Paradoxes to wreck your head.

We had a thread on books and a few philistines (Lex stand up) said they never read em. And snooty Purple said he (sniff) never reads fiction.

Well Here's a few paradoxes from a book I'm reading which provide good actual reasons for never opening a book!

• "This sentence is false". If the sentence is true, it is false, and if it's false then its true...?
• The river we step into today is the same as this water. But tomorrow the river will be the same as a different volume of water, so paradoxically it cannot be the same river,yet it is...
• Are there more even & odd numbers than odd numbers alone? Well no, if you match every odd number with an even and odd number there is exactly the same...an infinite series.
• One grain removed from a grain heap makes no difference to the heap and so on. Yet we end up without a heap even tho we only remove one which should make no difference?
• God,being all-powerful can make anything. Can he make a stone he cannot move? If he can, he cannot be all powerful, if he can't he cannot be all powerful.
• A bandit shoots a sheriff who dies a few days later. Meantime, the bandit is killed by the posse. When the sheriff died, the bandit was already dead so when did he kill him? The sheriff was alive after he shot him and the bandit was dead when the sheriff died?
• Telling TD X you intend exposing his philandering is not immoral. Asking TD X for money to go on a cruise is not immoral. Yet, combining the two amounts to blackmail, considered highly immoral-why?

Enjoy boys and girls. The book is "This Sentence is False: An introduction to philosophical paradoxes by Peter Cave"

Your work is done - my head is wrecked !

Totally

"This sentence is false". If the sentence is true, it is false, and if it's false then its true...?
This is logically the same as saying "1+1=5". It is flawed to begin with.

The river we step into today is the same as this water. But tomorrow the river will be the same as a different volume of water, so paradoxically it cannot be the same river,yet it is...
The river isn't defined only by the water it contains. A 'river' is a lot of things, it has a source and mouth, banks. These do not 'disappear' from day to day.

Are there more even & odd numbers than odd numbers alone? Well no, if you match every odd number with an even and odd number there is exactly the same...an infinite series.
I believe there are different 'infinities' in mathematics. A strange paradox though.

One grain removed from a grain heap makes no difference to the heap and so on. Yet we end up without a heap even tho we only remove one which should make no difference?
Removing one grain does make a difference. A tax inspector would probably notice it.

God,being all-powerful can make anything. Can he make a stone he cannot move? If he can, he cannot be all powerful, if he can't he cannot be all powerful.
Maybe he doesn't want to move the stone.

A bandit shoots a sheriff who dies a few days later. Meantime, the bandit is killed by the posse. When the sheriff died, the bandit was already dead so when did he kill him? The sheriff was alive after he shot him and the bandit was dead when the sheriff died?
He killed the sheriff at the moment the sheriff died. It does not matter the if the bandit was alive or dead at this point.

Telling TD X you intend exposing his philandering is not immoral. Asking TD X for money to go on a cruise is not immoral. Yet, combining the two amounts to blackmail, considered highly immoral-why?
Combining the two creates a different situation where choice has been restricted or removed for the TD.

Hope ye had fun replying to those Umo3...

1. A kind of logical fallacy of course, if A then not A... so anything follows. But if you dismiss it as meaningless you must explain why it is. And you are forced to conclude it is because it's a paradox. An interesting discussion on it can be found at http://www.iep.utm.edu/par-liar/

2. Agreed.

3.Agreed.

4.The question is not about what God wants it's about what he can do. Your answer does not solve the paradox.

5.It is impossible for the dead bandit to kill (a causal event) at time y if he already died at time x.

6. Only if both reporting him and asking him for money are in a causal chain. It is of course completely logically possible that they are unrelated events and have no such connection. To claim that they are neccessarily related is itself a logical fallacy, post-hoc ergo propter hoc. X followed y, therefore y caused x. Logical fallacy.The key to the Post Hoc fallacy is not that there is no causal connection between Xand Y. It is that adequate evidence has not been provided for a claim that X causes Y. Thus, Post Hoc resembles a Hasty Generalization in that it involves making a leap to an unwarranted conclusion. In the case of the Post Hoc fallacy, that leap is to a causal claim instead of a general proposition.

