A Good Infinite Regress Step of Some Cosmological Arguments

[Immanuel Can]

Here's something you could look at on Hilbert. It's quick and fun.

You linked to a vid about the Hilbert hotel?

I was assuming perhaps your knowledge was introductory. If I was wrong, I apologize.

Would you have preferred this:
https://arxiv.org/pdf/1403.0059.pdf
It's a more complete treatment of the subject, but assumes a certain degree of familiarity with concepts.

I'm having a hard time guessing your level of knowledge. If I get technical with the explanations, then I'm in danger of being pedantic. If I keep it simple, apparently I'm insulting your intelligence. There isn't much of a space for error in there, and if I guess wrongly, I would ask you to put it down to the fact that we're operating only by email and don't know each other. No insult intended.

P.S. "I feign no hypotheses" (Newton) is not a rejection of hypotheses. It's a rejection of feigned ones. That's a key distinction. You represent Newton as rejecting the Scientific Method.

[Immanuel Can]

Or perhaps if time is not part of the universe (as you obviously assume), then it is something not created by God, in which case we're back to that infinite regress thing again which you find impossible.

Non-sequitur. It does not follow that if there is an "outside of time" situation, that causality is possible to posit there. There would be no way of knowing what postulates are appropriate to the universe prior to its creation. Our science only works within the available laws. But the laws themselves would have had to come into existence at that moment.

Once again, what we know for sure is that there was, and can have been, no infinite regress of causes (which IS a feature of the known universe, by the way): so the universe had to have an origination point.

[uwot]

"I feign no hypotheses" (Newton) is not a rejection of hypotheses. It's a rejection of feigned ones. That's a key distinction. You represent Newton as rejecting the Scientific Method.

You really don't know what you are talking about. Here's what Newton said in a bit more context:
"I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy."
As you might now be able to discern, Newton explicitly rejected any hypothesis as unscientific.
As for "Scientific Method", that is just another of those things you believe you can make real by capitalising it. There is no "Scientific Method" you dolt.

[wtf]

Would you have preferred this:
https://arxiv.org/pdf/1403.0059.pdf
It's a more complete treatment of the subject, but assumes a certain degree of familiarity with concepts.

That wouldn't help at all, because you still haven't said (because you don't actually know) what Hilbert said that supports the point you were making when you name-checked him. The Hilbert hotel is just a restatement of Galileo's paradox. It's a thought experiment to illustrate the fact that an infinite set can be put into bijection with a proper subset of itself. So you are only confirming my observation that you should simply retract your Hilbert remark or else supply a reference specifically on target to the point you were trying to make.

I'm having a hard time guessing your level of knowledge. If I get technical with the explanations, then I'm in danger of being pedantic. If I keep it simple, apparently I'm insulting your intelligence. There isn't much of a space for error in there, and if I guess wrongly, I would ask you to put it down to the fact that we're operating only by email and don't know each other. No insult intended.

Your remarks about the digits of pi show that you don't know much basic modern math. That's not a crime, especially in a forum for the philosophy of religion, about which I am totally ignorant myself. I admit I have taken your tone to be very condescending. Your "Google Hilbert" remark really set me off, since Hilbert was a prolific mathematician. So if you name-check Hilbert but can't say which specific idea of his supports your point, that tells me something about your own level of knowledge.

If no insult is intended then I appreciate your saying that.

P.S. "I feign no hypotheses" (Newton) is not a rejection of hypotheses. It's a rejection of feigned ones. That's a key distinction. You represent Newton as rejecting the Scientific Method.

If you don't understand the point that's fine. This is a very famous quote and illustrates Newton's deep understanding of the nature of science. And for what it's worth, volumes have been written about the translation from Latin into modern English of the word "framed" versus "feigned." It doesn't affect the essence of Newton's profound point.

[Arising_uk]

...
Would you have preferred this:
https://arxiv.org/pdf/1403.0059.pdf
It's a more complete treatment of the subject, but assumes a certain degree of familiarity with concepts. ...

It appears obvious that IC is a Craigite but he might have some insight so I look forward to him rebutting this -
http://digitalcommons.unl.edu/cgi/viewc ... ilosfacpub which is a response to Craig's second axiom and its use of Hilbert’s Hotel Argument(HHB) to promote a version of the cosmological argument for a 'God'.

