The conclusion you put in a red frame in the attachment is a non sequitur
True, that is proof the the method you are using is invalid. If no Jews are known, looking for Jews that AREN'T Atheists cannot be used to conclude that the Jewish Atheists are known. It renders a false result. It's a false positive.
en.m.wikipedia.org
A false positive is an error in binary classification in which
a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present).
Attempting a binary classification ( using the law of the excluded middle ) with an empty-set fails everytime. It produces both true and false conclusions. That means the method is invalid.
It is ridiculously false, as anyone can see just by reading it
No, the speaker is claiming to know Jews, and that requires... knowing at least one Jew.
This is ridiculous:
"All the Jews I know are Atheists AND I don't know any Jews"
And that is natural. Because it is not true that my claim is both false and true.
Agreed. The method you are using is invalid.
No claim of the type "all x such that P(x), are also Q(x)" can possibly be false, if there is no x such that fulfills P(x).
Lying by omission ^^. Naughty-naughty. Just because the claim in that form cannot be false, does not mean that Q(x) is true. P(x) and Q(x) are completely unrelated. You have just proved that a non-sequitur is an invalid method for developing true conclusions.
I have no gremlins in my pocket DOES NOT imply that I have no money in my pocket.
I have 3 gremlins in my pocket DOES NOT imply that I have 3 coins in my pocket.
In the same way it is absolutely true that all phones in this room are both on and off, if there are no phones in the room. As the article, you thought made your point, shows.
BUZZZZZZZZZZZ! I'm sorry you've just been caught misquoting the article, distorting the truth. That's pretty much game-over for you. You simply cannot be trusted for accuracy in this thread. And probably others as well. Your personality seems to be the type to exaggerate.
It's not
absolutley true. That's not what the article says. The article calls this a
vacuous truth. A statement which has NO TRUTH VALUE.
"Absolutley true" =/= "No truth value"
en.m.wikipedia.org
"... when no cell phones are in the room. In this case, the statement "all cell phones in the room are turned on" would also be vacuously true, as would the conjunction of the two: "all cell phones in the room are turned on and turned off" ... "
"Such statements are considered vacuous truths, because the fact that the antecedent is false prevents using the statement to infer anything about the truth value of the consequent. "
All cell phones in the room are turned on and turned off is not "absolutley true" like you said. That's a false statement. It is, at best, a vacuous truth, which has no truth value relating to the non-existing cell phones. Obviously.
it is absolutely true There is NO TRUTH VALUE that all phones in this room are both on and off, if there are no phones in the room. As the article, you thought which made your point, shows.
Fixed it for you.
And that is also why the entire world that understands the basics of logic, agrees with me, and not with you
.
The entire world? Nope, I brought several sources that agree with me. Here's 4. You are exaggerting, again. Because the "empty-set" is not ACTUALLY a set, the method you are employing looking for matching elements in it fails everytime. In other words, your method does not match reality. You are using a faith-based method.
If A,BA,B are disjoint, then A∩BA∩B is not really defined, because it has no elements. For this reason we introduce a conventional empty set
, denoted ∅∅, to be thought of as a 'set with no elements'. Of course this is a set only by courtesy, but it is convenient to allow ∅∅ the status of a set.
The best attitude towards the empty set ∅∅ is, perhaps, to regard it as an interesting curiosity, a convenient fiction. To say that x∈∅x∈∅ simply means that xx does not exist. Note that it is conveniently agreed that ∅∅ is a subset of every set, for elements of ∅∅ are supposed to possess every property.
Now some students are bothered with the notion of an "empty set". "How", they say, "can you have a set with nothing in it?" ... The empty set is only a convention, and mathematics could very well get along without it. But it is a very convenient convention, for it saves us a good deal of awkwardness in stating theorems and proving them
In order to understand the faults in your method you need to ACTUALLY understand the empty-set. That requires going to some very high-level scholars. The fourth souce is excellent. PHD in physics.
As you can easily see by browsing, or reading any possible source available to mankind. It is usually in the first 10 pages.
And you have said this before, but have been unable to produce any sources that explain this in the "first 10 pages". I think, again, you are lying.
Please bring a book that explains this in the first 10 pages. You need to show an explanation that the empty-set obtains all properties in the first 10 pages.
Go for it. I am guessing that whatever you bring will make the same error. It will be looking for elements, when none can exist, and then making a conclusion about that lack of elements as if that has any value, when the empty-set cannot contain any. This is a false-positive. The test is invalid.
And of course this is assuming you can ACTUALLY produce a book that has this explained.
I can produce all kinds of books that define God as the creator of earth. A definition that is CLAIMING that "nothing" = "everything" is equally valuable.