Plato's Heaven

An attack on philosophy

2007-11-27T19:38:00.000+11:00

After reading Ayer's Language, Truth and Logic, everything became clear. I realised, then, that I no longer wanted to study philosophy. The following argument shows a major problem with philosophy:

1. The only way to know anything about the world is to derive information through the senses. This is why science places so much importance on experiment and observation.

2. Philosophy is a discipline with the primary aim of discovering truth about the world.

3. The method of philosophy is to derive propositions from intuitively plausible premises (not information from the senses).

4. Therefore, it is impossible for philosophy to achieve its aim.

Premise 4 is derived from all premises 1, 2 and 3. So if the reader believes in the first 3 premises, then they are forced to the conclusion that there is something fundamentally wrong with philosophy. It is, as Ayer put it, a nonsensical field (although Ayer was speaking of Metaphysics in particular).

It may help to go through some of the premises more carefully. Of course, the first premise is empirical in spirit. Any rationalist would reject it in an instant. One might object to premise by claiming that mathematical knowledge is a counter-example. Mathematical propositions, it appears, can be 'discovered' without any reference to sensory experience.

Ah, but here is the problem. Mathematical propositions tell us nothing about the real world. They tell us what the axioms imply. They are true by definition. All of mathematics can be deduced to a claim that if so and so axioms are true, then these results are true. But this says nothing about what is actually true.

One might respond to this by arguing that Mathematics has many applications in the real world, especially in physical explanations. Surely, Mathematical knowledge tells us something about the real world. But this is not so. Whether mathematical models apply to the real world is an empirical matter. Mathematical propositions or logical propositions therefore tell us nothing prima facie about the world.

The second premise represents the philosphy which I am interested in. If there are any fields of philosophy which do not satisfy this category, then I have no qualms about them.

The third premise is the one which separates philosophy from science. These two disciplines do, I believe, have the common aim of discovering truth. The former, however, aims to do so without any connection to the world; as though the mind itself is sufficient to discover universal truths. This is the issue I take with philosophy. Of course, one might argue that what I am writing now is philosophical, and thus refutes my own argument.

The power of this response makes me rethink the nature of my argument. I guess I would defend my argument by claiming that my first three premises are observations that I have made, and are thus empirical. So my argument is not entirely philosophical (at least not philsophical according to my argument).

The Game Show

2006-06-21T20:18:00.000+10:00

The Game Show puzzle has bewildered some of the greatest mathematicians. It's solution was so counter-intuitive that it was not accepted by the academic community for quite some time. See if you can get your head around it:

You are on a game show. In front of you are three boxes, one of which contains the keys to a brand new Porsche. If you pick the box with the keys, the car is yours. The game show host gets you to point to one of the three boxes. Now, before checking the box you have chosen, the game show host removes one of the other two boxes, and this is a box which does not contain the keys. So, if you choose box A, then the host will remove either box B or box C, depending on which box does not contain the keys. If the keys are in box A, then the host will remove either B or C - it does not matter which.

Now comes the dilemma. After the host has removed a box, should you change your decision? Does this increase your chances of winning the car?

People well-learned in probability would instinctively claim that it doesn't matter whether you change your decision or not: the probability of choosing the keys is always 1/3. But this is in fact false. You actually increase your chances of winning if you change your decision. The probability of choosing goes from 1/3 to 2/3.

But why? The probabilities for all the boxes should be 1/3. Well, probabilities are not concrete properties of objects - they change with situations. After the host removes a box, he has given you a new piece of information. Before he takes it away, the probability that the keys were in one of the two boxes which you did not choose was 2/3. So when he removes the box, the probability that it is in the box that he does not take away becomes 2/3. So there you have it - logic works in funny ways.

Einstein's Riddle

2006-02-26T23:25:00.000+11:00

I was recently forwarded this e-mail by a friend and I thought that the reader might enjoy its challenge. I've provided a solution at the end of the post.

ALBERT EINSTEIN'S RIDDLE ARE YOU IN THE TOP 2% OF INTELLIGENT PEOPLE IN THE WORLD? SOLVE THE RIDDLE AND FIND OUT.

There are no tricks, just pure logic, so good luck and don't give up.

1. In a street there are five houses, painted five different colours.
2. In each house lives a person of different nationality
3. These five homeowners each drink a different kind of beverage, smoke different brand of cigar and keep a different pet.

THE QUESTION: WHO OWNS THE FISH?

HINTS

1. The Brit lives in a red house.
2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The Green house is next to, and on the left of the White house.
5. The owner of the Green house drinks coffee.
6. The person who smokes Pall Mall rears birds.
7. The owner of the Yellow house smokes Dunhill.
8. The man living in the centre house drinks milk.
9. The Norwegian lives in the first house.
10. The man who smokes Blends lives next to the one who keeps cats.
11. The man who keeps horses lives next to the man who smokes Dunhill.
12. The man who smokes Blue Master drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The man who smokes Blends has a neighbour who drinks water.

ALBERT EINSTEIN WROTE THIS RIDDLE EARLY DURING THE 19th CENTURY. HE SAID THAT 98% OF THE WORLD POPULATION WOULD NOT BE ABLE TO SOLVE IT.

SOLUTIONS: (you may want to draw five squares in a row to represent the houses and then write the descriptions above the squares. You will need to do this to so that you can note which characteristics have already been used)

(a) The Norwegian lives in the first house (9)
(b) The second house is blue (14)
(c) The first house is yellow (1) & (4) & (c)
(d) The person in the third house drinks milk (8)
(e) The person in the first house drinks water (5) & (12) & (3) & (d)
(f) The second house smokes Blends (15)
(g) The third house is red (5) & (4)
(h) The fourth house is green and the fifth house is white (4)
(i) The person in the fourth house drinks coffee (5)
(j) The third house is owned by a Brit (1)
(k) The second house keeps horses (11)
(l) The person in the fifth house smokes Blue Master and drinks beer (12 - only place that both characteristics can stay together)
(m) The second house is owned by a Dane who drinks tea (3)
(n) The fourth house is owned by a German who smokes Prince (13)
(o) The fifth house is owned by a Swede who owns dogs (2)
(p) The person in the third house smokes Pall-Mall and owns birds (6)
(q) The person in the first house owns cats (10)

Therefore, the German must own the fish!!

