There are many proofs of young kids and also adults remembering
their lives in detail even when they have never been to that place
before, they remember the people they know, how they died, what was
their name, the street name and house where they lived etc.
If we believe in cause in effect, then there must be rebirth.
Otherwise, the people who have planted a lot of good seeds which
have yet to ripen in this life, will never see them ripen. And
similarly for evil deeds.
If you want a logical explanation, one place you can find it is
in the Shurangama Sutra when King Prasenajit asked the Buddha about
annihilation after death:
(...)
Then
King Prasenajit rose and said to the Buddha, “In the past, when I
had not yet received the teachings of the Buddha, I met Katyayana
and Vairatiputra, both of whom said that this body is annihilated
after death, and that this is Nirvana. Now, although I have met the
Buddha, I still have doubts about their words. How much I wish to
be enlightened to the ways and means to perceive and realize the
true mind, thereby proving that it transcends production and
extinction! All those who have outflows also wish to be instructed
on this subject.”
The Buddha said to the great king, “Now I ask you, as it is now is
your physical body like vajra, indestructible and living forever?
Or does it change and go bad?”
”World Honored One, this body of mine will keep changing until it
eventually becomes extinct.”
The Buddha said, “Great King, you have not yet become extinct. How
do you know you will become extinct?”
”World Honored One, although my impermanent, changing, and decaying
body has not yet become extinct, I observe it now, and every
passing thought fades away. Each new one fails to remain, but
gradually perishes like fire turning to ashes. This perishing
without cease convinces me that this body will eventually become
completely extinct.”
The Buddha said, “So it is."
”Great King, at your present age you are already old and declining.
How do your appearance and complexion compare to when you were a
youth?”
”World Honored One, in the past when I was young my skin was moist
and shining. When I reached the prime of life, my blood and breath
were full. But now in my declining years, as I race into old age,
my form is withered and wizened and my spirit dull. My hair is
white and my face is in wrinkles and I haven’t much time remaining.
How can I be compared to how I was when I was full of life?”
The Buddha said, “Great King, your appearance should not decline so
suddenly.”
The king said, .World Honored One, the change has been a hidden
transformation of which I honestly have not been aware. I have come
to this gradually through the passing of winters and summers.
”How did it happen? In my twenties, I was still young, but my
features had aged since the time I was ten. My thirties were a
further decline from my twenties, and now at sixty-two I look back
on my fifties as hale and hearty.
”World Honored One, I am contemplating these hidden
transformations. Although the changes wrought by this process of
dying are evident through the decades, I might consider them
further in finer detail: these changes do not occur just in periods
of twelve years; there are actually changes year by year. Not only
are there yearly changes, there are also monthly transformations.
Nor does it stop at monthly transformations; there are also
differences day by day. Examining them closely, I find that kshana
by kshana, thought after thought, they never stop.
”And so I know my body will keep changing until it is
extinct.”
The Buddha told the great king, “By watching the ceaseless changes
of these transformations, you awaken and know of your extinction,
but do you also know that at the time of extinction there is
something in your body which does not become extinct?”
King Prasenajit put his palms together and exclaimed, “I really do
not know.”
The Buddha said, “I will now show you the nature which is not
produced and not extinguished.
”Great King, how old were you when you saw the waters of the
Ganges?”
The king said, “When I was three years old my compassionate mother
led me to visit the Goddess Jiva. We passed a river, and at the
time I knew it was the waters of the Ganges.”
The Buddha said, “Great King, you have said that when you were
twenty you had deteriorated from when you were ten. Day by day,
month by month, year by year until you have reached sixty, in
thought after thought there has been change. Yet when you saw the
Ganges River at the age of three, how was it different from when
you were thirteen?”
The king said, “It was no different from when I was three, and even
now when I am sixty-two it is still no different.”
The Buddha said, “Now you are mournful that your hair is white and
your face is wrinkled. In the same way that your face is definitely
more wrinkled than it was in your youth, has the seeing with which
you look at the Ganges aged, so that it is old now but was young
when you looked at the river as a child in the past?”
The king said, “No, World Honored One.”
The Buddha said, “Great King, your face is in wrinkles, but the
essential nature of your seeing has not yet wrinkled. What wrinkles
is subject to change. What does not wrinkle does not change.
”What changes will become extinct, but what does not change is
fundamentally free of production and extinction. How can it be
subject to your birth and death? Furthermore, why bring up what
Maskari Goshaliputra and the others say: that after the death of
this body there is total extinction?”
The King heard these words, believed them, and realized that when
the life of this body is finished, there will be rebirth. He and
the entire great assembly were greatly delighted at having obtained
what they had never had before.
(...)
From the sutra, we know that that the seeing nature is not subject
to birth and death, which shows the annihilation does not happen
after we die.