[wtf]

...
Would you have preferred this:
https://arxiv.org/pdf/1403.0059.pdf
It's a more complete treatment of the subject, but assumes a certain degree of familiarity with concepts. ...

It appears obvious that IC is a Craigite but he might have some insight so I look forward to him rebutting this -
http://digitalcommons.unl.edu/cgi/viewc ... ilosfacpub which is a response to Craig's second axiom and its use of Hilbert’s Hotel Argument(HHB) to promote a version of the cosmological argument for a 'God'.

I've run across Craig's argument and it always impresses me as the worst kind of sophistry. If Craig is explicitly referencing the Hilbert hotel story that puts IC's comments into context. Thanks for that link, I'll take a look. Hilbert's hotel is just a simple story intended to illustrate the fact that an infinite set can be put into 1-1 correspondence with a proper subset of itself. It's a popularization of a fact of basic set theory. It has no evidentiary value in theology.

It's worth noting that the mathematics of infinity begins with the Axiom of Infinity, which states that an infinite set exists. (Technically it says a little more, namely that an infinite inductive set exists, namely the natural numbers). Once you accept this, everything else follows. The Axiom of Infinity is independent of the other axioms of set theory and you can assume its negation just as easily. it's harder to do math, but it's still logically consistent.

It's sad that Hilbert's little popularization has been taken as some kind of profound mystery by so many people. It's really the Axiom of Infinity that's the culprit.

https://en.wikipedia.org/wiki/Axiom_of_infinity

[Arising_uk]

If you want to understand where IC's coming from then his link has a bit on the HHA and it's use in Theology near the end.

[Arising_uk]

... Hilbert's hotel is just a simple story intended to illustrate the fact that an infinite set can be put into 1-1 correspondence with a proper subset of itself. ...

As a poor philosopher of science and mathematics and an even poorer mathematician this always gobsmacks me.

Although I never quite got past Cantor - from a philosophical point of view - as I thought him cheating by creating new number(integer?) symbols as though they were numbers(integers?). Told you I was poor.

[wtf]

... Hilbert's hotel is just a simple story intended to illustrate the fact that an infinite set can be put into 1-1 correspondence with a proper subset of itself. ...

As a poor philosopher of science and mathematics and an even poorer mathematician this always gobsmacks me.

Galileo made the same observation hundreds of years earlier. https://en.wikipedia.org/wiki/Galileo's_paradox

In fact we can take this as the very definition of an infinite set. A set is infinite if it can be put into 1-1 correspondence with a proper subset of itself. That's a beautiful bit of mathematical thinking. We take a counterintuitive mystery and turn it around into a basic definition. Now we divide the world of sets into those that can be put into 1-1 correspondence with a proper subset of themselves, and those that can't. The former we call infinite sets, the latter we call finite sets, and the mystery is gone. One is free to deny the existence of infinite sets entirely if one chooses. Finitism and its extreme cousin ultra-finitism are fascinating branches of the philosophy of math.

Although I never quite got past Cantor - from a philosophical point of view - as I thought him cheating by creating new number(integer?) symbols as though they were numbers(integers). Told you I was poor.

What Cantor did was to take Aristotle at his word, and then simply posit the existence of a completed infinity. Once you do that, everything else follows. That was Cantor's great conceptual breakthrough, to take the natural numbers as a completed set. Because once you do that, you can take its powerset and bam, you've got an endless hierarchy of infinities.

Thanks for the Craig reference. If Craig uses the Hilbert hotel story and IC is implicitly following Craig, then IC's discourse suddenly makes sense to me. It's still wrong, but at least now I know why IC is invoking Hilbert.

[Arising_uk]

Yeah, Hilbert's fast becoming the new Einstein for the religious weebles and internuts.

[ken]

But the point is the one prior HAS already happened, obviously. If there is some thing happening NOW, then obviously some thing happened prior, so on, infinitely. Nothing hard at all to grasp that most basic of wisdom.

My last response to "wtf" above will help clarify, if you have time to read it.

The only thing you are clarifying more and more is just how strongly you want to hold onto your belief.

If your belief is right or wrong does not play into any part of this. You will just keep fighting and fighting for your belief. The reason you keep reinstating the nonsensical things that you are is because of that belief.