Fighting for freedom

2006-02-10T12:03:00.000+11:00

Are we free beings? In politics, we would answer this question by considering one's rights in society. In philosophy, however, we look at in a different light. That is, we consider whether we can have freedom at all.

Hard Determinism is the view that there is no such thing as freedom. At first, I found this argument very convincing:

(1) If an agent freely performs an action, then the agent is responsible for the action.
(2) Agents are not responsible for actions that are caused by factors outside their control.
(3) Every action an agent performs is caused by factors (genes and early childhood environments) over which the agent had no control.
______________________
No action is performed freely.

Our actions are dictated by either our genes or our environment. These things are beyond our control, therefore, we are not free. This argument can be used to show that we cannot blame people for their actions. If Bob kills his mother, he either does it because he was born evil, or because his environment shaped him to act in this way. What other alternative is there?

Hard Determinism is fuelled by a scientific theory which suggests that the way the world will be in 10 years is already decided; things can only happen one way; everything in the universe is governed by deterministic laws. So our actions were already pre-determined, even before we were born. Unfortunately, Bob was destined to kill his mother.

In recent years, however, quantum physics has suggested that the tiniest of particles operate in random ways. These small particles are governed by chance, not laws. So maybe the universe is not deterministic after all.

But does this help us? Suppose God is rolling the dice on our decisions. He rolls a three and we end jump off a cliff. We seem to have as little freedom in a random world, as we do in a deterministic world.

So how can refute Hard Determinism? Well, we turn to Hume, who has a new and ready theory of freedom. Hume says that if you could have done otherwise, then you were acting freely (even though you wouldn't have, because of deterministic reasons).

Hume tries to get closer to what we mean when we use the word "freedom". We usually mean that we want to have the ability of doing it another way. But imagine the following situation that Locke described. Suppose that you lock the door of a room. There is a man inside this room that is unaware that the only way out of the room is locked: he thinks that he has the option of leaving the room. Nevertheless, he is quite happy where he is, and decides to stay. Is he acting freely? According to Hume's theory, he is not. But intuively, he is acting freely because he wants to stay. So it is not necessary to have the option of acting another way.

So another new and improved theory of freedom is: we act freely when we act according to our desires. But there are many orders of desires. Second order desires are approvals or dissaprovals about first order desires. For example, if you have the urge to smoke, you are having a first order desire. When you disapprove of this desire, you are having a second order desire. When your second desire corresponds with the first, and you are able to act in a way that fulfills that desire, you are acting freely. So if you feel like a smoke, want to feel like a smoke, and then you smoke, you have just exercised freedom.

But philosophy is never so clear-cut. A person who is brainwashed will have second order desires that are not their own.

Kant's ethics of duty

2006-01-27T18:07:00.000+11:00

Kant was a great philosopher who believed in the power of reason. He applied reason to many areas of philosophy, including the philosophy of art, maths and ethics. He is reknowned for his incredible theory of morality.

Kant believes that we can only have morality based on reason because morality based on experience is inconsistent and based on desires. He presses that we should "act only according to that maxim by which you can at the same time will that it should become a universal law."

By this, he meant that we could discover what was morally good and bad by taking an action, repeating it over and over again, and then observing the repercussions. For example, take the action of lying. If everyone was to lie all the time in society, no-one would ever trust anyone, and society would not function well at all. So, Kant says that a lie is an offence to mankind generally because it errodes the contract of truthfulness in society. On the other hand, telling the truth must be morally good because if everyone told the truth, then everything could be believed, and this makes things MUCH easier. Therefore, according to Kant, "truthfullness...is the formal duty of an individual to everyone, however great may be the disadvantage accruing to himself or another".

Every theory in philosophy has a problem, and the problem with this one is this. Suppose that a murderer was after your mother, and he appears at your door one day with a large, shiny kitchen knife. He asks you if your mother is home. You have read Kant's Ethics of duty and remember that truth telling is morally good. So you tell the murderer that your mother is in...

Is this right? Kant would have led the murderer to his mother! But there are other things to consider. What if Kant did decides to lie about the whereabouts of his mother: "She's out right now, come back later". Meanwhile, his mother escapes out the back window and runs into the robber outside. We can guess what happens after the this. So maybe Kant should have told the murderer the truth, because then his mother would have known that he would, and then crept outside the window.

Kant's view sides with deontic moral philosophy, rather than Consequentialist. Consequentialist theories dictate that we should act in ways that will produce the best consequences. So, a Consequentialist would not lead the murderer to his or her mother, because this would probably lead to an undesired result.

However, Consequentialist theories have problems of their own. Suppose that there is a small community of foreigners living within a certain society, and the general population strongly desires for this small community to withdraw itself. The foreigners do not really mind leaving (but they don't really want to) and so their leaving will produce more happiness in the vast majority than unhappiness in the minority. Is it therefore moral to have them removed? This is counter-intuitive, and perhaps for deontic reasons.

It seems that our idea of morality lies somewhere between the extremes of deontic logic and consequentialist theory.

Further Reading:

Kant, Immanuel, 1994, "The Categorical Imperative" and "On a Supposed Right to Lie from Altruistic Motives", reprinted in P. Singer (ed.)Ethics, pp. 274 - 281

Consequentialism

2006-01-25T21:23:00.000+11:00

Consequentialism is one of the more favoured theories of morality. It says that in any situation, the right action is the one that will produce the best consequences. What is the best consequence, you might ask. Well, we also need a theory of value. Namely, we choose something that we value, such as happiness, and then we go on to act in a way which will produce the most happiness. This, the Consequentialist says, is what morality is all about.

