There are more reals than naturals though, so which kind of number do you mean? — Pfhorrest

Me? Any will do, depending on context I suppose.

ℵ₀ is a quantity that's not a real number, and ℵ₀ is the quantity of naturals/integers/rationals
ℵ₁ is a quantity that's not a real number, and ℵ₁ is the quantity of reals

It was really just a colloquial "definition", pointing out that ∞ ∉ R, |R| is ∞

How's this, then?
Loosely, ∞ is a quantity that's not a number, and one ∞ is the quantity of numbers.

To simulate the universe in every detail would require more than just the simulation itself, presumably a good deal more, considering what we know about simulations.
Rather unparsimonious, possibly going the way of regress. (Simulations all the way down?)

Otherwise, such a simulation would be targeted specifically at experiencers, animals, us (kind of self-elevating).
So, the Moon would literally not be there when no one was looking, as it were.
This starts to reek of deus deceptor, dream thought experiments, Zhuangzi's butterfly, perhaps solipsism, the usual.

Moving towards such unverifiable-unfalsifiable hypotheses seems like a difference that makes no difference.
It would renders our's a "toy universe" at the whims of the simulators.

You are not able to give a satisfactory reason why the argument does not work, so I will keep posting it; it is a sound argument. — Devans99

A. assume infinite past moments
B. then there's no 1st moment
C. or 2nd ... or nth moment
D. so A can't be numbered with a 1st ... nth moment
E. ?

You allege yours to be a purely deductive proof, yes?
So, show your E (or F) deductively.

Whether A or not, we can (and do) put up a temporal flag pole (say, at 1970-01-01 00:00 UTC) and take it from there. Works fine either way, whether A or not, past and future. In fact, we have to, because we don't know of any definite 1st moment that we can adjust all our clocks to.

I fail to see why you cannot appreciate that an infinite causal regress is like a house without a foundation [...] — Devans99

I'm not so interested in your analogies per se, I'm just pointing out that the argument you keep posting doesn't work.

it is simply impossible [...] cannot exist — Devans99

The argument I've commented on a few times by now does not prove so.

, the worst that can happen if we act, is no worse than doing nothing, but could be better. (Wouldn't it be cool if we don't have to do a thing, and can just forget it and roll ahead?)

The responsible thing to do, is for subject matter experts to go through the motions of sober thorough examination, weighing risks of in/actions (there be ethics), the usual. Like we do with Ebola outbreaks, high-speed traffic, wildlife extinctions, military interventions, garbage disposal, ...

We could, at the very least, go shit where our children eat less frequently, as a start. Does that work as a "compromise"?

No — frank

Has Luboš Motl's theorizing been established (verified and not falsified)?

Why can we not number the elements in a causal regress? — Devans99

Didn't you show with B and C?
We can label events (A) in whichever way we standardize/choose, indexically, but not non-indexically.

Still doesn't follow:

A. Assume an infinite causal regress exists
B. Then it has no first element
C. If it has no nth element, it has no nth+1 element
D. So it cannot exist — Devans99

D. So A cannot be numbered so

Repeating a non-sequitur doesn't somehow make it so.

We have not merely been given the world from our parents, we are also borrowing it from our children. — some proverb

We don't go shit where our children eat either.

What's the worst that can happen if we act on climate change? What's the worst that can happen if we do nothing? What's the responsible thing to do?

I do not believe God is omnipotent. He can't just wave his hand and it be so. He must have generated the universe from something. The Big Bang was probably caused by some sort of device that led to a chain reaction causing all the matter/energy in the universe and the emergence of the 4 forces and the standard model. The device was specified such that a life supporting universe would be the result (IE God did all the calculations first and designed an appropriate device to generate a life supporting universe). — Devans99

Not "atemporal", then. "Atemporal" mind doesn't make sense anyway.