Aquinas gave an interesting answer to the God and the rock question. As a Christian he was committed to the idea of the God's omnipotence. He claimed God could do anything that it was logically possible to do. Thus God could not make a rock he couldn't lift not because he lacked power, but only that it was a logical impossibility. This is based on the logical notion that something cannot both be and simulanously not be something.

These aren't head wreckers.... some are barely even a paradox.

The first is interesting and is a re-working of the lying Cretan.

The second is a question of definition. What is a river? What is a river composed of? How do we know a river?

The third I can't comment on as I simply don't know enough about mathematics. I'll propose a laymans paradox on similar lines however. If 'infinity' as a concept is correct then a dart will never hit a dartboard. If you can't count 'up' to an end point then nor can you count 'down' through ever decreasing fractions. OR - Infinity as a concept is not correct and there is an end point when counting.

The grain of corn question is simply one of relative perception and not a paradox at all.

The all powerful paradox is another interesting one along the lines of the unstoppable meeting the immovable. In philosophical terms there is no 'correct' answer to this but in theology horusd has it right with Aquinus' description.

The issue of the bandit and the sheriff is one of action and consequence rather than a paradox.

Finally, the question regarding blackmail is merely proof of the old adage that the whole is more than the sum of the parts. Wheels are not a car, an engine is not a car, an axle is not a car, a chassis, seats and a boot lid are not a car........

As parting paradox consider this..... how can a cat in a box be both alive and dead at the same time?

QUOTE=PetrolHead;1152776]These aren't head wreckers.... some are barely even a paradox.

The first is interesting and is a re-working of the lying Cretan.

Yet still a paradox.

The second is a question of definition. What is a river? What is a river composed of? How do we know a river?

Hmm, a river is defined by water, without water it couldn't be a river. So if the water is not the same water, it cannot be the exact same river. (I actually accept your view Petrolhead but just being argumentative!)

The third I can't comment on as I simply don't know enough about mathematics. I'll propose a laymans paradox on similar lines however. If 'infinity' as a concept is correct then a dart will never hit a dartboard. If you can't count 'up' to an end point then nor can you count 'down' through ever decreasing fractions. OR - Infinity as a concept is not correct and there is an end point when counting.

Again a version of the Achilles and the tortiose how is movement/change possible.Another interesting version asks how to explain God's creation of the world. Creation is an causal act requiring space & time. If God preceded creation ie S&T then such an act would be impossible.

The grain of corn question is simply one of relative perception and not a paradox at all.

The all powerful paradox is another interesting one along the lines of the unstoppable meeting the immovable. In philosophical terms there is no 'correct' answer to this but in theology horusd has it right with Aquinus' description.

The issue of the bandit and the sheriff is one of action and consequence rather than a paradox.

Hmmm. all acts occur in time. The bandit's death ocurred before the sheriff. To assume the sheriff died as a consequence of being shot commits the logical fallacy I already mentioned.

Finally, the question regarding blackmail is merely proof of the old adage that the whole is more than the sum of the parts. Wheels are not a car, an engine is not a car, an axle is not a car, a chassis, seats and a boot lid are not a car........

As parting paradox consider this..... how can a cat in a box be both alive and dead at the same time?

Quantum Mechanics and it's weird observer influences the outcome scenario's!!! I have a cat so I'll not try to prove it!
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horusd said:

Hmmm. all acts occur in time. The bandit's death ocurred before the sheriff. To assume the sheriff died as a consequence of being shot commits the logical fallacy I already mentioned.

Click to expand...

If we accept that the sheriff died as a direct result of being shot (which is sort of suggested by OP's proposed question) and if we remove any assumption or assessment of intent then it is the action which ultimately decided that the sheriff was to die that 'killed' him. If we look at it semantically, 'death' is the point at which you die but 'kill' is the action that results in death (think of a man pushed out of a aeroplane for example).

Of course (with intent removed) the same logic would say that an individual who planted a tree at a roadside 100 years ago 'killed' the driver who ran into it last week. Potentially a difficult concept for hermeneutic acceptance.