Is religion dying?

[viole]

So A is not a set until it's put in { A }?

This question makes no sense. It is like asking if 1 is not a set until it is put in {1}.

Which is obviously absurd, because that would not make 1 a set, anyway. Only {1} is the set. And 1 and {1} are two completely different things.

I hope you also appreciate the fact that an object is different from a set containing it.

Ciao

- viole

 

[mikkel_the_dane]

...

Now. An empty set, is not a set. That is not reality. An empty set is not a subset of all sets. That is not reality. An empty set does not obtain all properties. That is not reality. If it's not proven false, it must be true, is not reality.

...

Just one problem. The idea of an empty set is a part of reality otherwise you couldn't talk about it. You are confusing logic with the world as such.
Logic can be an emergent property of the world without the world being logical as such.
It seems you are doing the standard subjective trick of believers in objective reality: You subjectively think that objective reality is the only thing real, but that you think that is not real according to its own standard.
In effect this debate is about 2 humans thinking differently and that is in both cases a part of the world, otherwise you couldn't have the debate.

 

[viole]

So there you have it. There's real valid arguments that can be made that the empty set isn't a set. And the empty set is only "called" a subset. It's not really a subset. And all of this is motivated reasoning based on pushing truth from a false premise. But as long as truthful conclusions are drawn from it, it should be fine. Otherwise, this author agrees, that is a "rather serious crime". Their exact words.

That does not entail that the empty set is not a set. Where do you read that? And for sure, the definition of the empty set does not generate falsehoods from truths. As I said, if you could prove that, you would have killed the empty set. But you cannot do that, because such contradictions never arise on account of the empty set, and its meaning.

What it says is that the empty set has been defined in such a way to make, say, statements of mathematics more elegant, or without creating special cases if a certain property does not obtain.

But defining that empty thing as a set, no matter what the motivation is, does not necessitate that that thing is not a set. And it cannot not be a set, because that it is exactly how it has been defined.

The only danger of a definition is if that leads to an internal contradiction. Like defining X to be at the same time odd and even. Which is obviously a self contradicting definition. But the empty set does not present any contradiction. It is not the case that it is defined to be empty and not empty at the same time, which would be fatal. In fact, it is contradictory to say that X is odd and even at the same time, while it is not contradictory to say that all elements in the empty set are even and odd at the same time. In fact, that is exactly what the empty set is: the set of all things that are odd and even at the same time.

And, as this guys also says at the end. The philosophical matter is irrelevant.

Ciao

- viole

 

[mikkel_the_dane]

This question makes no sense. It is like asking if 1 is not a set until it is put in {1}.

Which is obviously absurd, because that would not make 1 a set, anyway. Only {1} is the set. And 1 and {1} are two completely different things.

I hope you also appreciate the fact that an object is different from a set containing it.

Ciao

- viole

It is funny watch you two debating logic as if it is out there in the world independent of brains. The bold one happens in your brain as dependent on your thinking. So it is not an empirical fact, it is a cognitive fact.

 

[osgart]

It is funny watch you two debating logic as if it is out there in the world independent of brains. The bold one happens in your brain as dependent on your thinking. So it is not an empirical fact, it is a cognitive fact.

That's true that the universe doesn't have to obey the rules of logic. Logic is a powerful tool to obtain facts about our survival in the universe nevertheless. Nothing is under any obligation to follow from anything logical. I think logic is more a manipulation of true conditions to get a desired outcome. Given a set of true conditions certain things will follow from that. As a probe into reality itself I'm not sure logic obtains anything.

 

[mikkel_the_dane]

That's true that the universe doesn't have to obey the rules of logic. Logic is a powerful tool to obtain facts about our survival in the universe nevertheless. Nothing is under any obligation to follow from anything logical. I think logic is more a manipulation of true conditions to get a desired outcome. Given a set of true conditions certain things will follow from that. As a probe into reality itself I'm not sure logic obtains anything.

Yeah, logic works, but has a limit. Just like evidence. I mean if I think something is the case for which there is no evidence and yet I act on it and don't die or all that, then there is evidence, that I can act without evidence. Go figure.

 

[Kelly of the Phoenix]

Is religion dying i.e. waning in popularity?

Well, you guys are all old, so maybe I'm asking the wrong crowd...

Haha jk

You guys have a certain perspective.

As the youngins take the places of you lot, do you think religion will be as popular or influential?

Atheism seems to be on the rise. Institutionalized religion has traumatized much of millennials and I'm betting gen z too. I get mixed signals when I try to gauge the populace's ever changing opinion on religion. Will the millennials and gen z let religion be a dominating cultural force, as it has always been?