But consider the following situation:

"Jim finds himself in the central square of a small South American town. Tied up against the wall are a row of twenty Indians, most terrified, a few defiant, in front of them several armed men in uniform. A heavy man in a sweat-stained khaki shirt turns out to be the captain in charge and, after a good deal of questioning of Jim which establishes that he got there by accident while on a botanical expedition, explains that the Indians are a random group of inhabitants who, after recents acts of protest against the government, are just about to be killed to remind other possible protestors of the advantages of not protesting. However, since Jim is an honoured visitor from another land, the captain is happy to offer him a guest's privilege of killing one the Indians himself. If Jim accepts, then as a special mark of the occassion, the other Indians will be let off. Of course, if Jim refuses, then there is no special occassion, and Pedro here will do what he was about to do when Jim arrived, and kill them all. Jim, with some desperate recollection of schoolboy fiction, wonders whether if he got holg of a gun, he could hold the captain, Pedro and the rest of the soldiers to threat, but it is quite clear from the set-up that nothing of that kind is going to work: any attempt at that sort of thing will mean that all the Indians will be killed, and himself. The men against the wall, and the other villagers, understand the situation, and are obviously begging him to accept. What should he do?”[1]

What would you do? If Jim was a Consequentialist, he would kill. But imagine if, after murdering the Indian, Pedro turned around and said: "Ahaha! Jokes on you! I was only kidding about the special occassion; we'll proceed to execute the rest". Jim could not have anticipated this, and yet he thought that he was acting morally. Another problem for Consequentialist Jim is that he would kill his own mother, if she were that Indian.

[1] Smart, J.J.C., 1973, Utilitarianism: for and against, Cambridge University Press, pp. 98 - 99

The Liar Paradox

2006-01-23T13:29:00.000+11:00

The Liar Paradox was discovered by the ancient Greeks, and concerned them to a great extent. It concerned them because it seemed to be unsolvable. It seemed to offend the very nature of the world and reason itself. It goes like this...

One day, a traveller comes across a man who is sitting by the road. The man by the road cautions the traveller: "Don't believe a word from the first person that talks to you today - they are lying!" The traveller throws his head back in astonishment.
"But you're the first person to talk to me today!"
The traveller continues on his journey and ponders the strange exclamation made by the man. He thinks: "If he is lying, then he is telling the truth. But if he is telling the truth, then he is lying".

Hence, the paradox. So, which is it?!

The Ring of Gyges

2006-01-23T13:26:00.000+11:00

Plato once wrote a short dialogue called "The Ring of Gyges". It featured two characters called Glaucon and Socrates (Socrates was Plato's teacher but Plato often used him as a character in his dialogues) who demonstrate why there is no reason to have such a high respect for what we call justice. Glaucon is the instrument for voicing this opinion, and he does this by first offering a theory on the nature of the origin of justice:

"They say that to do wrong is naturally good, to be wronged is bad, but the suffering of injury so far exceeds in badness the good of inflicting it that when men have done wrong to each other and suffered it, and have had a taste of both, those who are unable to avoid the latter and practise the former decide that it is profitable to come to an agreementwith each other neither to inflict injury nor to suffer it. As a result they begin to make laws and covenants, and the law's command they call lawful and just. This, they say, is the origin and essence of justice; it stands between the best and the worst, the best being able to do wrong without paying the penalty and the worst to be wronged without the power of revenge"

In simple words, he thinks that justice comes from the laws that we create so that we can avoid being harmed. These laws are only created because we would rather give up our ability to wrong others, than be wronged by others.
So, if you possessed a magical ring - the ring of Gyges - that makes you invisible when you put it on, would it be foolish to keep abiding by the law? Glaucon suggests that we shall be able to make a correct judgement about it only if we consider the most just man, and the most unjust man.

For the most just man: we must take away his reputation, for a reputation for justice would bring him honour and rewards, and it would not be clear whether he is being just for the sake of justice, or for sake of the benefits he will recieve from being just. Though he does no wrong, he must have the greatest reputation for wrongdoing so that he may be tested for justice by not weakening under ill repute and its consequences.

For the most unjust man: someone who is caught must be considered a poor performer, for the extreme of injustice is to have a reputation for justice, and our perfectly unjust man must be granted perfection in injustice...

Glaucon concludes: "and let them be judged as to which of the two is happier."

By comparing the most just man and the most unjust man, we can see that there is no reason why the laws should be obeyed for their own sake. However, it makes sense for the owner of the ring to keep obeying the laws if doing wrong would leave them with unwanted feelings such as guilt. Another way that we could argue against Glaucon is to reject the nature of the origin of justice. It suggests that we are selfish beings who are prepared to do wrong to others if it will benefit ourselves. For a further discussion of this, see Are we really that selfish?.

If you are interested in reading Plato's dialogue, see The Myth of Gyges.

Argument against an infinite number of gods

2006-01-15T11:02:00.000+11:00

Suppose there were an infinite number of gods, with a number on their back. There is a God number 1, God number 2, and so on. God number one decides to create the world at 3:00, if no other God has created it by this time. God number two decides to create the world at 1:30, if no other God has created it by this time. God number three decides to create the world at 12:45, if the world has not created by this time. The pattern continues so that the next God will create it at 12:22:30, and the next God will create it at 12:11:15, and so on such that the time intervals are halved and approaching noon.

By 3:00, the world will definitely exist. But which God created it? What is the number on the back of the God who created the world?

The inconsistency here shows that there cannot be an infinite number of Gods who can create the world.

That's not art!

