Akatosh is an Aedra. He created the Dragons in his own shape. When he banished Mehrunes Dagon at the end of TES4:Oblivion, his earthly avatar turned to stone, but he is not dead.

Going to play devil's advocate here -- If the Nerevarine can destroy an aspect of a god (heart of Lorkhan), why is it so hard to believe that the Dragonborn can destroy an aspect of Akatosh (Alduin)?

I still don't believe that Alduin in an "aspect" of Akatosh, I believe he was created by Akatosh. If you want to view the creation of an Aedra as an aspect of itself, Nirn and all the races of men are aspects of Lorkhan.

The Nerevarine didn't destroy the heart, simply removed the enchantments causing the Tribunal/Dagoth Ur to lose their connection and thus their power, regaining mortality. The Nerevarine did destroy an aspect of a god in the sense that (s)he beat a third of Hicrine during the Bloodmoon prophecies. Aedra and Daedra however are fundimantely different beings, whether you count them as ancestors and not-ancestors or beings that took part in creation and those that did not, they are different. To kill Akatosh would likely be equal to killing time it self, and for as far as I know aspects of Aedra and Daedra work in completely different ways.
Where Daedra can manifest themselves on Nirn, Aedra can not (except for in relatively minor situations like Wulf).
It might be worth noting that the Aedra we know manifested himself most (Talos) is also the only Aedra that took no part in creation at all... Of course he mantled Shor, who did take part in creation but still he himself did not.

Also to return to an earlier question you asked, I don't think Alduin is dead. You didn't absorb his soul, dragons can only permantly die when a Dragonborn absorbs his soul, Alduin will come back one day. Probably when it's time to end the Kalpa for good and on Akatosh his terms.

One of the functions of Time (Akatosh) is that it eventually destroys all things. As I see it, Alduin is therefore the destructive aspect of Time (Akatosh). I don't know that that makes him a full Aedra, though...think of Alduin's relationship to Akatosh as your arm's relationship to your body.

Time is the Wheel turning. As we find ourselves moving upwards toward the zenith of this particular kalpa, we call the upward motion Akatosh. Alduin is the name for the same motion as it draws us inevitably downward.

Time and Change go hand in hand. Time provides Change the context to exist. And without Change, Time is meaningless. So even if the Time Dragon is an Aedra, Change is fundamental to Time and our understanding of it. And Alduin might be this more Padomay aligned aspect of Time.

You're assuming Akatosh has an individual personhood, will and ability to act on it: he doesn't. The Aedra explicitly lost their self-ness in the creation of Nirn. Akatosh doesn't exist except in the fragments of his scattered amongst the races of Nirn. Akatosh did not save the world in the way you think he did, Martin Septim (whose soul is a fragment of Akatosh due to being Dragonborn) shattered the Amulet of Kings releasing the souls of all the Dragonborn emperors before him and absorbed them, becoming, himself, a particularly large fragment of Akatosh, large enough to defeat Dagon. Alduin is also a very large fragment of Akatosh, and thus very powerful, but his will is entirely separate from the other fragments of Akatosh left in the world.

A note: Alduin had been a tyrant, not a destroyer. Tyranny is solidly in the Anu side of the equation, stasis via a rigid caste system, a single immortal ruling species, etc. His shift towards the Padomaic end of the spectrum may well be due to his absorption of the Nord souls heading to Songarde. Nords are, we're led to believe, the race most closely aligned with Lorhan spiritually, and thus Alduin's "feeding" on them would begin to taint him, driving him more and more towards destruction, change, and chaos.

Well Akatosh is the god of time, while Alduin is the end of time.
The end of time is a part of time while time is not a part of the end of time.
Its hard to be a benevolent god when your destined to destroy everything so Akatosh made Alduin, easy fix.

I was under the impression that the destruction of the status quo is pretty chaotic/padomaic. If Alduin is destined to be the World Eater and end the kalpa, that doesn't seem very Anuic.

And feeding on Lorkhan/Shor aligned souls should make Alduin more apt to preserve the current kalpa right?

Alduin being tyrannical may simply be a means to an end.

Ald (and other dragons) are too eternal to be Aedra. I doubt it's a mistake that the words "Mortal, Temporary, and Finite" are the words for Dragonrend (and are essentially curse words to Altmer). The Aedra are essentially are Dragonrended all the time, rather than just for a few moments.

Dragons are et'ada. The Ka Po Tun wish to become them, not simply go back to being old, dying, weak Aedra.

The Aedra cannot be killed.
You cannot kill that which is dead.
The Aedra became creation and in doing so were no longer what they had been.
The Aedra as seen now by mortals is how we meditate on their bones.

Edit: the enitire division of Aedra and Daedra into Padomaic and Anuic is a scholarly mispath.
They cannot either be any. All the original spirits are caused by the first interplay. All great remaining spirits encompass both.
By definition they are a meld of Anu and Padomay. I accept that some may seem alligned to one or the other, but I postulate that nor one nor the other can be without each other.
You can not tease what-is-there from the chaos without stability to anchor it, you cannot change the unending now that is stasis without change to meander meaning from it.

