Universe can't be infinite.

[devans99]

Eternalism+Finitism is testable and it makes predictions:

- A start of time. The big bang is evidence for this.
- Past present future all real. The quantum eraser experiment is evidence.
- The massive amount of experimental data supporting Relativity is also supporting evidence.

You call my ideas metaphysics but they are just logic and science should care about logic. There should be no scientific theories that defy logic. Actual Infinity and eternity are logically inconsistent ideas so they should not form part of scientific theories.

Deduction does need a starting point you are correct. I guess I mean a minimalist starting point. For example admission of truly self-evident truths as axioms. For example:

‘I think therefore I am’ - qualifies as a self evident axiom:

- I think therefore I am
- AND You think therefore you are
- SO we both exist

- We remember the past
- AND we experience the present
- AND we predict the future
- SO time exists

- Actual infinity is impossible so time must have a start
- If time had a start, Presentism is impossible and eternalism applies
- Every moment of time requires a preceding moment so time is a closed loop

[TimeSeeker]

Eternalism+Finitism is testable and it makes predictions

Yes. That's a tautology. Without finitism there are no such things as predictions.
A theory that predicts everything predicts nothing and therefore worthless.
Equivalently: a theory that predicts nothing is just as worthless.

Predictions must be finite, else they are unfalsifiable and the falsifiability criterion is mandatory.
If you don't know how to falsify your own ideas - you have scored an own goal. That is the mechanism by which confirmation bias manifests.

In fact one could argue that there is indeed an argument for God.

God predicts the existence of The Universe. But it predicts everything - so it predicts nothing

- A start of time. The big bang is evidence for this.

Yes, but The Big Bang is inferred FROM evidence. And so you need to review that evidence and see if it supports your new theory

- Past present future all real. The quantum eraser experiment is evidence.
- The massive amount of experimental data supporting Relativity is also supporting evidence.

I am not disputing ANY of that. The bug is in the scientific method itself!

What does it mean to "predict" things without a conception of "time" ?

Is a prediction not "guessing the future value of some variable at time + N".
Uh eh, future? In respect to what? Now? Ok.
time + N? N of WHAT? Seconds?

Do seconds exist and how do we know that it's a discrete, not a continuous phenomenon? What if time is irregular? Different things oscillate at different frequencies and while there is a limit to the highest frequency as per the Planck constant there sure is a whole lot of variance in the spectrum!

You call my ideas metaphysics but they are just logic and science should care about logic. There should be no scientific theories that defy logic.
Actual Infinity and eternity are logically inconsistent ideas so they should not form part of scientific theories.

And reality should care about logic why?
Also - which logic should reality care about? Modal, temporal, constructive, multi-value, fuzzy, mathematical?

We have invented very many logics. They operate by different rules and have different properties. Which of our man-made logic rules should reality care about exactly?

Deduction does need a starting point you are correct. I guess I mean a minimalist starting point. For example admission of truly self-evident truths as axioms. For example:

‘I think therefore I am’ - qualifies as a self evident axiom.

So if you don't think you aren't? Maybe what you are doing is "reasoning" not "thinking"?
How do you determine that what you are doing is, in fact "thinking" and not "reasoning" ?

- We remember the past
- AND we experience the present
- AND we predict the future
- SO time exists

Or we EXPERIENCE time. To claim existence is metaphysics.

- Actual infinity is impossible so time must have a start

By criteria for "impossibility" defined by humans

- If time had a start, Presentism is impossible and eternalism applies
- Every moment of time requires a preceding moment so time is a closed loop

A closed loop is a feedback loop. There is no beginning/end there. Unless you pick one arbitrarily.

[devans99]

Nature is deeply logical. We have found nothing in nature that it illogical. There are some things we don’t understand but that does not mean they are illogical it just means we have not worked them out yet. So actual infinity/eternity has no place in nature because they are illogical. They have no place in science because they are illogical.

Thinking is just another word for reasoning. ‘I reason therefore I am’ if you prefer. The axiom implies nothing about those who do not think.

All I claimed that was that something called time exists. This is evident from the fact that things do not all happen at the same time but have an order. I just gave it a name without specifying any properties.