2006-01-14T22:02:00.000+11:00

No-one is immune to the shock of contemporary art. It strays so far from the mainstream that sometimes we can't help thinking that it might not be art at all. It's imposter art. People only think it's art, it's really something else. But if we are to judge what is and isn't art, then shouldn't we be able to come up with a definition of art? Shouldn't there be a defining feature that makes something an artwork? In other words, what makes an artwork, art?

To answer this question, we need to find something that is common to every single work of art: an essence of art. You might think "Well, every artwork is created by an artist, so something is a work of art if it is created by an artist". Unfortunately, this definition is circular:

What is an artwork? Something created by an artist. What is an artist? Someone who creates artworks. What is an artwork....

So this definition gets us nowhere unless we can define what an artist is.

It's pretty hard to find something that is common to every piece of artwork, and yet we always seem to know what is and isn't art. How do we know? How do we know that the Mona Lisa is an artwork? Is it because it is in a gallery? That can't be right - there are some artworks that are never exhibited in a gallery, and yet they still seem to be works of art.

The quest for finding the common feature to every artwork has proven to be so difficult that some philosophers have given up entirely. Instead, they suggest a family-tree explanation of our ability to detect "art"; it's similar to the way we recognise people from families. For example, imagine that the Smith family have particularly large noses and small eyes. These features make them easy to distinguish from others. The aunts, uncles, cousins are not so easy to recognise. Some of them have the same small eyes, some of them have the particularly large nose. But once we can pick them out, we can pick out even more distant relatives, and so on. The story is the same with art. We are all well aware that Renaissance paintings are art. Impressionist paintings, however, are different because the images are blurred. But we can still recognise them because they're still painted with oil on canvas. It has now gotten to the point where we can recognise Andy Warhol's Brillo Boxes as art (although it debatable as to whether it is).

So there is no essence to art after all. It's art if it's only similar to what we traditionally recognise as art. Actually, there is one potential essentialist theory of art, and this is given by Arthur Danto. In his argument, he uses Brillo Boxes (shown above) to illustrate his point.

Brillo Boxes represents the edge of art. If it was on the family tree of art, it would be the most distant relative. It is completely on the border because it is indistinguishable from a stack of Brillo Boxes at a supermarket. The boxes are actually made out of plywood, and were painted by the artist, but this does not concern us because we are interested in finding out how we can distinguish art by just looking. There is one crucial difference between Warhol's boxes and the boxes at the supermarket: behind Warhol's painted boxes is a theory of art. In fact, behind every single work of art is a theory of art. Even behind the cave paintings at Lascaux. And this, Danto argues, is the essential feature of art. When we see the Brillo boxes at the supermarket, we see a stack of Brillo boxes. But when we see Warhol's Brillo boxes, we see something else. There is something which is much more intriguing and exiting about the artwork, and that is it's conceptual component.

It's a neat theory because it suggests that there is such a thing as art, and it gives us the ability to determine what is and isn't art. The only problem with Danto's theory is that it pre-supposes that Brillo Boxes is an artwork. Brillo Boxes is a work that quite a few people would protest as not being art. I'll leave this up to the reader to decide.

It is important to note that just because it is art, it is not necessarily good art.

Further Reading:

Danto, A., 1964, "The Artistic Enfranchisement of Real Objects: The Artworld", Journal of Philosophy 61, no. 19, pp. 571 - 84
Kennick,W, 1958, "Does Traditional Aesthetics Rest on a Mistake?", Mind 67, pp. 317 - 334

True and False

2006-01-12T21:14:00.000+11:00

What is truth? How can we describe it? Does it even exist? Some might laugh at this last question: "Does truth exist? Of course it exists! What kind of question is that?" Well, it's a philosophical question, and there's no such thing as a silly question in philosophy.

I find those areas of philosophy which question our most deep-rooted assumptions the most fascinating. Our belief in truth is an interesting one indeed. In Primary School, we are asked to sort out the true questions from the false ones, with that familiar "T" and "F". From there on, we associate true with right and good, false with wrong and bad. But is the world really divided into two halves? Heroes and villains, heaven and hell?

In philosophy, we call sentences which can be true or false, "propositions". So, "I am eating an apple" is a proposition but "eat an apple" is not a proposition because it is neither true nor false. Now, all we have to do to find the essence of truth is gather all the true propositions that we know, and see what they all have in common.

Let's see. We know that the two following propositions are true (if you don't agree, just pretend they're true anyway): "1 + 1 = 2" and "apples grow on trees". What do these two have in common, apart from the fact that they are both true? What makes them both true? Nobody knows. Nobody has yet found a commonality between all the true propositions in our knowledge. And this has lead many to the conclusion that there is no such thing as truth.

But let's not be so hasty. Maybe there is no essence of truth. Maybe "truth" is a word that simply describes all those propositions which accurately describe the state of things in the world. And, as the two propositions above show, there are different ways of ascertaining the truthfulness of propositions (the first proposition uses deductive logic and the second proposition uses sensory experience and inductive logic).

Philosophers who do not believe in truth are called "anti-realists". Among the anti-realists are people who believe in relative truth. These are the "relativists", and they believe that if something is true for you, then it is true. So if you think the world if flat, then the world is flat. The problem with this view is that it can't claim to be true, because it can only be true if you think it is true. As such, it is not taken very seriously.

The Experience Machine

2006-01-11T16:58:00.000+11:00

When you go into the experience machine, you can experience anything you like: eating the finest Swiss chocolate, climbing Mt. Everest, bringing about world peace. You can even experience the bad things, if you want, to make the good things seem better. The machine is designed to stimulate your brain so that you would think and feel whatever you liked. You're not really eating Swiss chocolate, you never really climbed Mt. Everest and countries all over the world are still fighting with each other. But the feelings that come with the fake experiences are very real indeed.

