Is religion dying?

[viole]

Yes, they are, that is in chapter 2. That is how a material conditional , the technical name for the "implication" is defined. If you scroll back and look up the truth table you keep using, it is "Assume it's true..."

Since you haven't moved past chapter 1, you remain ignorant.

I don’t care about chapters. forget the blessed chapters.

i want to know whether that definition is your official definition that we can use to evaluate claims, from now on, at least for what concerns being a subset, or not being a subset.

in other words, are you ready to defend it or not?

don’t be afraid, I don’t bite

just a simple yes, or no.

ciao

- viole

 

[dybmh]

I don’t care about chapters. forget the chapters.

You mean, you don't care about the remaining information in a book about "proof"?
You expect to be able to simply prove something, without reading beyond the first 12 pages?
And without advancing you expect to be able to identify what a proof is or is not in 12 pages?
And I have pointed out to you that a proof can be disproven, but this is not introduced in the first 12 pages, but that doesn't matter to you?

Well. No wonder you can't see any valid counter-examples or contradictions. You are ignorant of those concepts.

nobody is making that assumption

If you don't move beyond page 12, assumptions are not described. You wouldn't know what an assumption is. You don't know what conjecture is. You don't know what a counter-example is. You don't know what a contradiction is.

Of course there are assumptions being made:

1) You are assuming that you actually know something when you don't. That's been the problem all along.
2) Without any concept of disproof, which is addressed later in the book, EVERYTHING is true.

i want to know whether that definition is your official definition that we can use to evaluate claims, from now on, at least for what concerns being a subset, or not being a subset.

It can be used to evaluate a claim if the assumption is declared, and the vacuity of the conclusion is not omitted.

in other words, are you ready to defend it or not?

I'm ready!

don’t be afraid, I don’t bite

I only fear God.

And none of your arguments have teeth. Nor legs. And by your own admission, they're brain-dead, robotic, mindless, immature...

So, yeah, no worries.

My agreement is: the defintion can be used to evaluate a claim if the assumption is declared and the vacuity is not omitted from the conclusion.

Proceed.

 

[viole]

I'm ready!

Way to go! Boy's alive and has courage!

The good news is that you do not have to defend anything, since I totally approve what you wrote. it is actually 100% correct. So, happy we agree on something, after all.

So, let us repeat it here for reference:

It is *actually* this:
Suppose A and B are sets, and assuming that it's true that every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is proven that an element of A is not an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B.
See the difference?

Now, the bad news is that I need to go to Berlin for a few days. Therefore, I will not be able to interact with you for a while, at least not in a sober state. I might interact with someone else on the forum, but I will need special care, and the required lucidity, for your case.

So, that should you give you, and all readers of this thread, enough time to try to find out where the killing shot will come from, and where it will hit. A simple exercise in logic for you, and the interested reader.

Ciao

- viole

 

[dybmh]

Way to go! Boy's alive and has courage!

The good news is that you do not have to defend anything, since I totally approve what you wrote. it is actually 100% correct. So, happy we agree on something, after all.

So, let us repeat it here for reference:


Now, the bad news is that I need to go to Berlin for a few days. Therefore, I will not be able to interact with you for a while, at least not in a sober state. I might interact with someone else on the forum, but I will need special care, and the required lucidity, for your case.

So, that should you give you, and all readers of this thread, enough time to try to find out where the killing shot will come from, and where it will hit. A simple exercise in logic for you, and the interested reader.

Ciao

- viole

ok, have a good time,

don't forget, whatever claim you make will need to include the assumption, and the vacuity, and this is vastly different from what you have brought so far.

because of this, it will be the 3rd change to your claim. needing to change the claim shows that the original claim is indefensible. 3 changes = 3 indefensible claims. I haven't needed to change a single time.

 

[viole]

ok, have a good time,

don't forget, whatever claim you make will need to include the assumption, and the vacuity, and this is vastly different from what you have brought so far.

because of this, it will be the 3rd change to your claim. needing to change the claim shows that the original claim is indefensible. 3 changes = 3 indefensible claims. I haven't needed to change a single time.