You’d would rule out magic from scientific theories would you not? Why then would you not rule out Actual Infinity? An example of actual infinity would be the cardinality of the set of natural numbers. If thats not pure magic, I’m not sure what qualifies as magic.

The Big Bang/Big Crunch is the natural point to designate as the start/end of time.

[TimeSeeker]

Nature is deeply logical. We have found nothing in nature that it illogical. There are some things we don’t understand but that does not mean they are illogical it just means we have not worked them out yet.

OK. What do you mean by 'logical'? What is your criterion for discerning 'logical' from 'illogical' ?
It seems to me that you are mistaking the causal chain here? The universe came long before logic.

Why must the universe be logical? Shouldn't logic be universal rather?

So actual infinity/eternity has no place in nature because they are illogical. They have no place in science because they are illogical.

Again. What do you mean by 'illogical'? The moment we SUCCESSFULLY DEFINED "infinity" and we defined the rules by which it interacts with other things (even itself) it is (mathematically) real. And if any object in reality BEHAVES in the same way that infinity BEHAVES in the equation, then that real-world object is "infinity".

Now you are probably going to object that this is not what you "mean" by infinity, but mathematics doesn't care about the incongruity between what you THINK and what you DEFINE.

If you find an object in reality which when added to itself produces itself then that's "infinity". Or "zero" (not sure how you would tell them apart).

If you accept the inequality ∞ + 1 > ∞ to be "true" then ANYTHING in reality matches that description!

Mathematics computes consequences. Nothing more. Nothing less.

Thinking is just another word for reasoning. ‘I reason therefore I am’ if you prefer. The axiom implies nothing about those who do not think.

OK. How do I determine whether I am reasoning or thinking?

All I claimed that was that something called time exists. This is evident from the fact that things do not all happen at the same time but have an order. I just gave it a name without specifying any properties.

Right. So sequencing. What about things that happen in EXACTLY the same time, but have no causal effect on each other. Is that evidence that multiple time-dimensions exist?

You’d would rule out magic from scientific theories would you not? Why then would you not rule out Actual Infinity? An example of actual infinity would be the cardinality of the set of natural numbers. If thats not pure magic, I’m not sure what qualifies as magic.

Strawman. I am not talking about magic. Only determinism/computability.

Can you build a mechaism (function? algorithm?) which determines the cardinality of a set?

I will reduce this down to decision theory again:

Suppose I ask the question: Is the cardinality of any given set infinite? It's a yes/no question.

decision.png

What INPUT and what procedure do you propose such that it determines the answer is "Yes" for natural numbers?

Here's a fun challenge. Use the Margolus-Levitin theorem to contrive some algorithm which generates the biggest possible number in the <max age of the universe> (I wonder if anybody in comp sci has done this yet!)

The Big Bang/Big Crunch is the natural point to designate as the start/end of time.

Then you need to message your favourite science and object to the SI units of time being defined in terms of the caesium-133 atom!

Caesium-133did not exist AT the time of the Big Bang.

[devans99]

Logical means we can model and discuss with logic and maths. I think what I am pointing to, a complete lack of illogicality in nature, is inductive evidence that nature is logical. It’s very strong inductive evidence against infinity and eternity. Nature simply does not do insoluble paradoxes whereas infinity and eternity abound in insoluble paradoxes.

As I said earlier, anything that you can add to and not change is deeply illogical and runs against all the laws of nature. We will never find anything you can add to and not change. So I don’t see how anyone can claim infinity is useful or logical.

What about Hilbert’s Hotel? Do you claim this models real life hotels in some way? Surely the whole point of Hilbert’s Hotel is to demonstrate how stupid the idea of infinity really is?

You can never determine the cardinally of an infinite set because infinite sets don't exist. The set of natural numbers:

{ 1, 2, 3, 4, 5, ... }

Has no end so it's not completely defined. So it is not defined. So you can't work with it (reliably) mathematically or computationally.

[TimeSeeker]

Logical means we can model and discuss with logic and maths. I think what I am pointing to, a complete lack of illogicality in nature, is inductive evidence that nature is logical. It’s very strong inductive evidence against infinity and eternity.

