so what is everyone being for halloween? i'm gonna be buddy the elf
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Thursday, October 30, 2008
Thursday, October 23, 2008
Monday, October 13, 2008
The Raven Paradox
So, we've been talking about this in Philosophy, and I wanted to know what you all thought.
Basically, it starts with a few basic principles:
G1: Generalizations are confirmed by their instances. That is, if you have a hypothesis, any result that lends support to that thesis will confirm said theory--which does not mean it's irrefutable, just that it has some degree of confirmation.
E1: If two hypotheses are known to be logically equivalent, then any data that supports 1 also supports the other. This one kind of explains itself, and is easily seen.
Now, some generalizations:
R1: All Ravens are black things.
R2: All non-black things are non-Ravens.
L1: R1 and R2 are logically equivalent.
Now, then. That's all we need to lay out the paradox. And here it comes:
A sneaker is a non-black non-raven, therefore it lends support to R1; that all Ravens are black things.
Agree? Disagree?
Some proposed solutions/objections:
Solution 1: The conclusion the paradox comes up with is correct; we only find it so infeasible because we assume the degrees of support lent to be equal; that is, for one non-black thing to lend as much support as a black raven. However, they actually lend support equal to 1/(total number of objects). So one black raven out of, say, 6 million in the world would lend support equal to 1/6,000,000. However, there are trillions upon trillions upon trillions of non-black non-raven things. So the support one would lend to R1 would be small: on the order of 1/googol^(googol^(googol)), which is significantly less. It does lend support, but not nearly as much.
Objection 1: Not all generalizations are confirmed by their instances. For instance, take the theory that "All snakes are non-Irish." You go out, and start finding non-Irish snakes. First in proximity, but then further and further away. The more you find, and in the greater variety of ecosystems you find them (say you found them in, say, Scotland), the more likely you are to believe that they also dwell in Ireland. Therefore, this disproves the idea that all generalizations are confirmed by their instances.
Thoughts?
Basically, it starts with a few basic principles:
G1: Generalizations are confirmed by their instances. That is, if you have a hypothesis, any result that lends support to that thesis will confirm said theory--which does not mean it's irrefutable, just that it has some degree of confirmation.
E1: If two hypotheses are known to be logically equivalent, then any data that supports 1 also supports the other. This one kind of explains itself, and is easily seen.
Now, some generalizations:
R1: All Ravens are black things.
R2: All non-black things are non-Ravens.
L1: R1 and R2 are logically equivalent.
Now, then. That's all we need to lay out the paradox. And here it comes:
A sneaker is a non-black non-raven, therefore it lends support to R1; that all Ravens are black things.
Agree? Disagree?
Some proposed solutions/objections:
Solution 1: The conclusion the paradox comes up with is correct; we only find it so infeasible because we assume the degrees of support lent to be equal; that is, for one non-black thing to lend as much support as a black raven. However, they actually lend support equal to 1/(total number of objects). So one black raven out of, say, 6 million in the world would lend support equal to 1/6,000,000. However, there are trillions upon trillions upon trillions of non-black non-raven things. So the support one would lend to R1 would be small: on the order of 1/googol^(googol^(googol)), which is significantly less. It does lend support, but not nearly as much.
Objection 1: Not all generalizations are confirmed by their instances. For instance, take the theory that "All snakes are non-Irish." You go out, and start finding non-Irish snakes. First in proximity, but then further and further away. The more you find, and in the greater variety of ecosystems you find them (say you found them in, say, Scotland), the more likely you are to believe that they also dwell in Ireland. Therefore, this disproves the idea that all generalizations are confirmed by their instances.
Thoughts?
Wednesday, October 01, 2008
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