If someone gave you the opportunity to live in the machine for the rest of your life, would you? You can't go in for just 5 minutes - you can either go in for the rest of your life, or never.

Most people hesitate because there's a catch: we're never really going to see our loved ones again; we're never really going to make a difference. We are no longer of any use in the real world. In the words of Robert Nozick, going into the machine makes us an "indeterminate blob".

So what does this say about us humans? It says that we value things beyond pleasure and happiness. We value reality. One might see this as having implications for the theory of Psychological Egoism, which suggests that we do things only to make ourselves happy.

Further Reading:

Nozick, R., 1974, "The Experience Machine", Anarchy, State and Utopia, pp. 42 - 45

Two Arguments for God

2006-01-08T20:45:00.000+11:00

How can we be sure that God isn't a figment of our imagination? God has never shown himself to us. We have no proof of his existence. Many of us are content to listen to the authorities: the bible, the church, our parents. But even very devout Christians have been known to question their beliefs.

Questioning is a good thing, because it gets you somewhere. You don't necessarily have to take the other side. But you should be able to come up with a reasonable argument for your beliefs. This is what St. Thomas Aquinas did. Aquinas was a devout monk who lived in the thirteenth century, and tried many times to prove the existence of God with logic. Here is one of his more famous arguments:

First, he points out that every event has a cause. A glass will smash only if you push it off the table; it's not going to jump off the table by itself. Secondly, he points out that causes can be events. Pushing the glass off the table is an event which also had a cause (a tantrum, I suppose). In this way, we get chains of events, where each event on the chain is caused by a previous event: A called B fat, which caused B to get angry, which caused B to push the glass, which then caused the glass to smash into a thousand pieces. Aquinas strokes his chin and realises that these events must have had an initial cause. Because if A didn't call B fat, the glass wouldn't have smashed into a thousand pieces.

But how can you have an initial cause? What caused the initial cause? Aquinas strokes his chin again and realises that there can be only one thing in this entire universe which can give brith to an initial cause: God himself. Therefore, God exists.

This is a pretty sophisticated argument. It logically makes perfect sense (leaving besides what caused the existence of God). God pushed the first domino.

So why isn't everyone today convinced that God exists? Well, first I'd like to point out a small logical problem. It's called the Birthday Fallacy. The Birthday Fallacy is shown in the following argument:
1. Everyone has a birthday
2. Therefore, there must be one day which is everyone's birthday
It's a mistake to assume that just because everyone has a birthday, that everyone has the same birthday. Aquinas made this mistake when he assumed that every cause could be lead back to one common cause (God's initial cause). There could have been separated chains of events.

But this wouldn't have really hurt his argument because then he could have just said that God made more that one initial cause. The real problem with Aquinas's argument is the assumption that only God could create an initial cause. Quantum physics tells us that the rules of causation do not apply to the tiniest of particles. Scientists nowadays have also replaced God's initial cause with the big bang. Science has replaced God.

But we can't criticise Aquinas for this: the study of quantum physics developed six centuries after his death. It would be unfair to judge him on these grounds.

Now we shall have a quick look at what is probably one of the best arguments we have on the existence of God. It's called the clock analogy. The story basically goes like this:

You are walking along a deserted beach and you stumble across a watch. Curiously, you pick it up and open it. Inside, you see all the carefully crafted mechanical workings of a clock, and you wonder how this could have come about. You have two options: it was made by a craftsmen, or the watch came into existence accidentally.

Obviously, it was crafted by a person of the trade. The clockwork could not have been made by the subtle movements of the sand, or the risings of the tide. It was made by an intelligent being. Now we can make the analogy. The clock is a human being. The craftsman is God. The silly option of the clock coming about accidentally is evolution.

The argument has a point. Humans and other living creatures are immensely complex in structure, so much so that you would think that we were made by someone really smart. But what about Darwin's theory? Apparently we are the product of 3.7 billion years of evolution. That's a very long time. Darwin's theory also gives sound explanations as to how we came to be this way, without the helping hand of God (Darwin had trouble accepting this himself). Another problem with the analogy is that it is not analogous. Clocks don't reproduce. So the evolutionary changes that take place over thousands of generations of living organisms could not have taken place in the development of a single clock.

Further Reading:

Sober, E., 1995, Core Questions in Philosophy, Simon and Shuster, pp. 39 -60

The definition of God

2006-01-08T19:55:00.000+11:00

It often happens that when someone mentions the word "philosophy", another person will mention the tree that fell down in the forest. They're referring to the question: if a tree fell down in a forest, and no-one heard it fall, did it really fall? At first, it appears as a silly question. Of course it fell! But it's actually quite a serious problem that was pointed out in Bishop Berkeley's argument. Another common misconception that people have on philosophy is that is heavily concerned with spiritual matters, vague and meaningful. This is heavily misguided; philosophy is the rigorous pursuit of truth. It is not vague, and mysterious; it is clear, and logical. However, the arguments concerning God do form a branch on the tree of philosophy.

Why do we need to question the existence of God? Because we're rational, and we really want to make sure he's there. So we use the best methods we have of testing truth. In science, it's using the senses. In philosophy, it's logic. If God existed, we should either be able to see him, or come up with a good philosophical argument.

Definitions are important in philosophy. To understand what something is, we need to know some things about it. Here is the standard definition of the Christian God: he is omnipotent (absolutely powerful), omni-benevolent (absolutely good), and imniscient (knows everything).

A problem with this definition was found by medieval scholars, who grew very concerned over its conclusion. The problem came from the question: could God cease his own existence? Note that the question is not concerned with whether he would, but whether he could. According the definition, God is omnipotent. He can do anything he wants. Ruling out the ability to kill himself would infringe on his almighty power. So God must be able to commit suicide.

What worried the medieval scholars was that if God were to kill himself, we wouldn't even know.

