10 Jul 10
1 edit
Thesis
The proposition: All three legged, red eyed, two headed Japanese eat red bananas. is true.
Proof
Let's assume that the proposition is false. Then there is (ate least) one three legged, red eyed, two headed Japanese that doesn't eat red bananas.
Since this obviously isn't the case (there is no such specimen) we have proved, by reductio ad absurdum, that the proposition indeed is true.
Like Palynka and Melanerpes have already said we can state and prove (with the exact the same reasoning) the veracity of many mutually exclusive properties of three legged, red eyed, two headed Japanese simply because of the fact that they don't exist.
Simple really!
10 Jul 10
Originally posted by adam warlock[b]Thesis
The proposition: All three legged, red eyed, two headed Japanese eat red bananas. is true.
[quote]Proof
Let's assume that the proposition is false. Then there is (ate least) one three legged, red eyed, two headed Japanese that doesn't eat red bananas.
Since this obviously isn't the case (there is no such ...[text shortened]... yed, two headed Japanese simply because of the fact that they don't exist.
Simple really![/b]Why is it "obvious" there is no such specimen? It's simply likely, and most certainly not a logical necessity.
10 Jul 10
Originally posted by PalynkaYou guys are beyond me, here, so I hope you’ll bear with me as I just try to work through it...
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?
The “trick” in the original question seems to be that the logical conditional for the universal quantifier is not expressly stated, but that someone sufficiently familiar with predicate logic would realize that the logical conditional (“If x’s exist, then for all x, P”; or that the domain of discourse is “all x that exist” ) obtains, whether expressly stated or not—and would respond accordingly?
Or might be expected to ask the original questioner, just to make sure (perhaps having no reason to assume that the questioner is sufficiently familiar with predicate logic to know what their proposition entails? By this I mean—well, if I ask you, Pal, a question about microeconomic theory, you might need to ask me for some clarification, knowing that although I did some work there, it was long, long ago and hence that I might not recall all the entailments involved (e.g., you might ask something like: “Do you mean, “given the price elasticity of demand…”, or some such).
11 Jul 10
2 edits
Originally posted by twhiteheadIn that case why start your first intervention in this thread with this: I don't think a truth value can be assigned to it.
I probably have no idea by what you mean by 'truth value'.
It looks like a conceited position to take if you don't know the meaning of truth value.
What I mean with truth value is easily found on the web after a google search.
I think that was what Melanerpes did and he understood wonderfully what this test was about.
11 Jul 10
Originally posted by adam warlockAdam, Adam, Adam - this is the internet. Barely articulated bellowing of assumptions, snap judgements and prejudices is the currency round here. Your fancy-pants facts are the relic of a bygone era, and the ease with which people sitting in front of a computer can discover them irrelevant.
In that case why start your first intervention in this thread with this: I don't think a truth value can be assigned to it.
It looks like a conceited position to take if you don't know the meaning of truth value.
What I mean with truth value is easily found on the web after a google search.
I think that was what Melanerpes did and he understood wonderfully what this test was about.
11 Jul 10
Originally posted by adam warlockThough it turns out that you still fail at your own test.
In that case why start your first intervention in this thread with this: I don't think a truth value can be assigned to it.
It looks like a conceited position to take if you don't know the meaning of truth value.
What I mean with truth value is easily found on the web after a google search.
I think that was what Melanerpes did and he understood wonderfully what this test was about.
11 Jul 10
5 edits
Originally posted by KazetNagorra*sigh*
Though it turns out that you still fail at your own test.
Palynka has made you a very good question a few pages ago and you failed to notice it.
This was a very convenient slip, I must say.
1 - Anyway let me start serious mode. First we have this very odd question:
So if you can describe predicate logic in terms of proposition logic, what is the point of predicate logic?
Let me take this sort of an argument (for the sake of stupidity I'll forget that this question has nothing to do with the obvious fact that "all x are q" is equivalent to "p->q" ) of yours further: if I take this question seriously than I have to conclude that Feynman was a worthless chump. I mean he spent several years completing his own version of QM that he knew that was very perfectly equivalent to the two previous versions that existed.
Not only was Feynman a chump, but Schwinger was also a chump when he pursued his own version of QED.
But on this issue, the biggest chump of all may have been Freeman Dyson. I mean even though every Physicist "knew" that the versions of QED by Feynman, Schwinger and Tomonaga were equivalent he set himself to prove in a rigorous mathematical way that this was so.
And Dirac was just another chump when he went for another relativistic theory of the electron since by his time there were already two such theories available.
Right? I mean these things were all equivalent and still people persisted on investigating them.
The examples of theories that are equivalent in Physics and Math abound, but I guess that by your argument this is all wasting time. There is even a theory that studies these equivalences...
Try to figure out why people do things in Science that are equivalent and maybe you'll stop being a misguided chipmunk and start being a real Physicist with a real understanding of the things you are talking about.
2 - Just tell me if you really think that "All p are q" isn't the same as "p->q"?
This is obvious for anyone that only has a modicum of acquaintance with first year calculus (you being a Physics student have the obligation of having a lot more than a modicum of acquaintance), and for anyone that has an education in any kind of field where logic is relevant.
I'd even go further and say that this should be easy knowledge for anyone that is accustomed to think, but I guess that would be to presume too much of you.
To see the equivalence, one just has to notice that "all p are q" is the same as "if it is p then q" and this is just the verbal statement of the usual logic notation "p->q".
Let's go by an example "All men are blind". Anyone with half a brain would immediately say that the previous utterance can also be stated as "If it is a man then he is blind."
Even a putrefying amoeba is able to assert this.
Being that "if..., then..." is just another way to state an implication, thus our case is settled.
