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The set of all sets that do not contain themselves as members cannot contain itself, therefore it both does and doesn't contain itself.
Or to put it more simply:
A popularised version of Bertrand Russell's paradox is to imagine a place where there is a male Barber. He shaves all the men who do not shave themselves.
Does he shave himself?
He cannot, because he can only shave those who do not shave themselves. If he does not, then he does not shave himself and therefore is part of the set of those who do not shave themselves, and he must shave himself...
Wittgenstein claimed to have solved this paradox (Russell's theory of types) in his 'Tractatus'. Essentially he claimed it showed a problem with using language to describe the world and used logical symbols to refute it. You can read more on this here, at project Euclid
Siddharta Gautama, the Buddha, taught that all existence is suffering, and that all suffering is predominantly caused by want - or desire. In order to be free of suffering, we must rid ourselves of wanting.
The precepts seem quite sensible, but there is a paradox here.
We are told that we must end suffering by ending wanting.
But wanting to end suffering is in itself a further want.
So, by wanting to decrease our suffering we are actually increasing it.
John Visvader refers to this as an uroboric (like a snake swallowing its own tail) philosophy.
Today a though struck me, which I suppose could be posited as a moral dilemma.
It came to me, ironically perhaps, as I was meditating:
Would a true Buddhist save an animal species from extinction, if they were the only one who could, given the Buddhist belief in Nirvana (the end of the cycle of birth, death and rebirth) as the ultimate attainment and goal of being?
A Buddhist should also believe in the application of right thought and of right action. Is it right to let an animal species die out when it could be prevented?
Epicurus was an interesting ancient Greek philosopher, I find a lot of his conclusions quite sensible and moderate - that death is the end and not to be feared, that a life of moderate pleasure and doing no harm should be one's goal.
But, aside from his sensible and quite scientific ideas, he is well known for stating the following challenge to theistic arguments:
The Problem of Evil
"Is God willing to prevent evil, but not able? Then he is impotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Whence then is evil?"
Now, some philosophers state that what we consider to be evil is the product of free will. God created the universe and man to have the greatest good, and part of that good was the ability to choose to be good or to be evil, free will.
However, while this might explain moral evils, such as genocide or murder, where human beings choose to do evil, it does not explain natural evil. Say a baby born to die of leukaemia, or a faun caught in a forest fire, caused to die in prolonged agony by its injuries. (see this PDF of 'The problem of evil and some varieties of atheism, by William L Rowe')
Imagine that you are a Doctor.
You have five patients, each of whom has a terminal illness, each in a different major organ of the body. Without transplants from suitable donors they will certainly die.
Now, another patient comes in for a routine check up and in the course of this you discover that they are a perfect match for each of the five other patients respectively, and that by taking their organs and transplanting them, you will have a 100 per cent certainty of saving those five people. The one donor patient will die.
What should you do?
On September 10 2008, the large hadron collider was finally switched on. It is a machine that is at the cusp of human knowledge and endeavour, it will enable humanity to understand the universe and provide knowledge of benefit to all people, living and of the future.
However, tragically, a person was killed in the construction of the machine.
The dilemma is this. If you were the chief engineer of the project, and you were told in advance of starting construction that it was a certainty that one person would be killed, would you still continue with the project?
How about if the chance of one person dying was 75%?
A trolley (tram) is running out of control down a track. In its path are five people who have been tied to the track by a mad philosopher. Fortunately, you can flip a switch which will lead the trolley down a different track. Unfortunately, there is a single person tied to that track.
Should you flip the switch?
As before, a trolley(tram) is hurtling down a track towards five people. You are on a bridge under which it will pass, and you can stop it by dropping a heavy weight in front of it. As it happens, there is a very fat man next to you - your only way to stop the trolley is to push him over the bridge and onto the track, killing him to save five.
Should you push him?
As before, a trolley(tram) is hurtling down a track towards five people. As in the first case, you can divert it onto a separate track. On this track is a single person. However, beyond that person, this track loops back onto the main line towards the five, and if it weren't for the presence of that person, who will stop the trolley, flipping the switch would not save the five.
Should you flip the switch?
2. The Plank of Carneades
There are two shipwrecked sailors, A and B, treading water in the middle
of the ocean. They both see a plank that can only support one of them
and both of them swim towards it. Sailor A gets to the plank first.
Sailor B, who is going to drown, pushes A off and away from the plank
and, thus, ultimately, causes A to drown. Sailor B gets on the plank and
is later saved by a rescue team.
Can Sailor B can be tried for murder?
1. The 'famous violinist' thought experiment:
You wake up in the morning and find yourself back to back in a hospital
bed with an unconscious famous violinist.
He has a fatal kidney ailment, and you alone have the right blood type
to help. You have been kidnapped, and the violinist's circulatory system
has been plugged into yours, so that your kidneys can be used to extract
poisons from his blood as well as your own.
To unplug you would be to kill him. He needs to be attached to you for
only nine months. By then he will have recovered from his ailment, and
can safely be unplugged from you.
What do you do?