Originally posted by KazetNagorraAre you trying to use predicate logic on an empty set?
In this case you have a statement in predicate logic: for all A, x. Its truth value depends on whether or not you consider A to be contradictory (can a Japanese, by defnition, be e.g. three legged?), and whether or not those in the category of A hold the property x. It's not really a logical reasoning as such.
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Originally posted by adam warlockI generally don't care what "qualifications" a person in a debate forum has. Whether the poster has a PhD or is just someone in high school, I'm going to consider the argument and any links they post in the same way. If they're interesting, they're interesting. If they don't make sense, then they don't make sense.
It's on the OP, but I'll repeat it: Person X claimed to have a PhD on field of knowledge that if true would make him answer that question correctly in less than a second.
Edit: Do you think you can give a more complete justification of the truth value of the proposition... I don't want to be unfair with Fabian...
In general, I would expect someone with a PhD to contribute a great deal of interesting information. But if they don't, they don't.
btw - I started a thread earlier today on something I read in Howard Zinn - have you had a chance to look at it?
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Originally posted by MelanerpesExactly, but for some reason Person X felt the need to assert that he/she had a PhD. But enough with Person X. Can you give me a more complete answer, so that I don't end up being unfair to Fabian.
If they're interesting, they're interesting. If they don't make sense, then they don't make sense.
He gave basically the same answer that you gave in a PM, and I said it was wrong. In your case I said it was right because you backed it up with very good analysis.
Edit: yes I have. I'll make a few comments tomorrow.
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Originally posted by adam warlockThere is no three legged, red eyed, two headed Japanese who doesn't eat red bananas. Interestingly there is also no three legged, red eyed, two headed Japanese who eats red bananas.
Justification please.
So it's both true that:
All three legged, red eyed, two headed Japanese eat red bananas.
No three legged, red eyed, two headed Japanese eats red bananas.
Empty sets, huh?
Originally posted by PalynkaYou don't know for sure that those kind of Japanese don't exist. Maybe there was a secret government project...
There is no three legged, red eyed, two headed Japanese who doesn't eat red bananas. Interestingly there is also no three legged, red eyed, two headed Japanese who eats red bananas.
So it's both true that:
All three legged, red eyed, two headed Japanese eat red bananas.
No three legged, red eyed, two headed Japanese eats red bananas.
Empty sets, huh?
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Originally posted by adam warlockI don't think a truth value can be assigned to it.
What is the truth value of the following proposition:
All three legged, red eyed, two headed Japanese eat red bananas
Since three legged, red eyed, two headed Japanese do not exist, we cannot honestly make any statements about their behavior - but I don't think that makes any such statements false - but rather makes them without meaningful content.
If however we are talking about 'within a given mythology' then since the given mythology is not given, we cannot assess its truth value.
We could also create a 'three legged, red eyed, two headed Japanese', but it would not be clear whether our creation truly matched what is being referred to in the statement - again, the truth value cannot be determined.
Note: I don't hold any PhDs
Originally posted by twhiteheadThis is incorrect!
I don't think a truth value can be assigned to it.
Since three legged, red eyed, two headed Japanese do not exist, we cannot honestly make any statements about their behavior - but I don't think that makes any such statements false - but rather makes them without meaningful content
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Originally posted by adam warlockOnly if you add the following logical expression:
Exactamundo!
There exist no three legged, red eyed, two headed Japanese.
If you then paraphrase it using predicate logic, you get:
A = three legged, red eyed, two headed Japanese.
x = eats red bananas.
There exist no A. (1)
For all A, x. (2)
If (1) is true, then (2) is also true.
(2) by itself is not always true because three legged, red eyed, two headed Japanese may exist who don't eat red bananas.
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Originally posted by adam warlockYou have posted a universally quantified statement which could be either true or false if such beings as 3 legged, red eyed, 2 headed Japs existed.
This is incorrect!
It could only be falsified by the production of one such who did not eat red beans. Otherwise it would only be possible to verify particular cases since no matter how long and far one searched there could be at least one excepton hidden somewhere else in the world yet to be searched.
It could never be PROVED true.
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Originally posted by adam warlockyou never asked us to provide the "truth value" for "no red-eyed, three-legged, two-headed japanese people eat red bananas"
Exactamundo!
the original statement was:
p = "red-eyed, three-legged, two-headed japanese people" and q = "those that eat red bananas"
this new statement is:
p = "red-eyed, three-legged, two-headed japanese people" and q = "those that do not eat red bananas"
as I argued before -- if p is something that doesn't exist, then p-->q is true no matter what you specify for q. Since p would always have to be false, there would be no way for "p to be true and q to be false"
so Palynka was correct in saying that both statements were true -- indeed ALL such statements involving "all red-eyed, three-legged, two-headed japanese people" are true -- including a seemingly contradictory statement like:
"all red-eyed, three-legged, two-headed japanese people have only one head"
Originally posted by KazetNagorraDying inside...
Only if you add the following logical expression:
There exist no three legged, red eyed, two headed Japanese.
If you then paraphrase it using predicate logic, you get:
A = three legged, red eyed, two headed Japanese.
x = eats red bananas.
There exist no A. (1)
For all A, x. (2)
If (1) is true, then (2) is also true.
(2) by itself is ...[text shortened]... s true because three legged, red eyed, two headed Japanese may exist who don't eat red bananas.