Let

A = {} = empty set
B = {1,2,3}

We have two possibilities:

1) A is a subset of B
2). A is not a subset of B

Which one is true?

Let us remind us your definition:

It is *actually* this:
Suppose A and B are sets, and assuming that it's true that every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is proven that an element of A is not an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B.
See the difference?

What do you think?

Ciao

- viole

 

[dybmh]

What do you think?

Ciao

- viole

I think you know what I think.

My agreement is: the defintion can be used to evaluate a claim if the assumption is declared and the vacuity is not omitted from the conclusion.

The vacuity is missing from what you wrote.

Let

A = {} = empty set
B = {1,2,3}

OK...

We have two possibilities:

1) A is a subset of B
2). A is not a subset of B

Sorry, that doesn't match my conditions. There needs to be 3rd option. A vacuously-is a subset of B. But let's continue.

Which one is true?

Option 3: Assuming A is a subset of B, then A vacuously-is a subset of B, if A is the {}.

Let us remind us your definition:

"Suppose A and B are sets, and assuming that it's true that every element of A is also an element of B, then we say A is a subset of B, and we denote this as A ⊆ B. We write A ⊈ B if A is not a subset of B, that is, if it is proven that an element of A is not an element of B. Thus A ⊈ B means that there is at least one element of A that is not an element of B."

This addresses the problem of the undeclared assumption, but it does not address the problem of vacuity.

1) {} is a special set
2) it doesn't have any elements.

Both of these problems can be resolved with the concept of vacuity. Vacuity has interesting properties. It is intuitive when a property or element is proposed to be lacking, but it is counter-intuitive when a property or element is proposed to be obtained.

This is why in the wiki article for vacuous truth, there is a disitinction between the negative assertion and the positive and contradictory assertions. Also, in the wiki article for the empty set, in the section you kept cherry picking from, the distinction is there as well.



See the contradiction? The property holds vacuously, and simultaneously the property *actually* does not hold.

I found another good source for the behavior I have observed.

List of logic symbols - Wikipedia

Look at the row for XOR.



So, there's no way around it. The only way to maintain the law of non-contradiction is to abandon the vacuous truth. Or, abandon the law of non-contradiction for the empty set.

If the empty-set is considered as a set, there's 3 options in the framework:

1) true
2) false
3) vacuous

So, for your claim that "All the Jews you know are atheists" to be true in classical logic, you have to declare the assumption and include the vacuity. Otherwise, you're stuck with a XOR relationship between atheist and theist, and both are true, and you cannot violate the law of non-contradiction.

The true claim is: "Assuming all Jews are atheists, and I don't know any Jews, then all the Jews I vacuously-know are atheists."
And that is much different than "All the Jews I know are athiests and I don't know any Jews."

Another true claim could be derived by splitting the claim in half, and then inserting the vacuity into the original claim.
"I don't know any Jews that are athiests".

Here, the assumption does not need to be declared, because the XOR relationship negated is a tautology.

 

[viole]

Sorry, that doesn't match my conditions. There needs to be 3rd option. A vacuously-is a subset of B. But let's continue.

There is no third condition in classical logic. That is why it is called the law of excluded third. Either something is X, or it is not X. Either something is true, or it is not true. There are no maybes, nor third option. So, you are back into making up things.

If you need one third option, beyond being a subset and not being a subset, then you are clearly operating outside classical logic, and its basic rules. Admit it, and we are finished.

So, what is it? you just have to pick one, and we will submit it to rational analysis.

ciao

- viole

 

[dybmh]

There is no third condition in classical logic. That is why it is called the law of excluded third. Either something is X, or it is not X. Either something is true, or it is not true. There are no maybes, nor third option. So, you are back into making up things.

If you need one third option, beyond being a subset and not being a subset, then you are clearly operating outside classical logic, and its basic rules. Admit it, and we are finished.

So, what is it? you just have to pick one, and we will submit it to rational analysis.

ciao

- viole

Hmmmmmm.....

