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?
Yes, { Married-bachelors } = { {} }. They exist as an empty set.
What does it mean? Why do you think the empty set does not exist?
Because THE empty set does not behave like anything else that exists. It is different than AN empty set. {} =/= { {} }.
And what do you mean with "does not exist"? Isn't lack of existence represented as a null set to start with?
Yes. Null represents non-existence.
If I am right and there is no God, isn't that the same as saying that the set of Gods is empty?
Yes. If there is no God, The set of gods is empty. This can be described with the logical notation / symbolism: { {} }.
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?
No.
Consider again the set of all married bachelors. That is obviously the null set, by definition.
No, that is AN empty set, not THE empty set.
But if it that set does not exist, then there is not such a state of affairs without married bachelors.
Clearly you are confused. "If there is not" =/= "then there must be."
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.
This is coming from confusing {} with { {} }.
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?
OH! That's easy! If you have a bank account and it's overdrawn. The quantity of money that is in the bank account does exist and excludes any money you put in until you have payed the debt.
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.
No. I am arguing against that. "The empty set obtains all properties" claims a non-existent god is like Mariah Carey. "All the Jews I know are Athiests" claims a non-existent Jew is an Atheist, if you don't know any Jews.
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.
When you say "the empty set at face value" as in "an empty box" you are describing { {} } each and everytime. Yes, an empty box is very simple to imagine, and as long as the logical notation is consistent, then all conclusions developed about this "empty box" are true and easily understood naturally when compared to real life phenomena.
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.
Correct, disjointedness is a description of what doesn't exist. Here's a simple rule that is always true, 100% of the time. Without fail.
A contradiction is false. {} is defined, each and every time, as a contradiction. It is describing the action of non-existence. That's why any statement about what it is, what it contains, is always false.
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)
Yes. Both are true.
But if that is the case, then taking any set B, the intersection of B with {} must be {},
No. You are assuming that {} is a set. As soon as you do that, you are putting {} into a box. That is properly described by { {} }.
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.
No. Neither of those two conclusions are coming from what I said. I said that the empty set is disjoint from any other set. That means that it does not intersect with any other set. This prohibits it from being a subset from any set including itself.
Which negates what you have been claiming from the beginning.
nope.
this clearly shows that your reasoning is self contradictory, and therefore logically untenable, again.
also nope.
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.
You need to define X in order to continue with this rebuttal.
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.
Negative. It's actually the opposite. I am arguing against the catagory error where THE empty set is being conflated with an empty set.
I am arguing against the catagory error of misunderstanding THE empty set as a set which behaves similar to any other set that exists.
I am arguing against the catagory error of misunderstanding THE empty set as a subset whic behaves similar to any other subset that exists.
Let's look at the test for identifying a catagory error:
To show that a category mistake has been committed one must typically show that once the phenomenon in question is properly understood, it becomes clear that the claim being made about it could not possibly be true.
"All the Jews I know are Atheists is true even if I don't know any Jews" is an obvious catagory error.
This is no different than saying: "The gremlins in my hand have blue hair and sharp teeth". If there are no gremlins in my hand, there is no hair, it's not blue, there is no teeth, they aren't sharp.
Each and every so-called logical proof trying to assert that these statements are valid use faulty logic in the form of:
"If I can't prove it's not false, it MUST be true." How this is accomplished, is from the catagory error misunderstanding the notation and symbolism which is used to "work with" the empty set. These symbols make it appear as if the empty set is a subset like any other subset. In any other subset, a contrapositive, a proof by contradiction, develops a true conclusion. This does not work with an empty set because the same logic does not hold for something that is empty, compared to something that ACTUALLY contains objects/elements.
Because, the empty set is not like any other set that exists, it cannot be evaluated like any other set that exists.
Because, the empty set is not like any other subset that exists, it cannot be evaluated like any other subset that exists.
Calling it a "set" unqualified in english and a "subset" in english unqualified obviously can lead to miscomprehension especially if a person is most often working in algebra. It might be convenenient to call it a "set" and a "subset" as a short cut to remembering how the logical expressions evaluate on paper using symbols. But since those symbols don't MEAN the same things when translated into english, it is much much better to abandon those words. Or be very disciplined when using them.
So, if I remove all the balls from a box, then the box is not a box anymore?
Balls in a box is a poor analogy. Here is the definition of a set.
A set, wrote Cantor, is a collection of definite, distinguishable objects of perception or thought conceived as a whole. The objects are called elements or members of the set.
Once the objects are removed, there is no more set.
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.
No. The most important aspects of math and logic are below. I am following this closely and carefully. Because of this, all of the conclusions that I am developing are true.
1) Real world phenomena must be accurately and correctly translated in its proper logical notation.
2) Logical notation must be absolutley consistent.
3) The logical conclusion must be accurately and correctly translated back into english.
4) The conclusion in english must be compared to real world phenomena to make sure that the conclusion "makes sense"
As I said earlier, almost everytime you attempt to describe a real world phenomena of an empty set, you are not describing {}, you are describing { {} }. This is not translating the phenomena properly into logical notation. I'm also seeing this same miscomprehension at the end of the process. The symbolic logical conclusion is not being understood properly. The best example of this is claiming that an intersection resulting in {} somehow communicates a correspondence of properties between the original sets being compared inspite of this being fully defined as the opposite. Also, axiomatic set theory does not distinguish symbolically, in notation, between AN empty set and THE empty set. This is not your fault as an adherent to a dogmatic belief system. But it would be good for you to acknowledge this, recognize the limitations of this, and avoid accepting false conclusions even if they are written in books, published online, or even taught in university. Acknowledging these limitations comes from the last step, the most important step, for anyone working in math or logic. Simply put: "Always check your work at the end." Always.