I think Christianity is dying but spirituality is rising. I don't think religion is dying. But I think it is possible. I think atheism and agnosticism will keep rising, and as a result organized religion will lose its influence.

I believe at this point it should die in order to be reborn.

 

[dybmh]

Your job is to show that this definition leads to internal contradictions

I have done this multiple times.

The definition of the set contradicts with defintion of the empty set.

A set is a collection of objects/elements. That is Cantor's def, not mine. The "empty set" contains no objects/elements. This is your assertion. If it contains no elements, then it is not a set. "empty-set" is a misnomer.

Empty-set = Married-Bachelor = Flying-pig = square root of -1 = True-Lie = CONTRADICTION

A contradiction does not exist. Things that don't exist are false, fiction, untrue ...

There is no "empty-set". The definition is itself a contradiction.

All elements of the empty set fulfill any property. Because there is no element in that set that does not fulfills it, on account of the empty set not having any element at all. So, for the law of the excluded middle, the first statement obtains.

The very first sentence is a contradiction. "All elements of the empty set fullfill any property." The empty-set has no elements. That is a contradiction. It simply doesn't work.

 

[mikkel_the_dane]

I have done this multiple times.

The definition of the set contradicts with defintion of the empty set.

A set is a collection of objects/elements. That is Cantor's def, not mine. The "empty set" contains no objects/elements. This is your assertion. If it contains no elements, then it is not a set. "empty-set" is a misnomer.

Empty-set = Married-Bachelor = Flying-pig = square root of -1 = True-Lie = CONTRADICTION

A contradiction does not exist. Things that don't exist are false, fiction, untrue ...

There is no "empty-set". The definition is itself a contradiction.




The very first sentence is a contradiction. "All elements of the empty set fullfill any property." The empty-set has no elements. That is a contradiction. It simply doesn't work.

Yes, you talk about them.
The definition is itself a contradiction and yet it doesn't exist, so what are you talking about?

 

[dybmh]

This question makes no sense. It is like asking if 1 is not a set until it is put in {1}.

Which is obviously absurd, because that would not make 1 a set, anyway. Only {1} is the set. And 1 and {1} are two completely different things.

I hope you also appreciate the fact that an object is different from a set containing it.

Ciao

- viole

And this is the root of the problem. A concept "empty" is not a set until someone decides to make it a set. "Empty" has no elements. But once it is made into a set, it has an element.

So, if it is defined that all intersections are sets, which you did, that prohibits an "empty" set. It will never be truly empty. It will always have an element, even if that element is "empty". No matter what elements, if any, are returned from the evaluation, the elements are immediately put into a set. If "none" are returned, this itself becomes an element, an object, a construct when it is contained. This cognitive step is being ignored. It's the application of the defintion onto the result of the action of intersecting. From this application of the definition, yes the "empty" set will be a subset of all other sets, because all other sets have now been defined as having at least 1 element, even if that 1 element is "empty". The actual result of the intersection may not have elements, but that result, empty or not, becomes an element in the same way that 1 becomes { 1 }, or A becomes { A }, or Mickey-Mouse becomes { Mickey-Mouse }.

And because of this, when a person goes to compare this "empty" set with all other sets, there is obviously something to compare. Do the sets have more than "empty".

When someone says, there are no elements in the "empty-set" to compare. It's not that there aren't any actual elements. The element "empty" is being ignored. The cardinality of the "empty-set" as the definition is applied to the result of a failed intersection does have 1 element, but that cardinality is being ignored.

 

[viole]

Empty-set = Married-Bachelor = Flying-pig = square root of -1 = True-Lie = CONTRADICTION

Yes, and that is not a contradiction. For there are no married bachelors. Ergo, the set of married bachelors is empty. Exactly the same thing.

No contradiction whatsoever. There would be one, if the set of married bachelors would be not empty. But it is. Therefore there is no element in it that is a married bachelor. Which is the same as saying that all elements in it are married bachelors. I really don't see why you have a problem with this.

It is just a type of set. Like the singleton set, a finite set, an infinite set.

By the way, the set containing square roots of -1 is not necessarily empty.

CIao

- viole

 

[mikkel_the_dane]

And this is the root of the problem. A concept "empty" is not a set until someone decides to make it a set. "Empty" has no elements. But once it is made into a set, it has an element.