I'm not sure I believe you.

Either something is X, or it is not X

But you've said that in classical logic it's true "if you don't know any Jews, then all the Jews you know are both Atheist and Thesist ( not Atheist )."

So, if you are willing to admit this ^^ is false. Then maybe I'll believe you that there can be only 2 options. Otherwise there must be a third option, vacuity.

Also, why did ( I think ) all the videos you brought say that the assertion "the empty set is a subset of any set" is vacuously true?

Both true and false is an answer brought on the wiki-page for the empty-set. The property both holds and not holds simultaneously.

 

[viole]

Hmmmmmm.....

I'm not sure I believe you.

You do not need to. We are not talking religion here. Nor politics. Nor about opinions that can be challenged. We are talking of asserting things within a framework with a very well defined set of rules. And if you do not play by the rules, you are either a cheater/liar or you are playing a completely different game. It is your call, really.

Now, one of the pillars of classical logic, is the law of the third excluded. Propositions are either true, or false. There is no middle ground. No maybes, no third alternative, no nothing. I am sure the book you posted contains truth tables for only two values: T (true), or F (false). No mention of the V (vacuous) case which is, I am afraid, only a product of your imagination.

So, again, what would that be? I am still waiting.

Ciao

- viole

P.S. And the rest of your post is a waste of typing, since it does not show any contradiction whatsoever, anyway. Any contradiction you see there, is only in your mind. Again. And easily demonstrably so.

 

[dybmh]

You do not need to.

But you have been shown over and over to omit necessary information. I cannot trust you to be honest.

We are not talking religion here. Nor politics. Nor about opinions that can be challenged.

But you have repeatedly acted like a religious adherent. It's not that this is an opinion. But it could be that the empty-set and propositions including it are an exception. In fact it is likely because that's what an empty-set is. It is a special set, an exception to the rule: "A set is a collection of elements".

So, it could be that what you're saying is, again, incomplete. You could be ignorant, or you could be intentionally lying by omission.

We are talking of asserting things within a framework with a very well defined set of rules. And if you do not play by the rules, you are either a cheater/liar or you are playing a completely different game. It is your call, really.

You need to bring "the rules" in their entirety. Something which specifically addresses the empty set and vacuity. I have already brought multiple sources showing that the empty set permits simultaenous true/false evaluations. The contradiction is ignored by considering it vacuous.

Now, one of the pillars of classical logic, is the law of the third excluded. Propositions are either true, or false. There is no middle ground. No maybes, no third alternative, no nothing. I am sure the book you posted contains truth tables for only two values: T (true), or F (false). No mention of the V (vacuous) case which is, I am afraid, only a product of your imagination.

No, it's mentioned in virtually all the videos you brought. It's in the wiki articles you linked to. And since all of this started with an intentionally false statement being made similar to 2+2=5, and then using this false statement to imply another false statement similar to "All Jews are Muslims", I simply cannot trust you to bring all the rules, or even rules that are true.

For example, you know how to play chess. You could be telling me the rules in chess, but leaving out the rule that knights can jump. Here the empty-set permits permits a 3rd option.

So, again, what would that be? I am still waiting.

You're going to be waiting a long time. I already gave you my conditions. The definition can be used if the assumption is declared and vacuity is included in the conclusion.

And the rest of your post is a waste of typing, since it does not show any contradiction whatsoever, anyway. Any contradiction you see there, is only in your mind. Again. And easily demonstrably so.

According to your logic, all the Jews you know are both atheists and not atheists simultaneously. That's a contradiction.

Anyway,

Bring me the rule book. Be sure it is complete. It must discuss the empty-set, the law of non-contradiction, and the vacuous-truth. Virtually every source you brought says it's vacuous. That's what EMPTY means. So, if you want to reverse course and say none of those videos were correct. That's fine.

But you still need to produce this rule book. Oh. And if you claim it is a paper book, please take a few pictures of the pages that address the issue of the law of non-contradiction, the empty-set, and vacuity.

 

[viole]

But you have been shown over and over to omit necessary information. I cannot trust you to be honest.