[ken]

So what is this 'undoubtedly' thing of which you speak? I can't take it out of context since you really gave none.

Since infinite regression of causes is impossible, it is beyond doubt that there was a time when the universe did not exist. That's what I meant.

HOW is an infinite regression of causes impossible?

WHY is it beyond doubt that there was a time when the Universe did not exist.

Are you defining a view you don't hold?

I'm speaking about the follies of Materialism. I thought I was clear about that...

...the invalidity of your arguments against it.

Please show the invalidity point.

To Me, the invalidity point is your argument is based on an "experiment", where one is not permitted to write a number until you have written the previous number. That in itself does not provide conclusive reasons for your conclusion that there was an uncaused causer of the Universe.

IF the truth be known, your "experiment" further concludes an infinite regression of causes IS true. If the reason one can not write a number until the previous number is written first, then this is because the numbers go on infinitely. If, however, there was a 'stop' somewhere along the chain of numbers, then there would be a place where one could at least start and begin to write a number. If there was a beginning, then one could begin. But one can not begin anywhere. There IS an infinite regression of numbers, just like there probably is an infinite regression of causes.

[Immanuel Can]

HOW is an infinite regression of causes impossible?

Don't believe me.

Try the experiment yourself. Go on. I'm quite serious.

Write 5, but not until you've written 4, but not until you've written 3...and so on to infinity.

If you can do it, I'm wrong. I'll be happy to admit it.

But now, go and do it. Then you will know. Not because anybody says so, but because you tested it.

To Me, the invalidity point is your argument is based on an "experiment", where one is not permitted to write a number until you have written the previous number. That in itself does not provide conclusive reasons for your conclusion that there was an uncaused causer of the Universe.

That's valid. "Cause" means that the effect cannot happen until after the cause does. So that's like 5 and 4. But the cause at 4 can't happen until ITS cause happens. That's like 4 and 3....and so on.

It's perfectly easy. Just do it. Go on.

[wtf]

That's valid. "Cause" means that the effect cannot happen until after the cause does. So that's like 5 and 4. But the cause at 4 can't happen until ITS cause happens. That's like 4 and 3....and so on.

It's perfectly easy. Just do it. Go on.

So that I can better understand your argument, suppose I pick up a pencil and write down the numeral (not the number!) 5. Before I can do that I must have a pencil made of wood, so I needed a tree. Before the tree was the earth, and before the earth was the sun either capturing planets or ejecting matter that coalesced (I'm not up on my planet creation science) and eventually we need the big bang.

If I grant you that, what is your conclusion? I just want to understand your basic argument. Are you saying the age of the universe must be finite? Or it could not have started? What is the conclusion you draw from assuming (in the technical sense of making an assumption in a philosophical argument) that you must run this chain of causality forward from the past instead of backward from the present?

Just to be absolutely clear. I'm not arguing any point at all here. I just want to understand what you're saying. Suppose your argument shows that I can't write down the numeral 5. What does this prove?

[ken]

HOW is an infinite regression of causes impossible?

Don't believe me.

Try the experiment yourself. Go on. I'm quite serious.

Write 5, but not until you've written 4, but not until you've written 3...and so on to infinity.

If you can do it, I'm wrong. I'll be happy to admit it.

But now, go and do it. Then you will know. Not because anybody says so, but because you tested it.

I have tested it already. You are right I can not write any numeral down. But My findings are the exact opposite of what you were hoping I would find.

Did you read what I wrote?

I wrote;

"IF the truth be known, your "experiment" further concludes an infinite regression of causes IS true. If the reason one can not write a number until the previous number is written first, then this is because the numbers go on infinitely. If, however, there was a 'stop' somewhere along the chain of numbers, then there would be a place where one could at least start and begin to write a number. If there was a beginning, then one could begin. But one can not begin anywhere. There IS an infinite regression of numbers, just like there probably is an infinite regression of causes."

I discovered this AFTER I tried and tested your experiment.

Did you notice I can not do it, as you were suggesting, but to Me that just makes you convoluted argument more unsound?

Your experiment provides further evidence that an infinite regression of causes is much more likely to be true, than an uncaused causer starting a chain of causes is.

By the way you still did NOT answer My question, "HOW is an infinite regression of causes impossible?"

You also did not answer My other question, "WHY is it beyond doubt that there was a time when the Universe did not exist"?