Evidence for a god. Do you have any ?

[polymath257]

And here are my posts that you could not address because you got in way over your head:

1. An actual infinite consists of real (not abstract) objects.
2. In 100% of our experiences and 100% of our scientific inquiries, quantities of real objects can have all the operations of addition, subtraction, multiplication and division applied to them.
3. As Hilbert's Hotel shows, these operations cannot be applied to the concept of an actual infinite without creating contradictions and absurdities
4. Classical propositional logic does not allow for contradictory statements to be true.
5. Therefore an actual infinite of real objects is logically impossible.

Infinite set theory is not a defeater for (2) because infinite set theory is not itself a conclusion derived from a logical process. To defeat (2) you have to give logical reasons why we should expect an infinite quantity of objects to behave fundamentally different than a finite quantity of objects.

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1. An event is a change in a real object
2. From any point in the past, there is a finite amount of events to the present and can be counted down en...e3...e2...e1...e0(now).
3. If there are an infinite amount of events in the past, we could never count down from infinity to e3...e2...e1...e0 because there would always be an infinite amount of events that would still have happened on the leading edge of the series.
4. With an infinite series of past events we could never arrive to the present.
5. Therefore an actual infinite series of past events is impossible.

We can expect an infinite quantity to have different properties than finite quantities because they are different things. And, arguing logically from the properties of infinite quantities, we do, in fact, find that they are different in their arithmetic from finite quantities.

Your first 2 is simply wrong. Science uses those operations when they are useful for explanations. But there is no reason that the allowed explanation't have more than just those properties of finite sets.

Hilbert's hotel just shows that the properties of infinite sets are different than those for finite sets. But there is no *logical* contradiction: just a violation of intuitions derived from finite quantities. Again, that is to be expected because infinite quantities are not the same as finite ones: we expect differences.

Once again, we *know* that things like the Hilbert Hotel are paradoxes only, not actual contradictions. The rules for finite sets are violated, yes. But there are consistent rules which can be applied to infinite sets.

In your second list, 1 and 2 are true. In 3, you are assuming that there is a first event from which to count. That is exactly the point: there is no first event. There are only finitely many events between any two, but there are still an infinite number of events. That is not a contradiction. There is no *start* from which the counting begins. there is just always counting.

And 4 and 5 are derived from your mistake in 3, and are invalid.

Once again, you show no logical contradiction, just a violation of your intuitions from finite sets. But we *expect* infinite and finite collections to work differently because they are different.

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Once again, there is no *logical* contradiction with an actual infinity or infinite regress. It is a question of science whether either turns out to be the case. But that goes beyond mere logic to a question of observation.


The axioms and their lack of self-contradiction show that there is no *logical* issue with infinities.They differ from finite quantities, clearly, but there is no actual contradiction. So, assuming standard two-valued logic along with quantifiers, there is no logical issue with there being infinities that are 'completed'. That said, there is a lot of very poor philosophy about infinity that was done prior to Cantor's work. ANYTHING concerning infinity should take that work into consideration.

If the underlying assumptions or premises are illogical or have a contradiction, then there is a problem at the very foundation.   Now I will agree, that we can have an abstract concept of and actual infinity, and you can extrapolate out an infinite process.  We must have an abstract notion of an actual infinity as we are discussing it.  It would seem that you are either modifying the terms, and thus talking about something else, or that you have  contradiction.  You cannot have a quantity of things, that is both endless, and complete. It cannot exist  You can have a process that goes on without any bounds, but that is a potential infinite.

It doesn't matter how strong the house is, if it is built on sand.

And what I am saying is that your 'contradictions' are not actual contradictions, but merely paradoxes. There is no *logical* issue with a completed infinity. It causes no internal contradiction.

Yes, you can have a collection of things that is both endless (in once sense) and complete (in a different sense). The collection of all natural numbers is an example.

N={n: n is a counting number}

In this, 1, 5, 10, 129747 are all in this set. But 12.4 and pi are not in this set. This is NOT an ambiguous collection. It does NOT need to be listed in order to be a complete set of things. But, in a different sense, it is 'endless' in that there is always a larger number from any one you pick.

This is an *actual* infinity, not just a potential infinity. We can even talk about the even larger infinity of all subsets of this set. This larger set has the 'same size' as the collection of all decimal numbers. Again, this latter is a well-defined set. There is no ambiguity what is in the set and what is not. But it is 'endless' and even 'uncountable' and is a 'larger' set than the set of counting numbers.

This house is built on bedrock. The mathematics of the last 150 years shows that to be the case. The problem is that you are confusing the finite with the infinite and NOT using logic. If logic is done *properly*, there is no problem.