I cannot trust you to be honest. Nobody could. You are , in fact, changing the rules as you see fit to make your case. Which is the quintessential display of intellectual dishonesty and lying. It is the chess equivalent of moving the knight as a queen, when you are cornered. In other words. you are cheating. In the most blatant, and self evident way.

Logic entails, as a very basic rule the law of the third excluded. That means that all propositions are either false, or true. There is, by the very name of the law, no third alternative. There is simply no discussion about that. And you dictating new rules, is pathetically ridiculous. Who on earth are you to claim the right to redefine the laws of logic?

So, either you play by that rule, or you are playing according to laws of logic that are only a figment of your imagination, and have nothing to do with classical logic

And if you insist to be logically compliant, then there is no escape. Even a claim is true, or it is false.

And, until now, you failed to tell what it is. Which can only be explained by you not understanding what you are talking about.

Ciao

- viole

 

[dybmh]

I cannot trust you to be honest. Nobody could. You are , in fact, changing the rules as you see fit to make your case. Which is the quintessential display of intellectual dishonesty and lying. It is the chess equivalent of moving the knight as a queen, when you are cornered. In other words. you are cheating. In the most blatant, and self evident way.

I've been completely honest. Not changing any rules. You have been lying by omission.

Logic entails, as a very basic rule the law of the third excluded. That means that all propositions are either false, or true. There is, by the very name of the law, no third alternative. There is simply no discussion about that.

But you seem to be unable to produce this rule book you keep insisting on following. I've shown plenty of evidence that this vacuous truth permits contraditions. You just seem to be bothered somehow that your own so-called logical system considers contradictions true.

So, either you play by that rule, or you are playing according to laws of logic that are only a figment of your imagination, and have nothing to do with classical logic

Show me the complete rule book. If you can't / or won't, then based on the behavior in this thread, you're probably ignorant or intentionally lying by omission.

Again, your system of so-called logic considers it true if it can't be proven false. So, if that's your standard, then you can claim anything you want about a non-existent set of rules and you have no *actual* principles to prohibit lying.

And if you insist to be logically compliant, then there is no escape. Even a claim is true, or it is false.

According to your logic, all the Jews you know are simultaneously atheist and not atheist.

And, until now, you failed to tell what it is. Which can only be explained by you not understanding what you are talking about.

Sure I understand.

Assuming all the elements of an empty set are in any other set, even though the empty-set has no elements, the empty set vacuously-is a subset of every set, because there are no elements in the empty-set.

The answer is the identity. The empty-set is empty. Whatever a person says about it, it is empty, it is vacuous. The empty-set is empty / vacuous. The statement about the empty set is empty / vacuous. That vacuity is true. It's an identity, a defintion. Not a proof.

 

[viole]

I've been completely honest. Not changing any rules. You have been lying by omission.

Nope. You are not. You are violating a very basic rule that is at the basis of classical logic. Namely the law of the third excluded.
By the very fact that you claimed that it is not the case that propositions are either true or false, but that there is a third alternative. I can show you the post if you want, and expose your lie in full sight.

So, please confirm, in case I misunderstood. Or you like to revise your claim. What do you think it is applicable in classical logic?

1) All propositions are either true or false
2) There is a third alternative

Your call, that we will submit to logical analysis.

Ciao

- viole

 

[dybmh]

Nope. You are not. You are violating a very basic rule that is at the basis of classical logic. Namely the law of the third excluded.

There must be an exception, because I've brought multiple sources showing it. And according to your own logic:

all the Jews you know are simultaneously atheist and not atheist.

By the very fact that you claimed that it is not the case that propositions are either true or false, but that there is a third alternative. I can show you the post if you want.

Then "All the Jews you know are atheists" must be false.

So, please confirm, in case I misunderstood. Or you like to revise your claim. What do you think it is applicable in classical logic?

I'm not sure you are using classical logic. Again, you consider anything true, unless it is proven false. So, you could be talking about an imaginary or abridged version of so-called logic. And since I cannot prove anything about a non-existent rule, you have no principles to prohibit making it up.

