Buddhist Ontology/Reductionism vs Science Dear Mighty friends and learned colleagues, 

I am a Scientist and have been a philosopher (I don't want to reveal my identity) so far. I have been a strong theist, raised up in an orthodox Hindu Background, with vedic training. So I read Vedas and other texts and always believed in God. Sometimes by convention and sometimes by experiential intuition. God was - unfortunately or fortunately - presented to me in a dogmatic manner. Top-Down. Here is God. Take it. Accept it. Believe it. 

I was OK with it, till it started to disturb me deep down. Firstly due to my heavy involvement with the foundations of sciences, I was caught in the method of science. So I can't believe in God and do my science at the same time. At one point one has to give up traveling in two boats. 

Buddhism offered solace at that point. I thought it's a logical religion. Totally banishing the dogmas and blind beliefs. But I found some paradoxes in it as well. Perhaps due to my ignorance. I will be grateful if someone throw some light and enlighten me here: 

Buddhism's ontology posits a world which don't need a creator. That's fine. But how about the soul? What proof does Buddha have for soul? and What about reincarnation? What are the proofs for it? 

What about the Maitri? or Metta? When you close your eyes and let your heart radiate, should we imagine a field (akin to quantum fields) that radiates outside your heart? What's the proof for this again? 

Also what about Karma? How can I reap bad when I sow bad? Where does this transaction take place? In ordinary space-time? Because attributing causality to action and reaction posited by Karma principle, is against the modern science whose fundamental elements are quantum particles. Where are this Good and Bad situated? 

What about Amitabha? 

So the issue is simple. In for pound. In for penny. If Buddhism doesn't accept anything by blind belief, then these elements should be dropped. Because there's no scientific/cognitive proofs of the aforementioned elements given our sensorimotor apparatus. 

Can someone enlighten me? Or suggest me some books? Any brief answers addressing these things will be greatly helpful. 

Your humble servant.
It's a good question but has some erroneous assumptions. 

First, and this would be crucial, if we are speaking of the 'Middle Way' then there are no paradoxes in Buddhist doctrine . This is demonstrable and it has been demonstrated, most notably by Nagarjuna. Nor is there an individual soul or reincarnation.

Rebirth is the usual word and this is not quite reincarnation. Individual souls would not exist but we would share a common 'Self'. (Schrodinger writes well about this, dismissing monads and souls as unworkable ideas. As a scientist you might like to read him since he says a lot about the Upanishadic view and endorses it).  

Karma is about causation. Basically it says 'As you sow so shall ye reap'. If you jump off a cliff you'll get hurt, etc. But it operates in more realms than science observes. It operates in time, as you say, and it is able to operate because it is not a process external to our consciousness. That is, no Divine judge that is 'other' would be required for its operation, just our own internal records of our own motives and actions. We would be our own judge and jury.  

Karma is tricky in the context of ontology because by reduction it would evaporate along with the subjects and objects on which it operates.  

Regarding ontology, for a fundamental analysis nothing would really exist or ever really happen. The world we live in would be a creation of consciousness and as such would have the nature of a dream. To all everyday intents and purposes it would be real but this reality would be 'conventional'. To understand this as an idea would mean studying Nagaruna's doctrine of 'Two Truths' or 'Worlds'.

We normally say a piano is a real object but know that by reduction it's just a thin fog of quanta. The Perennial philosophy says it is not even this but is empty of inherent existence. For Buddhist ontology we need to study 'emptiness' and the idea that all phenomena are empty. Only if they are empty can they be explained, and this would be why Buddhist metaphysics is able to work where theoretical physics and western metaphysics ends in paradox and confusion. 

The idea of a field radiating from the heart may be meaningful and useful and perhaps there is such a thing, but in the end Buddhism asks us to look beyond extension. Extension is a paradoxical idea and thus all extended objects - the number line, the continuum, space-time, pianos etc - and by reduction Buddhism disposes of them, thus avoiding the paradoxes that arise for realism.

You say there is no scientific proof of certain elements of the teachings. This is inevitable since they dispose of mundane science and speak of what lies beyond sensory empiricism. This does not mean there is no proof. Buddhist teachers should not be teaching things they have not verified for themselves. The difficulty with discussing this with those unfamiliar with these ideas is that in a sense you'd be right, karma and rebirth are non-existent. This would be why it is possible to transcend them. But to all intents and purposes they would exist until we know they don't. 

As for where good and bad are situated they'd be in your mind, along with right and wrong and sin and evil and fear and guilt.                  

There are many good books. For ontology I'd suggest The Sun of Wisdom by Khenpo Tsultrim Gyamptso (Shamabala). Schrodinger is worth a read, perhaps What is Life and What is Mind. The mathematician Hermann Weyl is good on the continuum and explains the Perennial view. His The Continuum is too much maths for me but his other writings expand on his thoughts. If you're into maths you could try Spencer Brown's Laws of Form in which he reduces the world to formlessness. Bradley's Appearance and Reality is a more chatty reduction of the space-time world to a collection of conceptual imputations for a Reality that is 'non-dual'. If you can do the maths you might like Ulrich Mohrhoff and his text-book The World According to Quantum Mechanics, which gives the interpretation of QM necessary for Nagarjuna's universe.                         

The literature is so vast we're spoilt for choice. If you specify a topic I could give a more specific recommendation but all the topics overlap so it's just a question of wading in and following your nose. 

I'm happy to add to this if I've missed anything. I feel that when scientists ask questions it would be vital to answer them.