OK, but you missed the point! Mathematics doesn't care. If you define it and you are MANIPULATING IT MATHEMATICALLY it exists!

Nature simply does not do insoluble paradoxes whereas infinity and eternity abound in insoluble paradoxes.

Until you define them. Like complex numbers. Then they exist as mathematical objects.

As I said earlier, anything that you can add to and not change is deeply illogical and runs against all the laws of nature. We will never find anything you can add to and not change. So I don’t see how anyone can claim infinity is useful or logical.

Negative numbers, zero, complex numbers! All fit your definition of illogical then.

What about Hilbert’s Hotel? Do you claim this models real life hotels in some way? Surely the whole point of Hilbert’s Hotel is to demonstrate how stupid the idea of infinity really is?

Again. This is a philosophical word-soup. It is a SYNTACTIC/SEMANTIC error. Hilbert takes the conceptual notion of infinity, not the behaviouristic notion of infinity.

If a hotel can take extra occupants then it's NOT fully occupied, is it?
A fully occupied infinite-room hotel is an oxymoron.

Focus on how it INTERACTS with other symbols. That is its true meaning. The INTENDED meaning doesn't matter.

If you can define "infinity" in software and you can perform computation/operations on it:
1. It's not the conceptual infinity ( cardinality of natural numbers)
2. It exists mathematically

Computers are FINITE state machines.
Your mind is a FINITE state machine.

And yet you are computing infinity. So it's not "real infinity", but it doesn't matter! It's a real, mathematical object which you have MISTAKEN for infinity.

[devans99]

Negative numbers, zero, complex numbers are all logical. If you add 1 to any of these quantities it changes the original quantity.

Its only infinity you can add to and not change.

∞ + 1 = ∞
implies
1 = 0

How can you defend the above? It is the the most simple and complete proof by contradiction that actual infinity does not exist. We can’t find infinity in nature. It’s not part of maths. It’s completely mad. Why do you want it in science?

[TimeSeeker]

Negative numbers, zero, complex numbers are all logical. If you add 1 to any of these quantities it changes the original quantity.

Its only infinity you can add to and not change.

∞ + 1 = ∞
implies
1 = 0
How can you defend the above? It is the the most simple and complete proof by contradiction that actual infinity does not exist. We can’t find infinity in nature. It’s not part of maths. It’s completely mad. Why do you want it in science?

I defend it like this.

∞ + 1 > ∞
implies
1 > 0

The = is broken

[devans99]

Negative numbers, zero, complex numbers are all logical. If you add 1 to any of these quantities it changes the original quantity.

Its only infinity you can add to and not change.

∞ + 1 = ∞
implies
1 = 0
How can you defend the above? It is the the most simple and complete proof by contradiction that actual infinity does not exist. We can’t find infinity in nature. It’s not part of maths. It’s completely mad. Why do you want it in science?

I defend it like this.

∞ + 1 > ∞
implies
1 > 0

The = is broken

So what does ∞ + 1 evaluate to?

[TimeSeeker]

So what does ∞ + 1 evaluate to?

I am a scientist, not a computer. I test things.

Testing for inequality is WAY easier than testing for equivalence!

Go ahead and tell me if any two things are "the same" as each other! We end up in the realm of computational complexity.

Irrespective of what Mathematics tells you - I assert that ∞ + 1 > ∞ is TRUE.

And if that disagrees with some axiom, then I guess I have invented new Mathematics, with new axioms.

[devans99]

So what does ∞ + 1 evaluate to?

I am a scientist, not a computer. I test things.

Testing for inequality is WAY easier than testing for equivalence!

Go ahead and tell me if any two things are "the same" as each other! We end up in the realm of computational complexity.

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

∞ + 1 = ∞
implies 1 = 0


I know why this all happened. You know the spinning head feeling you get when you think about infinity? Cantor was very religious and he thought that feeling was something to do with perceiving God. That feeling is actually just your mind barfing on a very illogical concept, but Cantor went ahead and got actual infinity baked into maths. There was a big argument at the time about it but people were very religious in those days so the Finitists lost and the religious folk won. We are left with a spiritually inspired (to put it politely) branch of maths. Set theory is just a joke.