Where is the source on this?

If they lost their self-ness when Nirn was created, what was their driving force behind getting pissed and ripping Lorkhans heart out?

Unfortunately, time kinda gets muddled right around here, since time wasn't exactly established at that point. (If I'm not mistaken)

Myths, partially. Who ripped out Lorkhan's heart changes depending on the myth. Trinimac? Tall Papa? Himself? Fadomai's children? Which one is right?

The gods died at creation, from the Monomyth:

Finally, the magical beings of Mythic Aurbis told the ultimate story -- that of their own death. For some this was an artistic transfiguration into the concrete, non-magical substance of the world. For others, this was a war in which all were slain, their bodies becoming the substance of the world. For yet others, this was a romantic marriage and parenthood, with the parent spirits naturally having to die and give way to the succeeding mortal races.

From the Light and the Dark:

The old man chuckled. "The gods have an unusual origin, if some of the oldest tales are true. The oldest inhabitants of this world -- no one seems to be sure what race they were -- had a system of myths that they believed in for a thousand years. The people of et'Ada believed for so long and so well, that their beliefs may, just may, have drawn upon the energies surrounding Tamriel to bring the gods themselves into being. If that is so, the conflict between the Light and the Dark provided the energy, and the et'Adans the structure, that created the gods of Tamriel. No one really knows since it was so long ago and so little survives from that time. It no longer matters; the gods have their own existence now, and mostly align with the Light, except for a few who are, shall we say, a little ambiguous."

They died and lost their "self". They're now formed based on mortal thought.

http://www.imperial-library.info/content/monomyth
Text quoted above.

Looking to a myth for truth, quite ironic, I know.

SilentColossus, about Lorkhan's heart, I don't really think we'll know whodunit, but we do know for a fact it was done.

As for the Light and Dark, the old man doesn't really sound sure of what he is saying.

?"if some of the oldest tales are true"
?"that their beliefs may, just may,"
?"If that is so"
?"No one really knows"

I just have a hard time taking this book at face value.

I can't remember exactly what Paarthurnax says, but I could have sworn he said something like Alduin was Akatosh's first and most powerful creation. It's been several weeks since i've heard it so my memory may be a bit muddled.

Point one, you are correct, changing the status-quo is padomaic, but that's not what Alduin had ever done until now. When he ruled over the dragon cult, he was ruling over a very rigid static society, which is exactly what one would expect from a fragment of Akatosh. To end the world is his destiny, which means at some point he turns from a force for order into a force for chaos. I'm attempting to explain that shift.

Point two, Alduin eating Padomaic souls does not destroy them or change their nature. "Eating" is not literal here, it's more of a "adding to one's self". It's like if you (a being of meat) eat more meat, your body takes that meat and makes it into more meat. If your same meat-self eats, say, lead, it doesn't reduce the amount of lead in the universe, it sticks around in your fatty tissues as lead and drives you insane.

I don't think Alduin is conscious of this, he just knows he needs more power, and these little bits of Lorkhan are a good place to get it.

The gods didn't lose their selfness and they aren't dead. Remember, they are the spokes on the very wheel driving at "I AM".

Rather, they're semi-conscious, dreaming-but-not, and this allows mortals to pose them in all manners of compromising and amusing positions.

No. Arngeir confirms this. Alduin cannot 'die' - he's coming back to 'devour' the world again, and devouring essentially means he's going to undo everything (kinda like what the Thalmor want) back to the first stroke of Anu and Padomay and start a new kalpa. Referencing to the Aldudagga (and also Volume 4 of Camoran's 'Commentaries' and Volume 8 of 'The Song of Pelinal'), he has done this before, many times in fact, and there were a slew of previous kalpas.

Arngeir doesn't confirm anything. All he does is hypothesize about what Alduin's state my be, given that the dragonborn failed to devour Alduin's soul. He doesn't have any knowledge about what Alduin's state actually is, though he can certainly guess at it.

No he is not an aspect of the Dragon of time.

He claimed to be, but he was lying about it. He is the first born of Akatosh, so I suppose that would make him some kind of Ehlnofey.

Except dragons aren't born, they just are. And even among dragonkind, Alduin is special. Alduin is as much an aspect of the God of Time as Akatosh is.

I thought it was interesting that when you defeat Alduin the second time, his armor falls off and for a brief moment he has the same molten gold appearance as the avatar of Akatosh in Oblivion. Could be that he really is just a facet of Akatosh.

Alduin is nothing more than a piece of time, like all the other pieces of time. Even Akatosh and Airu-el. The dragons refer to Time as Akatosh, because you are an ignorant and moronic mortal.

Pretty sure Akatosh is just Auri-El renamed by the imperial cult.

And no Alduin is not an aspect of Akatosh. Even Paarthurnax admits to this. It's part of the reason he rebelled against him. He tried to usurp his father's throne and he felt as though that was a step too far.