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.

, just in case you're new around here, these things come up every now and then — Zeno "impossible!" ∞ "paradox" 1/0 ... — usually due to some misunderstandings. :)

While at it with the "paradoxes", here's Aristotle's wheel:



:)

(y)

The Law of Identity states that a certain thing is identical to itself, and I ask why. — Monist

(I suppose your inquiry itself is meaningless, if identity was abandoned; not just your inquiry, every inquiry.)

There cannot be anything in particular prior identity.

Why is identity necessary? — Monist

It's not. (Necessity presupposes identity, if we're talking modal logic at least.)

It's kind of self-evident, isn't it?
Meaning auto-supposes self-identity.
When talking about the soccer match, thinking of the neighbor, etc, we automatically go by identity.
Abandon identity and the posts here are meaningless.

What the...?

Trump rails against windmills: 'I never understood wind'
John Bowden
TheHill
Dec 2019

Incidentally: On Bullshit

Any such mathematical object always has zero Volume in higher dimensions (here I'm using generalized Volume):
A point has zero length, a line has zero area, a plane has zero volume, a unit sphere has ...
What's so odd about that? (How many of them do you want to banish anyway?)

Volume of an n-ball (Wikipedia)

Would the Archimedean properties be worth mentioning here (since they seem to be ignored all over the place)?
Infinites and infinitesimals aren't real numbers (nor rationals etc):

$\infty \notin \mathbb{R}$
$1/\infty \notin \mathbb{R}$ (archaic Wallis notation)

Don't use them as if they were (outside of convenience in specific contexts).

Continuum is a set of points where for every two points in the set there exists a point in the set that is in between the two points. — Magnus Anderson

Related to dense sets:

Dense order (Wikipedia)

You guys are so HARD on Cantor! — John Gill

Just some folk are. :)

We ought to treat the existence of non-computability and incommeasurability much more seriously than we do. Yet mathematicians push them aside and think somehow that they are 'negative' or something that ought to be avoided. — ssu

There are a bunch of areas in computer science on computability and such, e.g. ...

Computational Complexity Theory (Stanford Encyclopedia of Philosophy)
Computational complexity theory, Computational complexity (Wikipedia)
NP-completeness, NP (complexity), P versus NP problem (Wikipedia)

Within some limits you can write code to handle infinite sets.
Nowhere near what mathematicians routinely do, but some things are possible.

How are abstracts externalized in the first place?

Compare:
Some are loved, some are hated, many have known love, many have known hate. After an extinction, love and hate could be rediscovered. So, love and hate are existentially independent of any one person.
Love and hate are phenomenological experiences, qualia. Phenomenological experiences are existentially mind-dependent, i.e. subjective. So, love and hate are subjective.
Thus, commonality (independence) does not entail existential independence of persons.
Asserting otherwise might be charged with hypostatization (love and hate aren't somehow independent, though I'm sure some would say so).

What are the implications for abstracts and (the inert lifeless) Platonia, if any?
The unit-less number 7 (not a concrete count) isn't like love and hate, yet any/all concrete counts of 7 are subject to some ((re)discoverable) common rules and reasoning and such (algebra).
So, how are abstractions externalized anyway, supposedly inhabitants of some strange Platonia...?

@Devans99, you should know that the extended reals is not a semigroup, a group, a ring or a field.
There are certain contexts where such (sort of "artificial") constructs are convenient, as long as that's understood.
I don't think you can simply lean on this sort of convenience here and call it a day.

Again, we're moving in the direction of mystical, paradoxical phraseology. Philosophy - even language - is spectator to this sport. — ZzzoneiroCosm

You could say that.

Reminds me a bit the the Olympians. Once someone took a good look at Mount Olympus and didn't find them, they had relocated to :sparkle: "otherworldly" realms.

God as qualityless recession. — ZzzoneiroCosm

And now resigned from existence, too, of all things.

God does not exist. — Bishop Pierre Whalon

How is that different from atheism?

create ambiguity in the definition — Metaphysician Undercover

Disambiguation is what mentioned definitions do.