[TimeSeeker]

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

∞ + 1 = ∞
implies 1 = 0


I know why this all happened. You know the spinning head feeling you get when you think about infinity? Cantor was very religious and he thought that feeling was something to do with perceiving God. That feeling is actually just your mind barfing on a very illogical concept, but Cantor went ahead and got actual infinity baked into maths. There was a big argument at the time about it but people were very religious in those days so the Finitists lost and the religious folk won. We are left with a spiritually inspired (to put it politely) branch of maths. Set theory is just a joke.

OK then I guess you can credit me with inventing brand new mathematics where ∞ + 1 > ∞ is TRUE and ∞ + 1 is non-computable.

It's probably useless, but hey. At least I can get some academic credit!

[TimeSeeker]

P.S I agree with you that set theory is bullshit (or rather, it's not universally applicable). Which is why I said earlier that I come from Type Theory/Proof theory background.

In type theory ∞ + 1 = ∞ is NOT an evaluation, it is a proposition. And as a proposition it could be true, or it could be false.
And the algorithm you propose such that it can be asserted if ∞ + 1 = ∞ is "true" or "false" is the proof of your proposition.
This is straight out of https://en.wikipedia.org/wiki/Curry–How ... espondence

And let me tell you, the "=" proposition is rather hard in practice because computational complexity.

Here is a demonstration.

I propose that A.jpg = B.jpg. Is that true or false?

A.jpg

B.jpg

One way to do it is to sit and compare pixel-by-pixel!

Another way to do it is to employ the principle of least effort and test the alternative hypothesis.

Suppose that A.jpg = B.jpg is True. Can you find ANY evidence to the contrary?

[devans99]

The operator = on JPEGs I’ll define as all the bits are the same and the file size is the same.

So I can then say that A.jpg = B.jpg is true.

Note:

A.jpg + 1 bit <> B.jpg

So JPEGs conform to reality (unlike infinity).

If we return to

∞ + 1 = ∞

Which gives 1=0. So lets assume the above is NOT true, one of the following must be true:

∞ + 1 < ∞
∞ + 1 > ∞

The first is nonsense. The 2nd implies infinity is not infinity. It implies there is something bigger than infinity which is impossible according to the definition of infinity (Cantor’s diagonal proof is bollocks BTW).

So whichever way you turn, infinity leads to contradictions. These contradictions are actually proof via contradiction that infinity does not exist.

[TimeSeeker]

The operator = on JPEGs I’ll define as all the bits are the same and the file size is the same.

So I can then say that A.jpg = B.jpg is true.

And you would be wrong. Here are the SHA512 checksums for each file.

35d7a2e3fe6d17c98c3fe3cb4b816d30b550f13d3e61f21eb35d798a6e08141b24cde9432425f50c62233eff968c20841cfa41a5c7c8e245d83129622ca1989c A.jpg
b89bbd1626a735e08aedcd217d07500d10fdca06b27ce4f173dd95349f0dbb7248453468066e0f8db59cbfebeb5736ee18033026fb01ac1f02514992c9dc2b03 B.jpg

You can't tell me HOW they are different, only that they ARE different. With probability of being wrong of 1 in 2^512.

The first is nonsense. The 2nd implies infinity is not infinity. It implies there is something bigger than infinity which is impossible according to the definition of infinity (Cantor’s diagonal proof is bollocks BTW).

You are still missing the point. Mathematical equations are propositions.

1 = 1 is a proposition, not an evaluation.
∞ + 1 = ∞ is a PROPOSITION, not an evaluation.

There are two ways to assert its "truth" or "falsity".

You can either derive it as a theorem from previous axioms OR you can consider it as axiomatic and then see what happens. Whether it unifies with the rest of mathematics is neither here nor there. Maybe it doesn't. So what ? If using ∞/∞ = 2 in your equation makes it agree with experiment then whatever!

Yes, you have tossed the law of non-contradiction out. But your equation works! Use it as it is. Then figure out how to fix it later. It's just a fudge factor because mathematical equations are implicit, not explicit.

Which is exactly what QM did: https://en.wikipedia.org/wiki/Renormalization