Yes, my point is that a subset must exist inorder to be called a subset. If it does not exist, then it cannot be named, quantified, or qualified with any truth. If it does not exist then anything that is said about it is false by definition.
For example, right now, take your hand, open it, shake it out, look at your palm, and make a truthful statement about what you see in your hand.
So, if I denote with X the set of married bachelors, would you say that such a set exists, although married bachelors cannot possibly exist?
Because they are opposite. A subset exists and contains. THE empty set does not exist and excludes.
What does it mean? Why do you think the empty set does not exist? And what do you mean with "does not exist"? Isn't lack of existence represented as a null set to start with? If I am right and there is no God, isn't that the same as saying that the set of Gods is empty? But if the empty set does not exist, wouldn't that imply that God must exist, since there cannot possibly be a state of affairs without Gods?
Consider again the set of all married bachelors. That is obviously the null set, by definition. But if it that set does not exist, then there is not such a state of affairs without married bachelors. Ergo, married bachelors must exist, because if they did not, then their set would be empty, and since there is no empty set, we come to a contradiction.
And what do you mean with "does not exist and excludes". I cannot imagine anything that does not exist, while doing something like excluding. How can it be?
Therefore your ontological claim is absurd, and for that reason not logically tenable. It would immediately lead to the obvious conclusion that everything exists. Including, say, gods who look like Mariah Carey.
Because they do not behave like any other set. So it's not so simple. Why is {} =/= {} ? If we're just talking about an empty box, then certainly one empty box is equal to the same empty box? Why is {} = {} false?
I think it is very simple, if we just take the empty set at face value. Namely, as a set that has no elements. The rest is just simple logic. I wonder why you get so tangled up by something that have nothing inside. I know a lot of people with that property, lol.
You ask: Why is {} =/= {}?
Is it? What makes you think that the empty set is different from the empty set? How can the empty set be different from itself?
Don't you think that anything is equal to itself?
So, to your question, why is {} = {} false? the answer is simple. It is not false. And I wonder how you can defend the claim that there is at least one thing that is different from itself.
Again, your logic leads to absurdities, and it is therefore not tenable.
'm not making up any defintions.
I am using well established defintions:
Yes, but you said {} cannot possibly exist. Which is another way of saying that there is not such a thing as disjoint sets. Because if there were, then their intersection would be not existing. In other words, disjointness cannot possibly exist.
Even worse, you said in previous posts the following:
1) The empty set is disjoint from any other set.
2) A is a subset of B if and only if the intersection of A and B is A (you proposed that as criteria for being a subset)
But if that is the case, then taking any set B, the intersection of B with {} must be {}, because of 1) and your definition of disjoint here, which would entail that {} is a subset of B, because of 2). And given the arbitrary choice of B, that will entail that {} is a subset of B, for any B.
Which negates what you have been claiming from the beginning.
this clearly shows that your reasoning is self contradictory, and therefore logically untenable, again.
Cool, so what is between the curly brackets of {}?
Face value is not a proper way to evaluate the intersection of disjointed sets.
fair enough. So, what is, in your opinion, between the curly brackets of {}? Nothing, or something? What does your wisdom suggest?
No. { A,B,C } describes a bucket that is completely full. It is full of { A,B,C } and nothing else. If you add "nothing" to it that becomes { A,B,C,{} }. Adding "nothing" in a set means "making more room" or "emptying". This isn't algebra. Nothing is not the same as Zero.
Nope. if I add X to {A,B,C} and that turns it into {A,B,C,{}}, then I did not add nothing. I added {}. Which is not nothing. It is a set containing nothing. Two different things. I am sure you also agree that a box containing nothing is different from nothing.
Therefore, your argument suffers from a category error (equivocation of nothing with a container containing nothing), and it is therefore not logically tenable. Again, unfortunately.
Null. It's not even a set anymore.
So, if I remove all the balls from a box, then the box is not a box anymore?
Again, your argument suffers from a pathological logical fallacy, in this case the fallacy that containers cease to be containers if what it is contained in them is removed. Which is obviously untenable.
And, again, that leads to the conclusion that your arguments are fatally flawed, all of them, and serve therefore no purpose whatsoever in establishing truth values in statements involving empty sets. Or any other set.
QED
Tschüß
- viole
