyone liked them!
In other news, my thesis is complete and handed in. Now I have the defence to look forward to. Better eat more cake.
I presented a summary of my thesis today at Student Research Day and I thought I would post my notes for anyone who wanted to come and couldn’t, or for anyone who would just like to read them!
The Kalam cosmological argument has its origins in Muslim theology. It was first constructed by the mutakallimūm, a group of Islamic theologians whose area of thought was natural theology. While Kalam, translated literally, means “speech”, we can perhaps draw similarities between the Islamic Kalam and the Greek Logos to allow for a more thorough understanding. Logos is a very commonly used word and can be used to denote a variety of meanings, just as the meaning of Kalam evolved to mean a statement of intellectual opinion, and eventually became the name of an entire movement in Arabic thought.
Though the Kalam argument and its proponent philosophers saw their demise around the twelfth century AD, it is still alive in some Islamic schools of thought today, as well as in the philosophical work of William Lane Craig.
Craig is an American theologian and analytic philosopher who has devoted decades to reviving the Kalam argument. Having written a vast array of literature on the subject, Craig’s devotion to the Kalam argument is astounding. And while Kalam cosmology itself is attractive and seemingly thorough in its argumentation, there are some details that do not add up. They, unfortunately, bring down much of the argument, leaving little room for salvage. Using the philosophy and natural theology of Thomas Aquinas, that which I believe most accurately represents the nature of time and the universe, I will discuss the flaws in the Kalam argument and how they should be resolved.
Let us begin with the general structure of the Craig’s argument. Premise one says that everything that begins to exist has a cause of its existence. Premise two says that the universe began to exist. The conclusion, therefore, is that the universe has a cause of its existence. In this argument alone, there are quite a few assumptions that need to be proven in order that the argument be not only valid, but sound. As much of the argument hinges on proving that the universe began to exist, this is where we will begin our examination.
Craig’s reasons for believing the second premise, that the universe began to exist, are twofold. First, he says that it is impossible that an actual infinity can exist. Secondly, he says that an actual infinity cannot be formed by successive addition, and we will look at this one later using the example of the running man.
The ideas of actual and potential infinity are concepts that date back to Aristotle. A potential infinity is that to which more can always be added, whereas an actual infinity is complete in and of itself, and nothing more can be added to it. To talk about a potential infinity is to talk about what is not an infinity, but which can always be thought of with something more added. To talk of an actual infinity, however, is to talk of a fully realized collection of an infinite number of things.
Essentially, when we talk about instantiating an actual infinity in the real world, we arrive at a paradox. One example we can use to show this is that of the library containing an actually infinite number of books. Each book in the library could theoretically be assigned a natural number because even though the library is infinite, each book by itself is countable. But this seems contradictory to the notion of an actual infinity because natural numbers never reach an actual infinity, but rather continue on as a potential infinity. You could also imagine assigning colours to the books, making half red and half blue. Again, however, we reach the same paradox in that the half that is blue must not only be equal to the half that is red, but must also be equal to the entire set of blue and red books combined.
Another example used to show that the real-world instantiation of an actual infinity is absurd is that of a hotel with an actually infinite number of rooms, traditionally referred to as “Hilbert’s Hotel”. Imagine a hotel with an actually infinite number of rooms, all of which are occupied, thus leaving no vacancies. If a customer comes into the hotel and asks for a room, he must be turned away by the desk-clerk, who tells the customer that there are no vacancies even though the number of rooms is infinite. We immediately see the problem here and can understand why an actual infinity cannot exist in the real world.
Craig does not deny that an actual infinity is entirely acceptable within the context of mathematics. Math, after all, exists primarily within the realms of thought and theory. The real-world implications that these examples DO have is that they seem to demonstrate that, because an actual infinity cannot exist, time cannot be an actual infinity, and therefore that it must have begun at some point.
One may argue this point by saying that the library and the hotel do no accurately represent the nature of time because their contents are wholly and simultaneously instantiated, whereas events occur successively in time. Craig opposes this argument in his second reason for the necessity of finite time, saying that even succession cannot amount to an actual infinity. Take his example of the running man.
Imagine a man running from eternity, and with each step a new stone appears under his foot. If the man has been running from eternity, he will have collected not an actually infinite number of stones, but a potentially infinite number of stones. If with each falling foot, a new stone appears, the man will never be able to traverse an infinite series of stones and will thus never arrive at the present. Therefore, according to Craig, any successive infinity would bring us right back to the problem of trying to instantiate an actual infinity in the real world. Either we end up with a potential infinity, by which we would not have been able to make the transition to the present, or we end up with a paradox.
