Can reincarnation be proved with using a mixture of logic, science, and philosophical belief?

1. Matter is neither created nor destroyed.

In Theravada Buddhism, even the particle or smaller were imagined from elements, realities. The elements are arising and vanishing more than trillion times per second because of their many various origins.

2. Matter is made up of atoms.

In Theravada Buddhism, the atom is an imagination which imagined from the arising and vanishing elements more than trillion times per second. The elements could be formed by Karma, Mind, Temperature, or Nutrient.

3. I am made up of atoms.
4. I am matter.
5. Therefore, I cannot be created nor destroyed.

Yes, it is imagination based on imagination.

Can reincarnation be proved with using a mixture of logic, science, and philosophical belief?

I don't think so, but I know more than one successful people, some graduated from MIT and worked at US FED, who have hard practiced on Jhana, recalling-reincarnation skill and Abhidhamma follow to Pa-Auk Tawya.

They never get back to talk about science anymore.

So, I guess I should practice follow them to get their chosen knowledge (better than?) science like they did.

Let's go through the logic first.

The Kalama Sutta says to not rely on logic.

The following statements are suppositions that must be chronologically accepted.

Its is unlikely superstition must be acccepted.

Matter is neither created nor destroyed. Matter is made up of atoms. I am made up of atoms. I am matter. Therefore, I cannot be created nor destroyed.

No. In Buddhism, the "I" is a mere impermanent illusory mental formation or thought (SN 22.81). In Buddhism, the Enlightened One's have ended "I-making" and "my-making" (SN 21.2; AN 6.104; etc). Buddhism says in many places the "I" has been permanently destroyed.

And how is the bhikkhu a noble one whose banner is lowered, whose burden is lowered, who is unfettered? Here a bhikkhu has abandoned the conceit ‘I am,’ has cut it off at the root …so that it is no longer subject to future arising. That is how the bhikkhu is a noble one whose banner is lowered, whose burden is lowered, who is unfettered. MN 22

As for the basic physical elements or atoms (dhatu), DN 11 says it cannot be said they can cease without remainder, as follows:

Your question should not be phrased in this way: Where do these four great elements — the earth property, the liquid property, the fire property, and the wind property — cease without remainder?

In summary, the Buddha teaching is as follows:

1. Matter is neither known to be created nor destroyed.
2. Matter is made up of atoms (elements/dhatu).
3. The 'I' is not made up of physical atoms.
4. The 'I' thought is immaterial & not matter.
5. Therefore, the "I" can be both created & destroyed.

Your assumptions are a bit wild. For starters, most people think energy is neither cerated nor destroyed, not "matter". And your analysis of parts and wholes also needs elaborating (ham is tasty, a ham sandwich is made with ham, but I don't think ham sandwiches are tasty).

A better, if I may, presentation would be

1. I am just matter (I don't think the abhidharma agrees)
2. Matter is just atoms (I believe this is usually taken as a fact, though I forget whether things reduce to atoms in the abhidharma)
3. Atoms are just energy (atoms are usually thought of not just energy, but also things that have energy - nuclei etc. - which themselves are composed of smaller particles that are energy.... so yes, even-though energy is not just atoms, as there can be energy in empty space)
4. Energy cannot be created or destroyed
5. I cannot be created or destroyed (when e.g. I am born or die)

Is it a convincing argument? It follows that nothing mental or physical can be created or destroyed. If the conservation of energy meant nothing at all could be created or destroyed, this would be a surprise, and would fly in the face of our everyday beliefs about everything from suns and blackholes to, as you point out, individual lives. This is far from an assumption shared in by physicists etc..

In reality, the conservation of mass only holds approximately and is considered part of a series of assumptions in classical mechanics. The law has to be modified to comply with the laws of quantum mechanics and special relativity under the principle of mass-energy equivalence, which states that energy and mass form one conserved quantity. For very energetic systems the conservation of mass-only is shown not to hold, as is the case in nuclear reactions and particle-antiparticle annihilation in particle physics.

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

It's a nice mental image, but, as anyone who has had a lego chariot before knows, you can rearrange the parts of something to make something which is not conventionally designated in the same way (oh, a boat!).

You can show that reincarnation is the reasonable assumption but it's not a given that people will accept it.

It is also not something you need to prove because it is the reasonable assumption and arguing against it is the extraordinary claim. This is shown by this base line of reasoning;

'Before i was born there was no percepience of the world for me and after i die there will be no percepience of the world for me, the before & the after are the same and no further difference can be delineated.

Therefore given that percepience arose for me not having been before, it is thus reasonable to assert that this will repeat itself after death.

One can't really argue about this without appeal to assertions about the world and nature of percepience in particular.

This is where you go about cutting off wrong assertions on their part. Like this;

The Blessed One said, "What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. [1] Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range."

There are many ways of going about further cutting off wrong assertions and one can use physics, neuroscience and philosophy to keep disproving wrong ideas but you can not prove logic with logic and if a person doesn't accept the reasonable assumption argument to begin with then he is being unreasonable in misplacing the burden of proof.

The thing with logical or philosophical arguments for reincarnation is that they either cannot be proven empirically or rely too much on semantics. The minimalist reincarnation hypothesis is, AFAIK, the only falsifiable reincarnation hypothesis.

There is something essential to some human personalities, however we ultimately characterize it, which we cannot plausibly construe solely in terms of either brain states, or properties of brain states, or biological properties caused by the brain and, further, after biological death this non-reducible essential trait sometimes persists for some time, in some way, in some place, and for some reason or other, existing independently of the person's former brain and body. Moreover, after some time, some of these irreducible essential traits of human personality, for some reason or other, and by some mechanism or other, come to reside in other human bodies either some time during the gestation period, at birth, or shortly after birth.

Though vague-souding, it doesn't commit the common errors of other hypotheses, i.e. it focuses explicitly on humans, it doesn't assert that all humans reincarnate and it cares not how they would reincarnate.

Ian Stevenson (and to some extent, his protégé Jim B. Tucker) was the most prolific researcher who collected data for this hypothesis. The man had sound methodology and had been to all continents of the world for more than four decades to investigate claims of reincarnation. He has a lot of critics, unsurprisingly for a researcher of the 'paranormal'. However, it's hard to dismiss many of his collected cases as purely fraudulent or confirmation bias. To summarise, the common features of his cases are a combination of:

• Violent injuries or cause of death in the purported previous life.
• Statements pertaining to events in the previous life.
• Physical anomalies and extreme phobias in the current life corresponding to the cause of death.
• Physical or behavioural resemblance between the previous and current life.

There are many great threads on BSE discussing the doctrine of reincarnation or rebirth in Buddhism, to which I have little to add. I just want to say that beliefs in reincarnation or the paranormal in general are acquired experientially. From the perspectives of many natural sciences, they are inherently unreliable and most likely unprovable. Much to my dismay, I believe it's futile to try to prove the existence of reincarnation.

Currently I'm trying to distance myself from BSE. I may or may not response to your comments.