Let me start with a couple of statements. They are not meant to be exclusive definitions, but inclusive generalisations.
On morality
Science, on the whole, concerns itself with knowledge, with no regard to the way that knowledge affects behaviour.
Morality tends to guide our everyday actions.
To clarify: when a stranger needs help, your scientific knowledge may well help you to identify some skin blemishes as evidence of a contagious disease. Your moral sense will lead you either to help, or to pass by on the other side.
Knowledge on the one hand; action on the other.
Another example. You have been on E2 for some time; you have a lot of friends. You have the capability to vote and to C! as well as to comment. You see a n00b making a typical n00b mistake. The software permits many different actions. Only your moral sense informs your decision. Downvote and criticise, or see the potential, offer help and then reward.
This time the science has brought not knowledge, but capability. The science has opened the options, but morality still guides our actions.
A defensive aside. I'm not trying to promote any specific morality here. I'm proposing that people consciously develop a consistent, individual morality for themselves. If you want to borrow a lot of it from the religion of your choice, that's your own choice. I'm trying to argue that the more you understand your own personal morality, the less you will live to regret your actions.
Abrogating responsibility for one's moral behaviour is a recipe for chaos. The unbridled logicician will appear to others as an unfeeling, selfish jerk, always acting out of self-interest. At the opposite extreme, unthinking religious individuals who devolve all moral authority to one of the world's sacred books can use the absence of internal morality to justify atrocities which blatantly contradict the teachings of their deity.
Dangerous territory, that. I can see the hackles of moral majorities everywhere rising at the suggestion that blind adherence to the teachings of a sacred book might lead to atrocities. Let's cut to the heart of it Every sacred book favours understanding, self-sacrifice and mercy above murder, violence and intolerance. Every sacred book encourages learning and understanding over ignorance and revenge. The religious fanatics who claim that killing is the way to peace have their own morality, but it does not coincide with the teachings of the religion - or at least of the teachings of the deity.
It's easy enough to justify walking past a helpless stranger: there will be police questions, hospital bills, the risk of infection. The person may not need any help and will resent the intrusion. Perhaps they will litigate, no matter how well-intentioned I am. Maybe the religious extremists can also justify those atrocities through careful selection of ambiguous texts. They hurt my neighbour: I should kill them to stop further hurt.
One of the issues here is that the words contained in the books are not the teachings of the deity. The message is about morality and ethics and how to live a "good" life. However, the messages are carried in words, and words do not always carry the same message to different people. I'll look at the question of meaning and action below.
There is a second point about the relevance of these sacred books to modern life. Changes in established scientific theories have led to a progressive change in our perception of what the universe is, how it works and our place therein. Most of the sacred books were written around two to three thousand years ago. I do not think I am alone in believing that all these books contain much timeless wisdom. However, wherever they attempt to explain knowledge which we today see as the province of science, they get it sadly wrong.
In at least one area, however, the wisdom they contain remains as valid today as it was 2000 years ago. And that is in terms of morality and how it reflects on the individual. Bullying, jealousy and revenge caused pain then; they cause pain today. It is still appropriate to treat your neighbour as you would wish to be treated. If we see these books as containing wisdom applicable in all ages, to all people, then we can look for their moral and ethical content first, and see their attempts at explanations of the physical world as appropriate primarily to a contemporary audience.
Science and religion
Personally, I see no conflict between science and religion, but if there is one, it arose in the Renaissance when science relegated the omniscient god to a god of the gaps. From about 1400 onwards, science progressively replaced god as the most satisfactory explanation for the stars, life, emotions and other physical phenomena. Religion fought against each new advance in scientific knowledge, and when it was shown to be wrong, claimed for itself the areas science was unable to explain. God occupied in the gaps in scientific explanation. As those gaps have become smaller, god's role in explaining the workings of the universe has shrunk to the point of insignificance, except to a minority of die-hards who continue to believe the literal truth of books written thousands of years ago.
To look at it positively, science has removed from religion the distraction of explaining suns and genes, and re-emphasised the moral dimension. Religious belief - and the related internal moral sense - provides an ethical framework for real-life behaviour of individuals. Every religious tradition I know of insists its devotees should help the needful stranger. The best that science has to offer on that subject comes from game theory, and can be summed up in the phrase, 'help strangers, but only if they help you.'
I am not going to insult you by suggesting that all church-goers will help the needful stranger, while the atheists will pass by. Far from it. My feeling is that some internal morality drives the decision for each individual. In some people, that internal morality is based principally on the external teachings of an organised religion. In others, something else drives the decision to spend time, money and emotional effort to help the stranger.