God would not create a universe that is dead for the vast majority of its existence, he would create something self renewing — Devans99

You can come up with falsifiability that we can go out and check tomorrow? (y) (the more the better)

1. So you agree infinite causal regresses are impossible? (see the argument in the OP). — Devans99

You'll have to come up with a different argument for that ↑ one. I'll suggest that you'll have to go by evidence.

Anyway, "the universe turns out fine-tuned to be exactly what it is" doesn't really say much. Kind of tautological. An estimate would have to compare against all possible worlds (cf modal realism). Not sure how you'd go about that.

Hm. Wouldn't the supposed fine-tuner of the universe have to be uniquely fine-tuned to create fine-tuned universes? Surely can't be mere coincidence...? :D

What's with the universal self-elevating self-importance anyway?

Life's but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury,
Signifying nothing. — https://en.wikipedia.org/wiki/Macbeth

By heat death, there will be an unfathomable amount of time (even compared to 14 billion years), ruled by the lonely photon in deep cold. Heavier elements that came out of supernovae will have decayed, and perhaps even black holes will have "evaporated" (Hawking radiation).
The universe seems mostly "designed" or "fine-tuned" as/for vast, open (increasing) spaces, lots of radiation, rocks here and there, gases and suns, maybe some massive gravity wells whose gravity are so strong that light can't escape — and freezing lonely photons.

It does not matter if it the elements can't be numbered — Devans99

Then you'll need a proof without going by that.
FYI, not that it matters much, I harbor no particular personal belief either way.
I'm just pointing out that your suggested proof still doesn't work.

D. So the infinitude in A can't be numbered so — jorndoe

Just thought I'd point out that your D still doesn't follow. :D

A. Assume an infinite causal regress exists
B. Then it has no first element
C. If it has no nth element, it has no nth+1 element
D. So it cannot exist — Devans99

D. So the infinitude in A can't be numbered so

3. An infinite regress of fine tuner’s is impossible* — Devans99

I suppose we can be grateful to some of the Arabs and Muslims for attempting to keep ancient Greek writings alive during the Middle Ages, the Islamic Golden Age (largely prior Omar Khayyam (1048-1131)). They also made discoveries during those times.

Pathfinders: The Golden Age of Arabic Science (2010) by Jim Al-Khalili

Neither logic, mathematics nor the scientific methodologies have any inherent dependencies on Christianity.
That's just hijacking. ("if you can't beat them, join them"?)
Archimedes (-287 — -212), for example, predated Christianity, and contributed significantly to mathematics and physics; in a sense he showed that we can indeed understand things thus, for the benefit of later generations.
Aristotle (-384 — -322) had already expressed basic logic some years earlier.

You think everything has existed forever I think — Devans99

Mind reading fallacy? (I'm entirely irrelevant.)

The almost certain existence of a start of time mandates that something atemporal and intelligent exists. You have to remember that as humans we are only familiar with a small fraction of possible states of existence - God maybe something completely different to what we are experienced with. — Devans99

As shown, we already know some things about mind (versus whatever else), and these are inherently contrary to "atemporal".
Special pleading.
So, we're talking something inert and lifeless, perhaps like Platonia.
By the way, this also violates Leibnizian sufficient reason, but maybe we've tossed that in the bin already?

Hilbert's hotel, ?

Like Shandy's diary, a veridical paradox, i.e. counterintuitive, yet does not otherwise derive a contradiction.

I think of God as some sort of benevolent, timeless architect of the universe — Devans99

Example square circle: "atemporal" mind.

It's more or less the opposite, if you will.

Where body (for example) is object-like and spatial (left to right, top to bottom, front to back, inertial/movable), mind is process-like and temporal (comes and goes, interruptable, experiences, un/consciousness, anesthetic, dementia).

Barring special pleading, "atemporal" thinking sentience is nonsense.

I disagree — Devans99

Sure, which is not proof.

moments are arranged sequently so they must be representable by the real number line or the naturals — Devans99

Maybe?