So, if it is defined that all intersections are sets, that prohibits an "empty" set. It will never be truly empty. It will always have an element, even if that element is "empty". No matter what elements, if any, are returned from the evaluation, the elements are immediately put into a set. If "none" are returned, this itself becomes an element, an object, a construct when it is contained. This cognitive step is being ignored. It's the application of the defintion onto the result of the action of intersecting. From this application of the definition, yes the "empty" set will be a subset of all other sets, because all other sets have now been defined as having at least 1 element, even if that 1 element is "empty". The actual result of the intersection may not have elements, but that result, empty or not, becomes an element in the same way that 1 becomes { 1 }, or A becomes { A }, or Mickey-Mouse becomes { Mickey-Mouse }.

And because of this, when a person goes to compare this "empty" set with all other sets, there is obviously something to compare. Do the sets have more than "empty".

When someone says, there are no elements in the "empty-set" to compare. It's not that there aren't any actual elements. The element "empty" is being ignored. The cardinality of the "empty-set" as the definition is applied to the result of a failed intersection does have 1 element, but that cardinality is being ignored.

I think your post is a contradiction and it doesn't exist. Words are such fun. But non-existence is true as false, because everything is true one way or the other, even a contradiction that doesn't exist.
I do think you take logic a bit to seriously, but that is just me.

 

[dybmh]

Yes, you talk about them.
The definition is itself a contradiction and yet it doesn't exist, so what are you talking about?

Falsehood.

 

[viole]

When someone says, there are no elements in the "empty-set" to compare. It's not that there aren't any actual elements. The element "empty" is being ignored. The cardinality of the "empty-set" as the definition is applied to the result of a failed intersection does have 1 element, but that cardinality is being ignored.

Wrong., I am afraid. The cardinality of the empty set is zero. It is the number of elements it has which is, by definition, zero.

Ciao

- viole

 

[viole]

The very first sentence is a contradiction. "All elements of the empty set fullfill any property." The empty-set has no elements. That is a contradiction. It simply doesn't work.

Of course it does, for the simple reason that the statement "All elements,,,", does not assume the presence of at least one element. That would be a non sequitur.

Ciao

- viole

 

[mikkel_the_dane]

Falsehood.

Which exists, otherwise you couldn't talk about it and use it. Or what you did as in regards to your post is a case of actual non-existence.

 

[dybmh]

Yes, and that is not a contradiction. For there are no married bachelors. Ergo, the set of married bachelors is empty. Exactly the same thing

married-bachelor is a contradiction. empty-set is a contradiction. open-closed is a contradiction. right-left is a contradiction. black-white is a contradiction. etc...

No contradiction whatsoever. There would be one, if the set of married bachelors would be not empty.

any contradiction put into a set is not empty. the contradiction itself is the element, object, construct, which is contained in the set. A set can contain an idea. the contradiction is the idea.

Therefore there is no element in it that is a married bachelor.

married-bachelor IS the element. Here, like this: 1 >>>> { 1 }. Married-bachelor >>>>> { Married-bachelor }. Null >>>>>> { Null }. Contradiction >>>>> { Contradiction }.

I really don't see why you have a problem with this.

It's because you are ignoring the cognitive step where the definition of set is being applied to the concept "empty". It's happening automatically, instantaneously, and without your awareness. When the definition is applied, that is when the set is being generated and "empty" becomes the element. This is what I meant previously when I said that {} is being conflated with { {} }.

It is just a type of set. Like the singleton set, a finite set, an infinite set.

Can't be. Singleton, finite, infinite all have elements. The so-called "empty-set" has none.

A set is a collection of elements. "empty-set" is contradiction. That's what it does. A set collects. The opposite of a set, doesn't.

 

[dybmh]

Of course it does, for the simple reason that the statement "All elements,,,", does not assume the presence of at least one element. That would be a non sequitur.

Ciao

- viole

Yes, "All elements" assumes that "elements" exist.

"All elements" is the opposite of "No elements". This is the same as "White" is the opposite of "Black".

 

[dybmh]

Which exists, otherwise you couldn't talk about it and use it. Or what you did as in regards to your post is a case of actual non-existence.

Falsehood is real, but it doesn't exist.

 

[mikkel_the_dane]

....
A set is a collection of elements. "empty-set" is contradiction. That's what it does. A set collects. The opposite of a set, doesn't.

Well, the problem is that if you can talk about a contradiction but it doesn't exist, how can you then talk about it, because you talking, is doing something, unless you are actual doing really nothing. But how do you do that?

Let me explain what is going on. A contradiction is the experience of a feeling of being off, but that is still a feeling. It is just a negative feeling. So what you are talking about is the limit of human cognition as to always make positive sense, but it doesn't.
In empirical terms you are having a first person internal and not external sensory experience of a negative.
Your idea is that the world is logic and I just say no.