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Philiosophy and logic help needed?

I recently read a book on logic to help formulate better arguments. Unfortunetly, using that logic, there are a host of things that I would normally not hesitate to say: "I know are true", but now I can't. This statement is going to sound crazy, but it's an interesting excersice: " I can't prove that the country of Japan exists." I know that it does exist, but I can't prove it logically. The main evidence I have for the existance of Japan are: 1) Photographic evidence. However, I've seen photographs of Jesus in a bowl of spaghetti, and Osama bin Laden with a goat's body. It doesn't make them true. 2) Authorities (map makers, hostorians, travelers) all claim that Japan exists. Authorities have also claimed that the earth was flat, and Iraq had WMDs. 3) The majority of people believe it exists. Same as above. Is it logical to discount a statement because of it's exception? I'm just starting out with logic so I fear there's something I'm missing.

Public Comments

1. Consistency is the key. It is proper to discount a statement because of its exception; if it is a universal statement such as "all sheep are white", the discovery of a black sheep falsifies it.
2. You can't depend on formal logic alone. Formal Logic is the domain of reason alone. There's also Material Logic which is use of the senses for reason to ponder on. As for Japan, you cannot use that line of argument that pretending to blind yourself from the existence of Japan because of Formal Logic, you deny yourself of its existence, which is fallacious reasoning. Formal Logic is used mainly in deductive syllogistic arguments Material Logic is used in Inductive arguments. Here is where the rules of fallacious arguments you should study. Here, for example, you have committed the fallacy of Argumentum Ad Ignorantium (Appeal to Ignorance) about the existence of Japan. At times you should combine the two to arrive at a better understanding of truth.
3. You could place a call to a random person in the Tokyo phone book and ask him if he really exists. If you did this, the logical sequence of ideas would be this: 1) I wasn't talking to myself 2) Thus, I was talking to somebody else 3) the somebody else wasn't where I am 4) thus, he was someplace else 5) until there is a reason why I shouldn't do so, I will call that someplace else by the name 'Japan' 6) Japan, as defined in step 5, exists.
4. as far as i know there are many thing that all people believe it is true(axioms) without give reason for. in my opinion you must select a good reference.