Can't square a circle

2006-01-06T19:49:00.000+11:00

Before reading this post, it might help going throught the article on irrational numbers, if the reader is not familiar with them already. Irrational numbers are important to understand when talking about circles. This is because of the irrational number pi (3.1605....). Pi defines the relationship between a circle's radius and it's circumference and area. A circle has a circumference of length pi x diameter, and an area of pi x (radius squared), so all circles have a circumference and an area which is irrational.
Mathematicians and philosophers since ancient Greek times have tried to square a circle. Squaring a circle simply means constructing a square with the same area of any circle. Now here's the wierd part. Because the circle has these irrational properties, you can't construct a square out of any circle.

Consider the circle with radius of length 1 unit. The circle has an area of pi (pi x radius squared) and so the square that you would construct out of this circle would have a side length of the square root of pi. Now, since pi is irrational, the square root of pi is irrational. But the length of a square is measurable - rational. Lindemann proved the impossibility of squaring a circle in 1882, putting to rest the famous classical problem.

Food for thought:

A right-angled triange with two side lengths of 1 unit has a hypotenuse of length square root 2. This is an irrational, straight length.

Transcendental Numbers

2006-01-05T20:24:00.000+11:00

Maths is a philosophical concern for us, because it tells us of the many mysteries in the universe. One of these mysteries is transcendental numbers. They're the ones that come up on the calculator and you can't write down because they go on forever. They're also known as irrational numbers, so called because they seem to defy reason.

The discovery of irrational numbers has a curious story about to it. Apparently, it was discovered by someone who belonged to the school of Pythagoras (the well known ancient Greek mathematician). When the person who discovered it told the other Pythagoreans, they did not want anyone else to know about it, so they drowned him out at sea. I have heard many different reasons as to why they might have done this, but I think that it might have been because it went against everything they believed in. The Pythagoreans studied and worshipped Mathematics like a religion. To them, (and to the few who appreciate it nowadays), it was perfect and beautiful and complete. The idea that there were numbers that you couldn't express as fractions would have horrified them.

Here is the proof of the irrationality of the sqrt(square root) of 2. It is a reductio ad absurdum (latin for "reduction to absurdity") , which is an argument that shows that something cannot be true because it leads to a contradiction. In this case, we show that the root of 2 cannot be expressed as a fraction, by first assuming that it can:

Assume that the sqrt2 can be expressed as a fraction, say a/b (where a, b are whole numbers)
Let a/b be irreducible so that a and be have no common divisors (like 1/3 but not 2/6)

Now, we calculate:

sqrt2 = a/b

2 = (a squared) / (b squared) ________ (squaring both sides)

2 x (b squared) = (a squared) _________ (multiplying both sides by "b squared")

Since the left side is divisible by 2, the right side must be divisible by 2. The square root of a positive number is also a positive number, so we can now express "a" as "2c" for some integer c:

2 x (b squared) = (2c) squared ________ (by substitution)

2 x (b squared) = 4 x (c squared) __________ (expanding RHS)

(b squared) = 2 x (c squared) ___________ (dividing throughout by 2)

Since the right side is divisible by 2, the left side must be divisible by 2. The square root of a positive number is also a positive number, so b is divisible by 2.

But this contradicts the fact that a and b have no common divisors! It means that sqrt2 cannot be expressed as a fraction, which in turn means that it has an infinite number of decimal places.
The beauty of the classical proof is that we can know that such numbers go on forever, without actually checking that they do (which is impossible anyway).

For your interest - sqrt2 looks like this:

sqrt2 = 1.4142135623730950488......

On a line that is two units long, sqrt 2 is impossible to find. You can find an estimate, but you can't pin-point it because it exists way too deeply within the line. Now you can see why they're called transcendental numbers: they seem to transcend the number line. These sorts of numbers exist between every mentionable number. Other well known irrationals include pi, the exponential e, and other square roots like sqrt 3.

Questions to ponder

2006-01-04T22:20:00.000+11:00

1. Why am I me, rather than someone else? (this question does not stop at the writer- it is for everyone to ponder)

This question has been bugging me lately and I find it very intriguing. What is consciousness? The more you think about it, the more you realise that this is not a question of science, but a question of philosophy. Anyone like to have a go?

2. Is the glass half full or half empty? Or are these descriptions an example of the way language cannot capture truth in its objective form?

3. Is there really such a thing as good and bad or are these just meanings that we assign to things in order to understand them better?

Gettier clocks

2006-01-04T18:12:00.000+11:00

The part of philosophy called Epistemology is concerned with knowledge. What is knowledge? When can we say that we know something? Philosophers since ancient times have been pondering these sorts of questions.

In the post on Descartes, we saw that the only thing that we could be sure of knowing was that we had a mind. Descartes discovered this by deductive reasoning. Deducting reasoning, when correct, is absolute. The following argument is an example of deductive reasoning:
(1) Bachellors are single, middle-aged men.
(2) Bob is a single, middle-aged man.
(3) Therefore, Bob is a bachellor.
We deduced from the fact that Bob was a single, middle-aged man, that he must be a bachellor. Bishop George Berkely(1685 - 1753) used similar reasoning to show that the world didn't exist:
(1) We percieve ordinary objects (mountains, houses, etc.)
(2) We percieve only ideas
(3) Therefore, ordinary objects are ideas
That is, what we see of this world is only in our minds - it isn't really there. Descartes also showed that we couldn't be positive about physical reality.

