muhammad_isa
Veteran Member
Some people refer to complex numbers as imaginary
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The first cause argument
- Thread starter firedragon
- Start date
Yes, it is *true* even though it *appears* to be absurd.
Notice the list in the article. The paradoxes of the Hilbert Hotel are demonstrated to be true.
And the problem is that there isn't a *real* contradiction, just an apparent one.
firedragon
Veteran Member
Demonstrated to be true. Not true. Dont repeat the same thing. Its false.
And this whole thing is a strawman. Read the OP.
Have a wonderful day.
If it is demonstrated to be true, then it is true.
I have read the OP. it dismisses an infinite regress by an invalid argument. That argument is shown to be invalid by a consideration of the negative integers.
Unless you can show *why* the model of the negative integers cannot be a part of reality, you have failed in your argument.[/QUOTE]
firedragon
Veteran Member
Read and understand what a paradox is. You just made one of the most absurd statements I have ever heard. This time, I will make a promise to myself I will never respond to this argument again.
Ciao.
And now *you* are quoting in a way that changes the meaning. The original quote was
"It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion."
Notice the word "seemingly'. Do you know what that means? it isn't *real*. It is an *apparent* contradiction, not a *real* one.
Paradoxes are useful for thinking because they often show us errors in our reasoning or intuitions. In the case of the infinite, there are a number of paradoxes that are simply true. The Hilbert Hotel provides a number of them. For many people, there are true statements about infinite quantities that *seem* problematic. Once they are understood in detail, it is realized there is no *logical* contradiction and, in fact, they are simply true.
Once properly understood, veridical paradoxes are true statements that initially *appear* to be contradictory, but in the end are not.
leroy
Well-Known Member
Ok so do you grant that the objection "if God created the universe who created God" is a dumb objection?
If yes we can move to a different topic
If no then provide your arguments that show that this objection somehow show that the KCA fsils
muhammad_isa
Veteran Member
The Grand Hotel can never be full if it has an infinite number of rooms. It is therefore not correct to say that it is full of guests in the first place
.
leroy
Well-Known Member
My point is that:
-First you have to show that other universes exist
- then you have to show that the universe is not expanding / nor contracting(on average) otherwise it cant be infinite in to the past
_ then you have to show that the average entropy on the multiverse is nearly 100% (our bubble would be a rare exception)
- the you would have to show that the multiverse is not dominated by bolzmmsn brains
_then you would have to deal with all the paradoxes of infinity
If you do all that you could conclude that the multiverse may (or may not) be eternal being both possibilities moreless equally likelly. ..... or you can simply accept the evidence the way it is and conclude that the universe is less than 14B years old
Altfish
Veteran Member
No, I don't.
I'm not sure what KCA is????
My objection is that I have a science background, a maths background and I don't accept the "You must accept this before I can prove that" type of argument.
So, when scientists say the universe started with The Big Bang, I (and they) know that that is not the end of the explanation. Scientists are working on what came before the Big Bang.
So, no, it is not a 'dumb objection' to ask what was before 'god'
Why not?
It is therefore not correct to say that it is full of guests in the first place
On the contrary, it just takes an infinite number of people.
muhammad_isa
Veteran Member
Errr .. I thought it was well known that G-d is eternal?
That is a *claim*, not knowledge.
Altfish
Veteran Member
It is not even well known if he/she even exists
muhammad_isa
Veteran Member
Well, is it full up when there is a guest in every room? Yes.
..but playing with infinity is bound to throw up anomalies..
How many odd-numbered rooms would there be, infinity / 2 ?
Does infinity / 2 = infinity ?
It's a concept that is problematical.
muhammad_isa
Veteran Member
Same difference, you are just being pedantic
Anomalies are not contradictions.
Yes, the set of odd numbered rooms has the same cardinality as the set of all rooms. That is pretty typical of infinite sets.
Division is, in general problematic for infinite cardinals. For reasons similar to why you can't divide 0 by 0, it also makes no sense to divide infinities of the same size.
Why is that a problem? It violates initial intuition, sure. But there is no logical problem.
Infinite quantities act differently than finite quantities. That should be no surprise. Some operations that make sense for finite sets do not make sense for infinite ones.
Same difference, you are just being pedantic
Not really. I don't think that anything to do with Gods counts as knowledge. At best, it is speculation. Not all Gods are eternal, by the way.
muhammad_isa
Veteran Member
You are getting carried away with the "atheist stuff".
It was suggested that asking what caused God was not dumb..
It is dumb. The person asking the question already knows the answer.
It is just that they do not accept that God exists, in which case, why ask the question?
I'm going to expand on this a bit because it seems to cause a lot of people issues.
We should start with what it means for two sets of things to be the 'same size'. The correct term is 'cardinality'.
It means that there is a way of pairing off the elements of each set so that everything in each is paired with something in the other.
So, if we have three apples, A, B, and C and three oranges, 1, 2, and 3,
we can pair apples to oranges by
A<-->1
B<-->2
C<-->3
This is not the only way to pair them. Another would be
A<-->3
B<-->1
C<-->2
But, if there were four apples and 3 oranges, there would not be a way to pair them off in this way.
We use this as the *definition* of sets being the same size and apply it even for infinite sets.
So, the set of positive integers (1,2,3,4,..) is the same size as the set of odd integers (1,3,5,...) by the pairing
1<-->1
2<-->3
3<-->5
4<-->7
etc.
Every positive number on the left gets paired with some odd number on the right and vice versa. So the two sets are the same size (same cardinality) by our definition.
By the way, the cardinality of all positive numbers, 1,2,3,4..., is called aleph_0.
For infinite sets, it is possible for a 'part' to be the same size as the 'whole'. More accurately, a proper subset can have the same cardinality as the entire set. Sometimes this is even used as the *definition* of being an infinite set.
A set is infinite exactly when it cannot be paired off with some initial set of positive numbers 1,2,3,....
So, with the three apples, the act of counting makes the pairing between apples and positive numbers.
Now, can we add and multiply infinite cardinalities? YES. To add, just take sets of the appropriate size that do not overlap and put them together. To multiply, create an array and look at the cardinality of the array. Both of these generalize what works for positive numbers.
It turns out that aleph_0 +aleph_0 =aleph_0. Also, aleph_0 * aleph_0 =aleph_0, 2*aleph_0 =aleph_0, etc.
Now, what do subtraction and division mean? When can we do them?
Subtraction is, essentially, undoing addition. So, 7-3=4 since 3+4=7. This makes sense because there is only one possible number that, when added to 3 gives 7.
In the same way, 12/4=3 since 3*4=12. There is only one number that, when multiplied by 4 gives 12 and that number is *defined* to be 12/4.
Why is 0/0 not defined? Because, for example 1*0=0 and 2*0=0 and 3*0=0. So there is not just one number that, when multiplied by 0 gives 0.
In a similar way, if you divide an infinite quantity (say, aleph_0 ) by 2, you will get that same quantity back. That is because there is only one thing that, when multiplied by 2, gives that quantity. So, aleph_0 /2=aleph_0.
But, it turns out that aleph_0 /aleph_0 is NOT defined because there are many things that when multiplied by aleph_0 give aleph_0.
Anyway, these are often seen as counter-intuitive. And for many people, initially, they are. But they are NOT contradictions. And it is possible to modify intuition to understand how these infinite quantities work.
Once again, these are NOT deep things. Every math major has to learn them as an undergraduate. If you are interested, I can point to some good references (or even start a new thread), but it requires some diligence to understand if you need to modify your intuition.
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