1) All propositions are either true or false
2) There is a third alternative

If so then: Then "All the Jews you know are atheists" must be false if you know no Jews.

You can't have it both ways.

Your call, that we will submit to logical analysis.

The analysis shows that either "All the Jews you know are atheists" must be false or contradictions are considred true.
The analysis shows that you would not consider it a lie ( falsehood ) if I can't prove it false. So there is nothing in your principles to prohibit saying ANYTHING about a non-existent set of rules.

 

[viole]

There must be an exception, because I've brought multiple sources showing it.

LOL. nope. There are no exceptions. You are just making up things again. And your sources do not show anything like an exception to the laws of logic. That is only a delusion of yours.

therefore, we can conclude that you are operating outside the laws of logic.

And yes, all the Jews I know are simultaneously atheists and theists. There is no contradiction whatsoever, if I know no Jews. That there is one contradiction is, again, just a figment of your imagination.

Ciao

- viole

 

[dybmh]

LOL. nope. There are no exceptions. You are just making up things again. And your sources do not show anything like an exception to the laws of logic. That is only a delusion of yours.

No...You're claiming that a contradiction is true.

You're saying that all the Jews you know are both atheists and not atheists.

So, which is it?

therefore, we can conclude that you are operating outside the laws of logic.

No..... I am not accepting you're opinion about a skewed version of so-called logic.

And yes, all the Jews I know are simultaneously atheists and theists. There is no contradiction whatsoever, if I know no Jews. That there is one contradiction is, again, just a figment of your imagination.

Jews cannot be simultaneously atheists and non-atheists. So, you have made a false statement.

And you cannot simultaneously know and not know Jews.

So yeah, there's 2 contradictions there.

And if we count the number of Jewish athiests you know, there are ZERO. ZERO Jewish atheists means you don't know any Jews who are atheists.

So that's 3, THREE contradictions. But you'll never admit it, because the imaginary math-god hath ordained...

 

[viole]

No...You're claiming that a contradiction is true.

The contradiction is only in your mind. You just made it up to make your case, like you made up that logic statements have three possible truth values. And making up things, and ad-hoc changing the rules, is intellectual dishonesty.

In fact, it is obvious that the two sentences

1) All the Jews I know are atheists
2) All the Jews I know are non-atheists

Are not contradictory at all. In fact, it is not the case that one is the negation of the other. And therefore they can both be true, or false, at the same time. And trivially so.

Jews cannot be simultaneously atheists and non-atheists. So, you have made a false statement.

Another lie. I never claimed that Jews can be simultaneously atheists and non-atheists. In fact, I claim the exact opposite. Namely that the set of all Jews who are simultaneously atheists and non-atheists, is empty.

Therefore, your entire case is based on made up contradictions, arbitrary and dishonest ad-hoc changes of the most basic laws of logic, and lies concerning what I claimed.

And that is more than enough to dismiss it altogether.

Ciao

- viole

 

[dybmh]

The contradiction is only in your mind. You just made it up to make your case, like you made up that logic statements have three possible truth values. And making up things, and ad-hoc changing the rules, is intellectual dishonesty.

No, I'm not making things up. I brought sources for all I've said. And the longer the debate goes on, the more sources I've brought to support me.

Anyone can see the trend. My position is much much stronger than yours. And it keeps getting stronger.

In fact, it is obvious that the two sentences

1) All the Jews I know are atheists
2) All the Jews I know are non-atheists

Are not contradictory at all.

Sure they are! They absolultely contradict.

~(All the Jews I know are atheists and not-atheists) = I know at least 1 Jew that is neither atheist nor theist.

That's a contradiction. No one can be neither simultaneousy. You lose again.

Splitting them and processing them indendently, and ignoring the defintion of a Jew... Ah-gain.

In fact, it is not the case that one is the negation of the other. And therefore they can both be true, or false, at the same time. And trivially so.

There it is. "Trivially". Employing trivialsm, but also denying it. Another contradiction.