That is about 5 proofs I've given that time has a start — Devans99

I've just addressed a couple of them — Leibnizian sufficient reason and your mathematical induction (and similar) — neither of which work. No use in repeating them I s'pose. I can show you again why they don't work. Here's the latter again:

1. suppose no definite earliest time, no 1^st moment (premise towards reductio ad absurdum)
2. then there's no 2^nd moment, obviously, since it would be the next number following the 1^st
3. if there's no n^th moment, then there's no n+1^th moment (n ∈ N)
4. thus
4.1. there can be no such moments at all, contra 1 :fire: (n)
4.2. there can be no such numbering of such moments (y)

Vs 0 proofs you have given that time has no start — Devans99

I'm not aware of any such proof. As mentioned somewhere, it's not a mere logical matter.

if you remove a previous moment, all subsequent moments become undefined — Devans99

I take "become undefined" to mean more or less "cannot exist". In the abstract, supposing a (definite) 1^st moment = "removing all previous moments", which then, by this ↑ supposition of yours, implies that "all subsequent moments become undefined".

Repeating won't make this right:

1. Assume time has no start
2. Then there is no first moment
3. If there is no nth moment there is no nth+1 moment
4. But we have moments (contradiction) — Devans99

4. so we have no such numbering of such moments

I'm thinking lack of (or poor) education is a factor.

We know that educated women have less children, for example, so it's a factor in overpopulation in some way.

Someone quite literally told me the other day that, if they broke a leg, they wouldn't head off to the doctor/clinic, "I'm good thanks".
My impression is that they'd just ask Jesus, something like that.
It was just an example; I guess poor education might work both ways.

I am not claiming time is actually numbered, just that in order to think about time, it is useful to have numbering — Devans99

A different deduction, then. Cool, let's have it. (y)
^{(Despite the connotations, mathematical induction is fine as far as deduction goes.)}

If there is no first moment, then there is no time at all — Devans99

Let's have the proof (I mean, not just saying so). (y)

The first moment of time is caused by the creation of space time — Devans99

Everything in time has a cause — Devans99

Subtly switching between moments and causes in mid-run. :meh:
So, "the creation of space time" is supposedly the 1st cause and the 1st moment?
Anyway, let's have the proof instead.

It's not about the numbering of moments — Devans99

Then what's 1st and nth about here? ↓

4. If time has no start, it has no 1st moment. If it has no nth moment, it has no nth+1 moment — Devans99

So, without such a 1st moment, you can't number such moments like that. (y) (though whatever indexical numbering will do, it's what we already do anyway)

the fact that the previous moment defines/determines the next moment — Devans99

A supposed 1st moment, having no defining previous moment, is then undefined?

And logic suggests it stops at an intelligent, timeless, fine-tuner — Devans99

Timeless? In that case, you break the principle of sufficient reason. (and some other things)

Errata (already shown in the thread):

4. If time has no start, it has no 1st moment. If it has no nth moment, it has no nth+1 moment
5. So time with no start has no moments in it — Devans99

5. such time has no such numbering of moments

When did God create time, and how long did it take him? — Yohan

Augustine had a somewhat humorous take on that stuff. :)

How, then, shall I respond to him who asks, “What was God doing before he made heaven and earth?” I do not answer, as a certain one is reported to have done facetiously (shrugging off the force of the question). “He was preparing hell,” he said, “for those who pry too deep.” — The Confessions (400) by Augustine (354-430)

If ...

The previous moment defines the next — Devans99

... then a 1^st moment is "undefined".

assuming time has a start [...] If time has no start, what then? — Devans99

Then you've started out with a contradiction.

Anyway, still no proof, then.
Leibnizian sufficient reason doesn't work (may not be applicable at all), the induction doesn't either.
I don't think it's a mere logical matter (as I'm sure Kant and Hume would have agreed); to learn more (and more still) we have to go look.