Here's a link that may take you out of your misery, since you seem the type of chipmunk that would rather believe an argument of authority, than to have a real debate going on:
http://abstractmath.org/MM/MMConditional.htm
(This link is brought to you, by courtesy of google and the relevant words to the case being discussed)
Lets take special care with this section: http://abstractmath.org/MM/MMConditional.htm#_Toc133208748
A conditional assertion may be worded in various ways. It takes some practice to get used to understanding all of them as conditional. The most common ways of wording a conditional assertion with hypothesis P and conclusion Q are:
¨ If P, then Q.
¨ Q, if P.
¨ P only if Q.
¨ P implies Q.
¨ P is a sufficient condition for Q.
¨ Q is a necessary condition for P.
Let us look into the link that defines a sufficient condition: http://abstractmath.org/MM/MMGlossaryS.htm and I quote:
P is sufficient for Q if the statement “If P, then Q” is true. You can also say P suffices for Q. The idea behind the word is that to know that Q is true it is enough to know that P is true.
Which is the case of my proposition: "All three legged, red eyed, two headed Japanese eat red bananas".
Being a three legged, red eyed, two headed Japanese is sufficient information for you to know that he is a red banana eater.
That is, of course, if you're willing to use your brain in the first place.
I hope this is enough, but if it isn't you can always hit those books again. 🙂
By the way: there's no need to thank me for this lesson. You can believe that it was my pleasure.
11 Jul 10
1 edit
Originally posted by adam warlockWow, such a long post and you still failed to get my point. Sure, you can describe your proposition in proposition logic, too. I'm not sure what you mean by "equivalent" in this context so I'll just let that rest. I was just saying predicate and proposition logic aren't the same (which is obviously true).
*sigh*
Palynka has made you a very good question a few pages ago and you failed to notice it.
This was a very convenient slip, I must say.
1 - Anyway let me start serious mode. First we have this very odd question:
So if you can describe predicate logic in terms of proposition logic, what is the point of predicate logic?
Let me nk me for this lesson. You can believe that it was my pleasure.
My point, all this time, which you appeared to ignore all this time, is that you cannot know anything about the truth value of "p -> q" unless you know something else; e.g. that "not p" is true, which is an implicit assumption in your solution, but which you should have mentioned explicitly.
The important thing to note is that logic can never add information, it can only rearrange.
11 Jul 10
Originally posted by KazetNagorraWow! You're have absolutely no idea of what you're talking about.
My point, all this time, which you appeared to ignore all this time, is that you cannot know anything about the truth value of "p -> q" unless you know something else; e.g. that "not p" is true, which is an implicit assumption in your solution, but which you should have mentioned explicitly.
I wash my hands.
11 Jul 10
Originally posted by adam warlockAre you saying you know for a fact that no three legged, red eyed, two headed Japanese exist?
Wow! You're have absolutely no idea of what you're talking about.
I wash my hands.
Here's a logical proposition for you:
All electrons like apple pie.
Would this proposition be true in 1500, when people had no idea of the existence of electrons?
11 Jul 10
Originally posted by KazetNagorraSo you're comparing a three legged, red eyed, two headed japanese (which everyone knows what it is in the 21th century) to an electron (which everyone didn't know what it was in the 15th century)?
Are you saying you know for a fact that no three legged, red eyed, two headed Japanese exist?
Here's a logical proposition for you:
All electrons like apple pie.
Would this proposition be true in 1500, when people had no idea of the existence of electrons?
Are you really saying that this comparison is sane?
Will you be telling me that I didn't get your "point" too?
You started by saying that the proposition wasn't an implication (at least two times), then you moved to the relationship between predicate logic and proposition logic (given that predicate logic doesn't end itself with the utterances "All p are q" and proposition logic doesn't end itself with "p->q" logical affirmations this detour of yours is highly unnecessary and just goes to show that you don't know what the Hell you're talking about)
Then you dodged Palynka's question: Are you trying to use predicate logic on an empty set? (which by the way you're dodging as we speak), that utterly destroyed whatever argument you may think you have.
Then you went change your ideas (while never acknowledging the volte-face) and said that: Sure, you can describe your proposition in proposition logic, too. and made the most inane comment I think I have encountered in this forum for the last two or three days...
And now, to top it off you have to make a comparison that would make Captain Ridiculous blush?!
All of this just because you can't solve a simple logic puzzle?!
Pipsqueak here's a wikipedia (something that may be more on your league) link (to think that I only had to google vacuous truth to find this page) to help you break away the notion that you're something extraordinaire:
http://en.wikipedia.org/wiki/Vacuous_truth
A vacuous truth is a truth that is devoid of content because it asserts something about all members of a class that is empty or because it says "If A then B" when in fact A is inherently false. For example, the statement "all cell phones in the room are turned off" may be true simply because there are no cell phones in the room. In this case, the statement "all cell phones in the room are turned on" would also be considered true, and vacuously so.
A proposition that follows the same kind of structure of mine ("All... are..."😉 and says the exact same thing that I've said.
They even point out that for the exact same reasons the opposite proposition is also true.
Just like three people have already said in this thread...
Who woulda thought?!
If you want to take that half baked solipsism of yours seriously, you should apply it to any universal proposition you encounter, but of course you don't do such a thing because you know how ridiculous it is.
This thread was supposed to be embarrassing to Person X, but now you just stole his/her thunder and that is wrong, you know?
Ps: Don't forget to answer Palynka's question.
11 Jul 10
Originally posted by DrKFOh....
Adam, Adam, Adam - this is the internet. Barely articulated bellowing of assumptions, snap judgements and prejudices is the currency round here. Your fancy-pants facts are the relic of a bygone era, and the ease with which people sitting in front of a computer can discover them irrelevant.
😳