The problem is, when we want to show that what we see is real, we have to use abductive arguments. Abductive arguments are arguments to the best explanation:
(1) Things fall downwards
(2) The world looks flat
(3) Therefore, the world is flat
As you can see, abductive arguments can sometimes be wrong. We don't have the certainty that comes with deductive reasoning. But, nevertheless, there are good abductive arguments:
(1) Both you and I percieve a red chair
(2) Therefore, there is a red chair before us, causing us to perceive it (rather than it existing only in our minds)

So now the challenge is to come up with a theory which accurately describes how we can know that there is a red chair before us. We come up with conditions that we need to satisfy. These were the conditions that were stated by the ancients:
If p is any statement (eg. there is a red chair before us), then we know that p only when:
1. p is true
2. p is justified
3. we believe that p

These three conditions were widely accepted to be sufficient for having knowledge. However, it was only forty years ago that Edmund Gettier found a serious problem with it. He asks us to imagine that a person, let's call him Bob, who wants to know the time. It is 10:00. Bob looks at the clock and it says that it is 10:00. Naturally, he believes that it is 10:00. So Bob has a true, justified belief; according to the above theory, he has knowledge.

But let us also imagine that the clock had stopped, and it was only by sheer chance that it had shown the right time. Does Bob know that it is 10:00? Intuitively, it would seem that he did not: if the clock had shown that it was 10:30, then he would have thought that it was 10:30. So the classical theory is not an accurate theory of knowledge. For decades now, epistemologists have been trying to successfully overcome the problem of Gettier clocks.

Further Reading:

Edmund, L. G., 1963, "Is Justified True Belief Knowledge?", Analysis Vol. 23, pp. 121 - 23

Are we really that selfish?

2006-01-03T16:38:00.000+11:00

There is a well known theory called Psychological Egoism. Most people don't know that it by this name, but it has been discussed many times before, even in the TV show, 'Friends'. It's the episode where Joey challenges Phoebe by saying that there is no such thing as a selfless deed. In other words, every deed is selfish. Phoebe tries to prove him wrong by getting stung by a bee and saying that she did it so that the bee's friends would be impressed. Joey points out that the bee would have died and that would have done him little good. But he also fails to point out that even this deed is selfish: the only reason Phoebe let herself get stung was to prove Joey wrong. So ta daa! Not a self-less deed at all.

You can think of any charitable action as a selfish deed. Look at Mother Teresa. According to the psychological egoist, the only reason that she helped all those people was to make herself feel better. But is this an accurate picture? Many people have sacrificed their lives for their country, or to save a loved one. But does that mean that they did it for self-glory?

As of yet, there hasn't been one counter-example found to this theory. But that doesn't necessarily make it correct. In this case, it makes it suspicious. It seems like every situation has some selfshiness in it, and the Psychological Egoist says 'aha!' - this must have been the prime motive of the action. Not only is this pessimistic, it's unjustified. If we only cared about our self-gratification, then the following situation would be true: Bob is only interested in feeling happy. He doesn't care about art, music, other people, and anything that you can imagine being worthy of value. He only cares about his own happiness. So selfish Bob does whatever he can to make himself happy. But he doesn't care about anything else, so making someone laugh wouldn't make him happy. Saving the lives of a hundred people wouldn't make him feel happy. In short, caring only about happiness is the fastest way of losing it.

So the idea that Mother Teresa cared only about herself when she helped others makes no sense. She must have cared about the people in order to have felt any sense of satisfaction.

Feeling good about helping others makes it clear that we can't be that selfish.

Further Reading:

Feinberg, J., 1995, "Psychological Egoism", Ethical Theory, Belmont, Wadsworth, pp. 62 - 72

Socrates's question

2005-12-30T17:58:00.000+11:00

Do morals have anything to do with religion? Supernaturalists say they do. Their theory is, an action is good if God commands that it is good. Alternatively, an action is bad if God says that it is bad. So murdering is bad because one of the ten commandments says "thou shalt not kill". This kind of theory of morality is nice because it makes morals objective (have an truth value that is independent of what we think). We can resolve the differences between cultures by saying that there is only one right way of doing things, and that is what God commands. So cultures which practice polygamy (custom of having more than one wife) are wrong.

Generally, arguments which rely on the existence of God are considered bad arguments. This is because the existence of God is controversial in itself. Nevertheless, a stronger way to attack such an argument is to assume that there is a God, and show that the argument doesn't work anyway. Socrates, an ancient Greek philosopher, thus managed to show how Supernalism fails as a theory.

He asked: are actions good because God commands them, or does God command them because they are good? This question is very significant for Supernaturalism because it creates a dilemma. If it's the latter, then Supernaturalists must find another theory for what is good; if it's the former, then we can generate some pretty counter-intuitive examples as to why this cannot be. If murdering is wrong because God says it is, then God could say that torturing babies is good and then it would be! But this is absurd: we would never believe that torturing babies is good, no matter how much God said that it was. Some argue that God would not command such a thing. But what if he did?

So you don't have to be religious to be moral.

Further Reading:

Gensler, H. J., 1998, Chapter 2, Ethics: A Contemporary Introduction, Routledge
"Euthyphro" by Plato from The Collected Dialogues of Plato Including the Letters, Ed. Edith Hamilton & Huntington Cairns, Princeton University Press

Do numbers exist?

2005-12-30T17:01:00.000+11:00

What would you say if I were to ask you, "do numbers exist"? You might say yes: we can count things so there is such a thing as number. On the other hand, you might say no. There are objects but there are no numbers; we make up numbers to make life easier.

This is a big ongoing debate in the philosophy of mathematics. What is maths? Nominalists say that its like a game of checkers. There are pieces (numbers) and there are rules (methods of calculation) but there is no meaning. This view is not widely accepted. If maths was just a made up game, then why does it have such useful applications in the real world? And why does each culture end up following the same rules?

A more plausible position is Aristotelianism. This view says that numbers exist as concepts. So we can't see them in the real world but they still exist because they exist in our minds. But what would happen if there were no people in the world, and no other intelligent life which could count? Would numbers still exist?