Craig has argued that an actual infinity is a paradoxical impossibility. If, he argues, the universe has always existed in the past – if it were eternally in existence – this whole past series of events would constitute an actual infinity. But since an actual infinity is impossible, the past cannot have been always in existence. If it must not have always been in existence, it must have had a start – a beginning.
It seems, then, that Craig has been able to prove his second premise: that the universe began to exist. The first premise, that everything that begins to exist has a cause of its existence, is comparatively easier to prove. All Craig does in proving this premise is to suppose that either the universe began spontaneously on its own, or it was created. Given the previous arguments about the finitude of time, it seems counterproductive to suppose that time and space spontaneously self-generated. While we may be able to imagine something coming into existence on its own, it is highly unconvincing to argue that because we can imagine it, its existence is possible. As far as logic can dictate, everything that comes into existence within time must be caused, and therefore because the universe exists within time, it too must be caused.
Thus, having proven his first and second premises, Craig’s conclusion that the universe had a cause of its existence seems to follow and the Kalam argument appears to speak accurately about the universe and its real state of affairs. However, allow me to step back for a moment and re-examine Craig’s examples of the library, the hotel, and the running man.
If we take the example of the library and apply it to time, we find a problem in comparing books to temporal events. While books must be wholly instantiated and wholly actual, temporal events are not the same in any respect. Events occur in time have a sort of fluidity to them that a book simply does not have. Craig may understand this difference as a hindrance to his argument, and respond by saying that the collection of past events, all of which are actual, can be added up and counted. There is, however, a fundamental misunderstanding in his reasoning regarding past events. In order for past events to have the same reality as present events, they would have to exist within a universe where all of time is simultaneously real, more commonly known as B-theory time, whereas Craig himself does not believe that this is the case with time. He subscribes rather to A-theory time, which says that time passes from future, to present, to past, only achieving actuality in the present moment.
Even though an actual infinity cannot exist in the real world, if books are not like events, we cannot use the example of the library, nor that of the hotel, to explain the reason why it cannot exist. Consider now the example of the runner. While Craig focuses on the collection of stones, the example really revolves around the man running. Craig says that the man who runs from eternity demonstrates that past time must be finite, otherwise we would never arrive at the present. But suppose that instead of running in a straight line, the man is running around a track. If we think of the example this way, the problem seems to resolve itself. Rather than a new stone appearing under his foot with every new step, the runner’s feet land on the same stones over and over again. If we modify the example in this way, we can make a case either for the creation of the world, OR the eternal existence of the world. If we think of this example in terms of days, we can liken each 24-hour period to one revolution of the track. Since each revolution is complete and countable, we can have a succession of revolutions that add up to an infinite number. Taking into account Craig’s notion of a God by whom the universe was created, we still do not run into any trouble by saying that the universe could have existed from eternity. If we think of God as an almighty being who, by His very definition must exist before creation, there is nothing that stops us from supposing that by his perfect will the universe could have existed from eternity. That being said, it is important to note that while Thomas does not think that this is really the case when it comes to time and creation. In the end, Thomas believes that the universe was created and has a finite past temporal duration, but such a belief in no way limits the power of God.
So, if we can imagine that it is possible for time to be composed of a successively infinite series of events, we can essentially say that Craig’s second premise, that which says that it is necessary that universe began to exist, is false. Rather, let us accept that, while it is impossible to instantiate an actual infinity in the real world, it is not for the reasons presented to us by the examples of the library, the hotel, and the running man.
As a further point of interest, Thomas says that another reason it is possible that the universe came into existence without a beginning because according to him, the universe was created ex nihilo, that is, out of nothing. Therefore, because motion is only measured when substances undergo a change from one state of actuality to another, all the while holding the potential for other actualisations, the beginning of the universe does not meet the requirements necessary for change. If it was created out of nothing, then there is nothing for it to change from, but only something for it to change to. From this argument, in addition to the possibility of a successive infinity, we see no necessity for an absolute beginning, a necessary change in the state of affairs, when the universe began.
Therefore, the Kalam cosmological argument, while seemingly precise, does not really tell us anything about whether or not the universe began. We must endeavour to delve deeper into the depths of philosophy and natural theology in order to acquire a better understanding of the nature and metaphysics of time and its presence in the universe.
