Originally posted by Melanerpes http://en.wikipedia.org/wiki/Truth_table
[quote]Logical implication
Logical implication and the material conditional are both associated with an operation on two logical values, typically the values of two propositions, that produces a value of false just in the singular case the first operand is true and the second operand is false.
The truth ta rue and q is false -- the mutant banana-eater exists, and this being never eats red bananas
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.
Originally posted by adam warlock What is it then? True or false and why.
the statement you made is an example of "logical implication" -- that is, a statement that is of the form, if p, then q (p-->q) (such statements can also be worded all members of set p are also members of set q)
when you are dealing with logical implications, the only way in which p-->q can be false is if p is true and q is false (or there exists at least one member of set p that is not also a member of set q). That is -- the mutant that you described exists, AND at least one of those mutants does not eat red bananas.
Originally posted by adam warlock After receiving an unsolicited PM by a member whose identity I won't disclose, let's call him/her Person X, it has transpired that this user has a PhD in a very respected field of knowledge.
From what I could get from his/her interventions in this forum I didn't think that his/her claim was true (in the very unlikely event that it was true it had to told me but do believe that this is a 100% accurate paraphrase of what Person X has said.
Here is my own pathetic answer:
It is true, insofar as it can't be proven false.
edit: Although I did suffer through three semesters of philosophy for my bachelor's degree, it was a while ago and I've forgotten most of it.
In order for your answer to be correct you have to give the correct truth value and a correct explanation.
To spice things up a bit if someone fails to answer correctly just one of the two things that have to be answered I'll just say that the answer is wrong and won't specify what part is wrong.
Thus I have to say that pawnhandler's answer is wrong.
If you're having difficulties answering this just remember that Person X, a PhD in in a highly intellectual field, also got it wrong.
Originally posted by adam warlock Mel my man I got you the first time.
All of this correct, but you're not answering the question.
Just tell me directly if the proposition is true or false and why.
I am assuming that the mutant creature that you described does not exist.
In that case, your proposition is true -- (p false means p-->q is true).
And your proposition would be true no matter what q was -- eats red bananas, regularly beats Fritze, believes that Obama has 32567 social security numbers, or whatever. All of these propositions are true and cannot EVER be false.
Unless the mutant creature that you described DOES exist. In that case, we would have no way of knowing the truth of the proposition until we offered all such creatures a tempting entree of red bananas (perhaps we could arrange for the meal to be personally prepared by Chef Warlock?)
Originally posted by Melanerpes I am assuming that the mutant creature that you described does not exist.
In that case, your proposition is true -- (p false means p-->q is true).
And your proposition would be true no matter what q was -- eats red bananas, regularly beats Fritze, believes that Obama has 32567 social security numbers, or whatever. All of these propositions are true an ...[text shortened]... f red bananas (perhaps we could arrange for the meal to be personally prepared by Chef Warlock?)
It's not a p -> q reasoning because it's predicate logic.
on the other hand -- this whole concept of "existence" is tricky.
If I imagine the creature that you described, then that creature DOES exist within my own mind. It is very easy to imagine such a creature refusing to eat red bananas.
Therefore, if we include any and all imaginary things, your proposition must be false.
Originally posted by Melanerpes on the other hand -- this whole concept of "existence" is tricky.
If I imagine the creature that you described, then that creature DOES exist within my own mind. It is very easy to imagine such a creature refusing to eat red bananas.
Therefore, if we include any and all imaginary things, your proposition must be false.
Tell me if the statement is true or false without metaphysical/ontological worries.
An answer like "The proposition is true because..." or "The proposition is false because...".
Person X
09 Jul '10 19:041 edit
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