The question is being presented a bit awkwardly. If the question refers to something like Homeopathy, Reflexology or other similar "pseudoscience" then I would have to say yes. Many people will try to pass those off as scientifically sound practices but there is no verifiable science behind them. On the other hand, many of the aforementioned sciences have been tested and proven to have no real use by science.
No, it is not. In fact, referring to science that is not provable is misleading. There is some science that can't be proven 100 percent, but it is assumed to be true as a result of many other factors and situations. For example, we can't prove why gravity works the way it does, but we have theories as to why.
Believing something without proof is not silly; belief is something that does not require proof. That being said, I do think it is silly to believe something so strongly that you refute any and all evidence that you might be wrong. Regardless of what one believes, a person should be open-minded to the possibility of something else being true.
All historical science is based on inference. To scientifically prove something means to prove it by trial and error, by repeating over and over. You can't repeat history over and over so I cannot prove that anything has happened, I can't prove that Abraham Lincoln wrote the Gettysburg address but there is large, undisputed evidence for it.