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evaristegalois » February 13th, 2015, 2:03 pm wrote:Not quite. I think the case for "It is rational to believe that ticket #1 won't win" is much harder to make than what I am looking for. You may have partial beliefs about lottery tickets.
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evaristegalois wrote:(3p) It is not rational for me to believe that pi is 3.14 and that pi is 3.142.
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Dave_Oblad » February 13th, 2015, 3:03 pm wrote:Ok,
R(X): All Humans are Animals.
And
R(Y): All Dolphins are Animals.
Thus
R(Z): All Humans are Dolphins.
That help?
Regards,
Dave :^)
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evaristegalois » Fri Feb 13, 2015 2:24 pm wrote:I think a conjunction of the following is sometimes true:
(1) It is rational for S to believe X.
(2) It is rational for S to believe Y.
(3) It is not rational for S to believe X and Y.
Here is an example:
(1e) It is rational for me to believe that the tomato in front of me is red.
(2e) It is rational for me to believe that the tomato in front of me is orange.
(3e) It is not rational for me to believe that the tomato in front of me is red and that the tomato in front of me is orange.
Is my reasoning sound? Are there other examples?
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evaristegalois » Fri Feb 13, 2015 4:34 pm wrote:Dave,
X and Y stand in for any propositions, which may or may not be related. Naively, one may think that R(X) and R(Y) imply R(X and Y), where R(Z) means "it is rational for S to believe Z." I want to find counterexamples.
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Dave_Oblad wrote:...
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Dave_Oblad » February 13th, 2015, 8:44 pm wrote:Ok,
R(X): I am looking at the Moon. (True if I believe I am looking at the Moon)
R(Y): I am NOT looking at the Moon. (True if I believe I am NOT looking at the Moon)
R(Z): I am both looking at the Moon and Not looking at the Moon.
I think I am having trouble with the word Believe. Is it the case that Proposition (X or Y) must be true at all times? Or do I merely need to believe them to be true?
Regards,
Dave :^)
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