Talking for a moment about those who take their morality from an organised religion, it is difficult, when analytically following the external teachings of an written authority, to carry it off effectively. The moral sense must come from inside. An individual who tries to adhere to the moral precepts of an external system, without having an internal sense of the associated morality, will eventually reveal their lack of moral integrity. They will try to remember rules and concepts, without having the internal confidence that guides the actions of the truly committed. Inconsistencies in their actions will eventually betray the lack of a consistent moral code.
And this is, I believe, where faith comes in. Faith transforms the external moral teachings into internal moral attitudes. In this context, faith does not rely on some anthropomorphic god, or on rituals or on dogma. And especially not on regular attendance at the temple of your choice. While all of these things play some role in the established, organised religious movements, the core of morality, and hence "right-thinking", is an internal moral sense that guides daily life and interactions with other people.
You see a wallet on the floor. What do you do? Take the cash, sell the credit cards and have a good time? Or hand it to a trusted third party to deal with? Or seek out the owner? Or just walk on, leaving the moral judgement to someone else?
Faith in a religious context is the certainty of knowing something without the need for formal, logical evidence. I'm no expert on faith, but I think it translates to moral confidence, without the arrogance that can accompany moral certainty.
What I do know is that every religion on earth has it's own version of the golden rule: do as you would be done by. I also know that I find myself drawn to people who have an inner strength that comes from moral confidence, combined with tolerance, understanding and a willingness to help. Often those people are deeply religious.
Symbols and meaning
In my travels I have spent some time with devotees of Zen Buddhism. Because Zen is relatively unfamiliar to many westerners, and has never, to my knowledge, triggered a religious war, I will try to phrase this in Zen terms. That way, devotees of specific religious traditions may find my musings less challenging.
In the West, Zen is known, if anything, for its apparently illogical koans. The point of these koans is to encourage the student to separate the symbolic use of the letters 's-t-i-c-k' from the reality of a stick that inflicts pain when used as a weapon A bamboo stick is used as an aid to walking, or to beat the idle student. Thus, to assert in abstract words that "I am holding a stick, yet my hand is empty" is to provoke the student to realise that the symbols we use to represent a stick are quite different from the reality of a wooden thing that snaps when bent.
Science is all about symbolic representation. You write equations, build models, compile theories, all of which attempt to describe the real world by increasingly sophisticated reductionist analyses. Newton calculated how a cannonball flies in a vacuum. Stokes modified Newton's equations to deal with air resistance. About 100 years ago, Einstein modified the mathematical model once more to deal with things that go very fast. A few years later Riemann modified it yet again to cope with unfamiliar geometries.
The metallurgists described the cannonball in terms of its crystal structure, and then of its atoms, and about a century ago, the quantum physicists started to show us that the heavy cannonball is only a statistical side-effect of wave-particle duality.
Zen says the only reality is walking in the woods, smelling the damp earth and feeling the warmth of the fire. Zen knows that words and symbols can be useful to think about that reality, but laughs at anyone who confuses the symbols with the reality.
In this respect, Zen is no different from other religions: all religions are primarily about that Zen reality of living and behaviour. They give a moral code which guides the behaviour of real individuals in the real world. Do we help a stranger? Do we liberate pens from our workplace? Do we kill our neighbour?
Science on the other hand, is not real. At least, not in this sense. What reality is there in mathematics? Mathematics can describe the arc of a cannonball, but can it help us comfort a friend? Science depends on symbols, simplifications and assumptions. Science helps us to think about reality, but science has nothing to say about feeling wet in a graveyard.
Conclusion
This started out as an attempt to reconcile the differences between science and religion. I wanted to look at how the two approaches to life differ. It ended by clarifying - for myself at least - where religion can speak to a modern generation. As traditional religions fade, we are left with a lack of moral guidance. I am not talking fundamentalist morality, but rather a pattern of ideas and beliefs that enable people to make consistent decisions about how to live their lives. That's what religions have done over the millenia; that's what they continue to do well. It's just that they got lost, trying to fight science over descriptions of the universe.
I'm not trying to promote any specific moral pattern, just observing that each individual's moral code informs almost every decision they make in their waking hours. If an individual has no consistent morality, then their life is going to be more difficult, as they have to make spontanteous decisions every moment of their life, while others will see them as inconsistent, jumping between moralities from moment to moment.
For myself, I think I have developed my own internal sense of morality, I do not ally myself with any organised religion. I do, however, find myself drawn to people with strong religious convictions. Go figure.