I have frequently noticed people commenting that there are many unanswered questions but science may not be able to provide all answers.

I have always placed complete faith in science and have probably never thought in this direction or probably I am ignorant.  Considering that science deals only with the nature, it is understood that it cannot be asked to find answers to questions about the supernatural. After finding the truth about the origin of the universe and the origin of life, the remaining questions are in my opinion just missing links. What are such questions then that science will not answer and why? What are its limitations? Time? Funds? Human resources? Lack of interest or efforts on the part of humans? Or is the present knowledge inadequate for further research? I would like my more enlightened friends here to educate me on this subject.

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There's a lot of anti-government attitude in the USA that perhaps goes way back ... I think Charles Dickens wrote about it.  Maybe it's related to the refugees from persecution who come here.  Maybe Australia is similar, with so many criminals who were exiled there. 

Nuclear power generates a lot of the electricity for France, and I read that part of the reason for this is that the French trust their technocrats, so there isn't as much of an anti-nuclear movement there.  Perhaps the Germans don't trust government and technocrats because of Nazism.

"I don’t want knowledge. I want certainty!"

"I am certain the sun goes around the Earth, just watch what moves. The proof is the Earth doesn't move, the sun moves; same for the moon."
"I am certain god answers my prayers. The proof is I survived heart surgery." 
"I am certain the house is haunted. The proof is I saw a person when I woke up." 
"I am certain there is life after death. The proof is my dead mother appeared as I prepared her memorial dinner." 
These, and other certainties end inquiry, even if the evidence can be produced to disprove such claims. Thought-stopping acts like mind-binding. It limits questions. It brushes aside doubt. It ignores other options. 
Health care is like religion. I told others I have heart trouble and then when I learned I have cancer, remedies started flooding into my email. Do this, don't do that. A little questioning, a few phone calls, a bit of Googling, frank discussions with my doctors and I had all the information I needed to know which protocols I would follow. The scientific method requires uncertainty, it deals in probabilities. When a new protocal becomes available, it is because of new knowledge. 
Stephen Hawking was told he had two and a half years of life when he was a young man. He has a motor neuron disease related to amyotrophic lateral sclerosis (ALS). Today, he is almost entirely paralysed and communicates through a speech generating device. He is now 71 years old. 
Hawking offers an anecdotal piece of evidence that illustrates the reality of certainty statements as opposed to probability ones. Why did he outlive the prediction? What is different about him that he could survive so long? Will others benefit by answers to these questions? 

Science can't answer questions that its methods can't address. In the 19th century Positivist science declared that consideration of "volition," whether natural or supernatural, ie, God's will or human free will, was to be excluded from the practice of science. This was wise, since science had no way of controlling for the effects of god or free will. Elements of consciousness seem not to obey laws of conservation, for example. But one result is that science still knows nothing about free will, even whether it exists or not. We still don't have concepts sufficient for talking about it. Anything we do can as easily be declared to be the result of determinism, or free will. Neuroscience can't tell what it is happening when we come to a decision based on what appears to us to be a conscious stream of thoughts. Would we have come to the same decision if we were not conscious, or was consciousness necessary? I think the methods of current science can't tell.

So I think this is a question science will not answer, and the reason is because it's methods can't address it. Must one therefore say that consciousness is supernatural? Or can one say it's natural but inaccessible?

There have been experiments testing the power of prayer on hospitalized people (the prayed-for people did a bit worse).

Religious people can easily object that "God hides".  Maybe God doesn't want anything supernatural to be proved, so God made the experiments show no power of prayer. 

Science is based on the assumption that the studied objects don't have the wish or ability to influence what the scientist observes.  Nature is manipulated and observed by science, it isn't supposed to be manipulating the scientist!

Would we have come to the same decision if we were not conscious, or was consciousness necessary? I think the methods of current science can't tell.

Free will, consciousness, qualia are all aspects of lived experience, and as subjective experience they are a kind of non-physical world generated by the physical world, and hard to study. 

Consciousness may have arisen because humans are social, capable of deception, and needed to be able to model themselves in order to understand other people.  That's one theory.  So if a creature can "model" the thoughts and mental world of other creatures, you might guess that the creature is conscious. 

Science is a methodology that only attempts to answer the question  as asked. IMO the jury is out as to where inquiry will lead in this new branch of science. It is premature to say it can't address the content in thought process. 

It is also premature to say it can address aspects of the thought process, such as whether experiencing thoughts in consciousness can change subsequent thoughts.  I do expect methods for studying consciousness to arise, but I doubt they will be science as we know it today, so I think looking back people will say, we solved it but not by 21st century science. This makes me think labeling as "science" how consciousness will be finally understood could hold us back from the solution.

You might look at research on consciousness, such as the Cambridge Handbook of Consciousness, to see what is being done. 

Consciousness is wholly a philosophical subject and science has nothing to do with it. Brain is the seat of our consciousness. A person is dead, that is, a person looses his consciousness when his brain stops functioning. Science will never speak of consciousness, we will have to interpret our scientific knowledge for our understanding of consciousness.




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