Trivialism - Wikipedia

en.m.wikipedia.org

"In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction."

Another lie. I never claimed that Jews can be simultaneously atheists and non-atheists. In fact, I claim the exact opposite. Namely that the set of all Jews who are simultaneously atheists and non-atheists, is empty.

Sure you claimed it. You just have been programmed / brainwashed / trained to ignore the actual meaning of the words you're using. Or willfully ignorant. Or dishonest. All are possibilities.

You're saying you claimed the opposite. See below.

And yes, all the Jews I know are simultaneously atheists and theists. There is no contradiction whatsoever, if I know no Jews.

You just admitted that you are claiming the opposite of "all the Jews I know are simultaneously atheists and theists". But here, you're denying the contradiction. A contradiction IS saying the opposite of the *actual* meaning.

The true statement is "All the Jews I know CANNOT be atheists and theists." Or "I don't know any Jews that are atheists and theists."

But you said the opposite, and then.... confessed. The confession normally would indicate a moral person. But in this case, not so much.

Therefore, your entire case is based on made up contradictions, arbitrary and dishonest ad-hoc changes of the most basic laws of logic, and lies concerning what I claimed.

Nope. Nothing dishonest. Everything above board. Here's the sources I've been using.

Empty domain - Wikipedia

en.m.wikipedia.org

Empty set - Wikipedia

en.m.wikipedia.org

Vacuous truth - Wikipedia

en.m.wikipedia.org

Material conditional - Wikipedia

en.m.wikipedia.org

Paradoxes of material implication - Wikipedia

en.m.wikipedia.org

Contradiction - Wikipedia

en.m.wikipedia.org

Natural deduction - Wikipedia

en.m.wikipedia.org

List of logic symbols - Wikipedia

en.m.wikipedia.org

Connexive Logic (Stanford Encyclopedia of Philosophy)

Natural Deduction Systems in Logic (Stanford Encyclopedia of Philosophy)

Contradiction (Stanford Encyclopedia of Philosophy)

And I wrote formal rigorous sound proofs using classical logic showing both the claim about "all the Jews you know" is false, AND that ANY positive assetion in that form is always false, while the negative assertion is ALWAYS true. This behavior is a result of the XOR and ~XOR condition when considering mutually exclusive properties, like atheist and theist.

Let me say that again: I wrote a formal proof showing you're wrong and you cannot defeat it.

And this proof demonstrates the behavior below. It is supported by one of the sources above, namely the one on Contradiction from Stanford:

​

If Socrates doesn't exist, “Socrates is wise” and its contrary “Socrates is not-wise” are both automatically false (since nothing—positive or negative—can be truly affirmed of a non-existent subject), while their respective contradictories “Socrates is not wise” and “Socrates is not not-wise” are both true.​

And you haven't been able to refute any of this. Not a single iota. All you have are short youtubes which don't address any of these things, and forums which are unreliable and also don't address these things. And you've been clinging, deperately, to the first 12 pages of one of my sources, but you refuse to read beyond it. And then there's the cherry picking of the wikipedia page on the empty-set, which you did at th beginnning of the thread.

Here's what it *actually* says:

So, you intentionally removed the words "vacuous truth" AND you intentionally omitted the contradictory TRUE statement:

There is no element of the empty set for which the property holds.

That's proof positive that you intentionally omit necessary information. That's cherry picking.

And that is more than enough to dismiss it altogether.

That's because you cannot admit that you're wrong. Completely hopelessly wrong. And you seem to be willfully ignorant, nd you show signs of moral bankruptcy.

By your own admission, your methods are mindless, brain-dead, and robotic. So, why use them?

They clearly consider contradictions true, they clearly have no awareness of evidence or relevance. What's useful about any of this other than permitting lying my omission?

 

[viole]

Sure they are! They absolultely contradict.

~(All the Jews I know are atheists and not-atheists) = I know at least 1 Jew that is neither atheist nor theist.

That's a contradiction. No one can be neither simultaneousy. You lose again.

