Evidence for a god. Do you have any ?

[polymath257]

I know you like to think that I couldn't address your points, despite the effort and patience it took me to respond to pretty much all your responses to me in that thread. And I also know how much you love to project. It's you who gets in way over your head, and you see it in others instead.


And here we're at it again. Oh, well, I guess I'll have to try responding again (because why not).

The problem, Steve, is that indeterminacy does NOT mean logical contradiction.

0/0 is indeterminate. Does this mean an actual zero of real objects is logically impossible? Of course not.

Math is one thing, "plain English logic" is another thing. If you conflate both systems, you're just going to get yourself confused. How about using "plain English logic", via some reductio ad absurdum argument, you demonstrate to us that an actual infinity of things is logically impossible?

You also have to remember that infinity is not a real number (in the sense that it is an element of the set of real numbers). It's a concept that is related to quantities of things, just like "finity". So when you're doing addition or subtraction or whatever on infinity, it's not really the same as doing these operations on real numbers. It's more like doing operations on ideas that could mean a lot of things without context.

If you look at the concept of "finity", for example, "finity" - "finity" could be any real number as well. But we don't know which one until we have a clearer context. Similarly, we can't know what "infinity" - "infinity" is exactly without context. Mathematically speaking, we say the answer is indeterminate.


What do you mean by "fundamentally different"?

If I have four apples, and you take two away from me, I'm left with two apples, right?

In this case, "finity" - "finity" = 2.

If, on the other hand, I have four apples, and RR took three apples from me, that's "finity" - "finity" = 1.

You have two different answers to "finity" - "finity". Does this mean that a finite number of real objects is logically impossible? Of course not.

What in the world are you talking about? I know you get kudos for some of your posts--but that's usually just because you replied to me--not that you made a point that anyone actually understands.

Your whole counter argument is:

A. Let's not call them logical contradictions--let just say they are 'indeterminate'. 
B. Indeterminate is not the same as logically impossible
C. Therefore an actual infinite is possible.

That is HORRIBLE logic.

Fortunately, that is NOT the logic. We define addition and multiplication in very specific ways. Addition by the cardinality of a disjoint union and multiplication by the cardinality of the collection of ordered pairs. These are the fundamental definitions and are common to both finite and infinite quantities.

Subtraction and division are defined in terms of addition and multiplication *in those cases where the result is well-defined*. So, we say that 5-3=2 because 3+2=5 and the only number with 3+x=5 is the number 2. We say that 15/3=5 because 3*5=15 and the only number with 3*x=15 is the number 5.

Now, there are cases where the existence and uniqueness of the required solution are not true and in those cases *we do not define subtraction and division*. So, 3*0=0 and 5*0=0, so we do not define 0/0. It is a case where there is more than one solution to 0*x=0, so division is not defined in this case.

In the same way, subtraction of infinite cardinals is not always defined. So, if A is the cardinality of the set of counting numbers, it is true that A+2=A and A+5=A and A+A=A. All this means is that A-A is not well defined.

On the other hand, if C is the cardinality of all decimal (real) numbers, then the only cardinal with A+x=C
is x=C, so in this case, C-A is defined and, in fact, C-A=C.

Technically, when we say that a certain operation is indeterminate, we really mean it isn't well defined. And logic requires something to be well defined *before* we can say anything about it.

The demonstration that infinities are consistent (no *logical* problem) is a different one and is substantiated by the math of the past 150 years.

Again, this implies the A-theory of time is true. So even if you have successfully shown a problem in this argument against traversal of actual infinity, you're making the wrong assumptions on time.

I mean, I've told you this so many times, Steve. I don't know why you keep bringing this up like a broken record, lol. 

NOPE. Answered that too:

B THEORY OF TIME
Another argument that has been made is that if the B Theory of Time is correct, spacetime is infinite in extent. But there is nothing in the theory that says our spacetime is infinite in the past. To get that, you must also posit an infinite cosmology model. But such models are not thought to be the best candidates for our universe, so, while possible (broadly speaking), there are not good reasons to believe this to be the case. But, such a combination of theories seems possible, so then doesn't that show that an actual infinity is possible. No, not at all.

Under any theory of time there is some sequence that is countable whether you call it causes/connection/light cones/changes in entropy/states of affairs/or whatever. I'll call it causal connections (but insert whatever you want).  Any timeline would show that the causal connections that created the present were preceded by causal connections which were preceded by causal connections for an infinite series in the prior-to direction. If you posit an infinite number of these causal connection going back, you have a problem. How could we have traversed through an infinite number of sequential causal connections to get to the one that caused the present (causal connection 5, 4, 3, 2, 1, 0)? There will always have to be infinite more causal connections that still need to happen. We will never arrive at the present.

No, at any point in that sequence, there are only finitely many more steps to take to get to 0. So, if I am at 100, there are only 100 steps to take to get to 0. At no stage in this process are there infinitely many steps to get to 0.

To illustrate it with a thought experiment, imagine a being who is counting down from eternity past to the present: 5, 4, 3, 2, 1, now. How is that possible? Wouldn't he have an infinite amount more numbers to get through to get down to 3, 2, 1? If you insist that this could be done, why didn't he get done 1000 years earlier or for that matter, an infinite time ago?

In this, you are assuming there is a *start*. That is the faulty assumption. What happens is that this being is simply always counting. At any point in time, there is a definite place in the counting that is being done.

Your problem is simply that you don't understand that an infinite regress has no start. It is simply always going.