Aristotelianism is actually part of a bigger debate over the Universals. It tries to answer the following question: if all red things in the world were destroyed, would the colour red still exist? Aristotelianism says yes! The colour exists in our minds as a concept. But this faces the same problem as before. What happens if there are no minds to hold the concept? Does the concept die?

A popular position in the debate over the existence of numbers is platonism. This view holds that numbers and colours and all other properties (any adjectives you can think of) exist in a separate world - plato's heaven. So mathematics has an abstract existence. Unfortunately, this view is also problematic. If numbers do exist in this separate realm, then how do we know about it? Usually, if we know something, we had some sort of causal connection with it. For example, if I said that I knew there was a chair in the room, I would know because I saw it with my own eyes (or someone else who saw it told me about it). But in the case of abstract objects, we have no causal connection. Therefore, if numbers are abstract objects, we cannot know about them.

But we do know about them. We have an established discipline called mathematics. There is one more thing that is worth mentioning about platonism. It is called the Indispensibility Argument. It was formulated by Quine-Putnam and basically says that mathematics must exist because it is indispensible (it cannot be eliminated from) science. Field tried to show that Newton's gravitational theory could be proven without mathematics but it is doubtful whether he has succeeded in his endeavour. Even if he has, it is even more doubtful that he could achieve the same for quantum theory (our best theory of very small things). So it seems that mathematics must exist. But where?

Maddy has recently attempted to solve the problem. She suggests that mathematical entities have an abstract existence, but they do not reside in a separate realm. Rather, they are down here, with us. This solves the problem of our knowledge of mathematics. Maddy says that we know about mathematics because we have causal connections with the abstract objects. When we see three eggs for example, we can see the "threeness" as a set (group of objects). She attempted to prove this by showing that we have set-perceptive mechanisms. Also, once we understand the concept of number, we are able to deduce the rest through our use of logic.

So we have finally arrived at a view which allows for the existence of numbers as abstract objects and explains our knowledge of them. Please feel free to challenge this view...

2005-12-30T13:11:00.000+11:00

Introduction to Plato's Heaven

Art and Aesthetics
That's not art!

Epistemology
I think, therefore I am
Gettier clocks
True and False

Metaphysics
The definition of God
Two Arguments for God
Argument against an infinite number of gods

Miscellaneous
Questions to ponder
The Liar Paradox
Einstein's riddle
The game show

Morality
Are we really that selfish?
The Experience Machine
Socrates's question
The Ring of Gyges
Consequentialism
Kant's ethics of duty

Philosophy of Mathematics
Do numbers exist?
Transcendental Numbers
Can't square a circle

I think, therefore I am

2005-12-30T00:35:00.000+11:00

"I think, therefore I am." Almost everyone has heard of this famous saying before, but what does it mean?

It comes from René Descartes, a great philosopher who lived in the 17th century. The phrase sums up one of the arguments he gave in his Meditations. Of all the philosophical reading that I have ever done (and I've done quite a few), none have been quite so shocking to me as this one. It's similar to the shock that you get when you realise that Bruce Willis was dead the whole time in the Sixth Sense. You have to reasses everything and suddenly everything that you had previously believed seems like a false illusion...

Descartes is sitting comfortably by the fire. He decides to take on the challenge of discovering if there is anything that we humans can be certain of knowing. Can we be sure, for instance, that he is in fact sitting comfortable by the fire? He thinks that he could be having a dream. We think that we might be in a matrix. If we can't be sure that our reality is real, what can we be sure of?

Descartes begins his search by pretending that there is a demon who is continually inserting false beliefs into his head. So now, when he sees and feels the warmth of the fire, he can't be sure that the fire is there; the beliefs that he is having these sensations could have easily been made by the demon. Descartes leaves his writing for a little in this skeptical frame of mind, being cautious not to be deceived by the demon. Everything that he sees, hears, touches, smells and tastes is no longer an indication of what is.

So when he returns to his writings, what does he find? He has realised that the whole world might be an illusion created by the demon. Nothing around him, not even his own body, necessarily exists. But there is one thing that he can be sure of: that he has thoughts. His mind must exist. Otherwise, if the demon wanted to make him believe that he had no mind, he would have to insert that belief into his head, and he couldn't do this unless Descartes had a mind. Therefore, logical necessity suggests that if there is anything that we can be sure of, it is of the existence of our minds. Hence, "I think, therefore I am."

This doesn't mean that everyone must have a mind - it means that you can only be sure that YOU have a mind. You might like to try mistrusting everything you see for the next few days, it really is bizzarre. Of course, you don't have to believe in the demon, only the possibility that what you believe about this world may be entirely false.

Further Reading:

Descartes, R., Meditations on First Philosophy
Bouwsma, O. K., 1949, "Descartes' Evil Genius", Philosophical Review 58, pp. 141 - 151

Welcome to Plato's Heaven!

2005-12-29T22:44:00.000+11:00

Have you ever wondered whether morals really exist? Have you ever wondered whether you were the only person with a mind, and that everyone else only seemed to think? Have you ever wondered whether there was a God? If you have, you have been thinking philosophically, and have come to the right place to find out more.

Many people only have a vague idea about what philosophy is about. To put it short, it's a pursuit of truth. One lecturer that I had once said that philosophers are scientists without coat labs. We use reason to discover the possibilities and nature of the world we live in.

In philosophy, plato's heaven is a world of abstract objects. Every property is said to exist in this place. The colour "red", for example, is a property of apples, so it exists up there. This site was named after plato's heaven because it is concerned with beautiful and abstract ideas.

More specifically, Plato's Heaven is a battlefield for philosophical discussion and debate. In each post a philosophical issue or argument is raised, and at the end the reader is invited to leave his or her opinion on the matter. The posts have been written in a way that is comprehensible to those new to the field. Nevertheless, if you do find something that is difficult to understand, I'd be happy to answer any questions.