13.77 ± 0.059 billion years

• Age of the Universe: How Old is the Universe? (Edward J Wollack, WMAP, NASA)

the universe is flat with only a 0.4% margin of error

• Shape of the Universe: Will the Universe expand forever? (Edward J Wollack, WMAP, NASA)

4. if they cannot be assigned a definite numbering, they cannot exist — Devans99

Gah non sequitur again.
Sure they can; you can use whatever numbering.
Let's put up a temporal flag pole (indexical) at 1970 Jan 1^st 00:00:00 UTC, and call it epoch 0 (incidentally commonly used in computing, I just checked, epoch time rounded off to seconds was 1578080549 when I typed this up).
Whatever back/forth can now be determined/used from that.

Please explain. — Devans99

Just did ...

You've shown that such causes don't have such (definite) numbers, that such causes aren't numbered so. (y) — jorndoe

1. suppose there's no 1^st cause
2. if there's no n^th cause, then there's no n+1^th cause
3. so, by induction such causes don't have such (definite) numbering

3. So by mathematic induction, there are no causes/effects at all — Devans99

Not so.
You've shown that such causes don't have such (definite) numbers, that such causes aren't numbered so. (y)
But 3 is a non sequitur.
(That's roughly what I meant by "you can't number all such moments non-indexically".)

Incidentally reminds me a bit of Pólya's horses.

Leibnizian sufficient reason doesn't work to this end, the mathematical induction above doesn't either. :confused:

, looks (to me) like you want to show that you can't number all such moments non-indexically, but then you call it a day there, still no contradiction derived. :meh:

By the way, still treating ∞ as a number (integer in this case)...? (n)

I've demonstrated it several times quite clearly to you — Devans99

You haven't.
Mostly just something like "... which is impossible", no contradiction derived.
The opening post started out with Leibnizian sufficient reason, which didn't really hold up, so you switched to

if there is no first cause, no effects are possible — Devans99

instead, without showing so.

Then there is nothing — Devans99

... is hence bare assertion. :confused:

- But if there is no first cause, no effects are possible (contradiction) — Devans99

You keep saying so without showing it. :confused:

cannot logically exist — Devans99

an impossibility — Devans99

Well, merely saying so doesn't make it so.
Can you at least deduce a contradiction then?

Mathematical induction precludes it: Assume there is no first cause. If there is no nth cause then there is no nth+1 cause. Then there is nothing. — Devans99

How does that work? Can you set it out concisely?

An atemporal, "eternal" cause of a universe that has a definite age (like 14 billion years) is incompatible with the principle of sufficient reason, since such a cause lead us to expect an infinite age of the universe — there's no sufficient reason that the universe is 14 billion years old and not some other age, any other age in fact.

Something strangely "atemporal" would be inert and lifeless.

It's not as if the world exists objectively apart from us as subjects. Subject and object are co-arising or co-defining. — Wayfarer

Merely declaring so is much like saying the Moon didn't exist until onlookers noticed it in the sky.
We differentiate perception and the perceived; always elevating their relation to existential dependency is poor philosophy.

Now people are saying objects have no size. Oh boy! — Gregory

Whether they can be said to exist or not, these are abstract objects, not my sandals. :)
The formalisms, theorems, etc, is how you treat them, you don't wear them on your feet.

Say, there's 10 meters over to the neighbor's front door.
That's a distance between two places here in the world.
Maybe some prefer saying "there's roughly 10 or 11 meters over there"; doesn't really matter much.
Unless you walk the wrong way, then it's almost 40,000 km longer.
The mathematical treatment (or modeling) of these things hold up just fine.

, MathJax is supported:

$\displaystyle\frac{1}{3} = \displaystyle\sum_{n \in \mathbb{N}} \frac{3}{10^n} = 0.333\cdots$

where $\mathbb{N}$ does not include $0$

To render:

Anyway, to 's point, the three expressions around the $=$ symbols are just different ways of writing the same number, out of any number of ways.