Splitting them and processing them indendently, and ignoring the defintion of a Jew... Ah-gain.

~(All the Jews I know are atheists and not-atheists) = I know at least 1 Jew that is neither atheist nor theist. ?

Embarrassing.

The correct one is:

~(All the Jews I know are atheists and not-atheists) = I know at least 1 Jew that is not atheists and not-atheist.

Which is actually expected from any Jew acquaintance. Since Jews, like anyone else, cannot be atheists and not-atheists at the same time. So, not only that is not contradictory, but it is trivially true, for anyone knowing Jews . So, that also epically failed.

Again, you are making up your definitions. Including completely inventing the rules of how to negate propositions, in order to fit your conclusions. And I am doing you a compliment by thinking you are intentionally cheating.

Actually, the rule for negating propositions correctly is in the same book you posted. I can show you the chapter, if you want. Therefore, I would recommend you read it first.

Therefore, again, your case is predicated on a violation of the rules of logic. In this case the rules to negate propositions.. Which you blatantly made up, again.

Case closed. Even though we are having lot of Spass here, lol.

Ciao

- viole

 

[dybmh]

~(All the Jews I know are atheists and not-atheists) = I know at least 1 Jew that is neither atheist nor theist. ?

Embarrassing.

The correct one is:

~(All the Jews I know are atheists and not-atheists) = I know at least 1 Jew that is not atheists and not-atheist.

No.... you didn't distribute the the NOT all the way through. This is pretty obvious, at least to me.

Section 1.6 Review

~(All birds are flyers) = At least 1 bird is NOT a flyer.
~(All birds are flyers and feathered) = At least 1 bird is NOT a flyer or is NOT feathered.
~(All Jews I know are atheists and not-atheists) = At least 1 Jew I know is NOT atheist or is NOT not-atheist.

See it? You dropped the second NOT. It's OK. You have primitive training.

"At least 1 Jew I know is NOT atheist or is NOT not-atheist." = At least 1 Jew I know is neither atheist nor not-atheist.

I know, I know, englsh is your fourth language, and you don't pay attention to what words actually mean, you just evaluate like a robot who is uninformed of contradictions.

Which is actually expected from any Jew acquaintance. Since Jews, like anyone else, cannot be atheists and not-atheists at the same time.

Right. But they are at least one of those options.

So, not only that is not contradictory, but it is trivially true, for anyone knowing Jews . So, that also epically failed.

Yes, it is. A person is either an atheist or a theist. At least one of those is true, but you're saying a Jew is simultanesouly both, and simultaneaously neither.

Good work. Super-duper-good-logique.

Again, you are making up your definitions. Including completely inventing the rules of how to negate propositions, in order to fit your conclusions. And I am doing you a compliment by thinking you are intentionally cheating.

No..... you just keep contradicting yourself. I recommend turning on your brain, and setting aside the mindless robotic immature method.

Anyway, let's use your own statements.

"All the Jews I know are atheists and not-atheists." - FALSE, a Jew cannot be both, must be one of them.
"I know at least 1 Jew that is not atheists and not-atheist." - FALSE, A Jew is either one of those.

Actually, the rule for negating propositions correctly is in the same book you posted. I can show you the chapter, if you want. Therefore, I would recommend you read it first.

Sure, do that. But you still need to distribute the NOT.

~( P AND Q) = ~P OR ~Q
~( atheist AND not-atheist ) = ~atheist OR ~not-atheist
OR ~ = nor
~( atheist AND not-atheist ) = neither atheist nor not-atheist

You lose again. You forget, I'm a pro at boolean logic.

De Morgan's laws - Wikipedia

en.m.wikipedia.org

Therefore, again, your case is predicated on a violation of the rules of logic. In this case the rules to negate propositions.. Which you blatantly made up, again.

Nopey-nope. Your lack of attention to detail has failed you again. Fully distribute the NOT, and even if we don't the statement is still false.

Case closed. Even though we are having lot of Spass here, lol.

I'm enjoying watching the so-called logical gnostic demonstrate their illogic and ignorance. Keep going.