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according to Jewish tradition does the mitzva of emuna mean to believe without rational reason (blind faith). Or does it mean to investigate and come to a conclusion based on the evidence.
(hence if the mitzva is blind faith, then if one investigates and comes to a conclusion based on the evidence then he has not fulfilled the mitzva since his faith is based on reason. conversely, if the mitzva is to investigate, then one has not fulfilled the mitzva by blind faith alone.)
There are many sources that discuss this issue, some of which give complicated accounts as to exactly what "emunah" should be, and suffice it to say that this is subject to significant dispute. While some did believe that the better form of faith is one that you might call 'blind', it appears that most of the Rishonim held that the commandment to believe in God (assuming it exists) is to know that He exists by reasonably justifying this belief, so that your knowledge of Him isn't like a statue that might fly away. Rabbi Obadiah Seforno defends this position at length throughout the first two sections of his work, Ohr Amim. Similarly, according to the Rokeach on the Rambam (Yesodei HaTorah 1:1), the Malbim (to Shemos 20:2) and the Maharam Shick (Taryag Mitzvos no. 25), there's a commandment to justify one's belief in God.
This blog post of Gil Student's may help answer your question as well as show you that the true picture is probably rather grey (as in, not 'black and white')
You touched upon the difference between two complimentary themes - emunah vs. bitachon. Ramba"m discusses this quite extensively. I'll try to link a source, later, b"n.
However, I think that this article explains the main concepts quite well. The example about Pharoah to illustrate the difference, I think, is very good. Some excerpts:
The Rambam defines emunah as the knowledge that HASHEM created and continues to run all of Creation. Simply put, nothing can exist and no activity can occur without HASHEM.
Bitachon, however, is a quite different. The Chovos Halevovos defines bitachon as trusting in HASHEM. It is a sense of relying on HASHEM to watch over and protect me, as if to say, “I take my heavy burden and place it on HASHEM.” While I am responsible to be proactive, I am not in charge of the outcome, and I am not the determinant of the results. I rely on HASHEM to care for me.
Emunah is a state of understanding; bitachon is a state of trust. Emunah means knowing that HASHEM is involved in every activity on the planet; bitachon means trusting in HASHEM in every situation.
A person can have emunah and not bitachon
Aperson can have emunah and not bitachon. Pharaoh was a classic example. When threatened by the Jewish overpopulation, Pharaoh’s solution was to throw the baby boys into the Nile. The Medrash explains that this wasn’t a flippant reaction – it was highly calculated. Pharaoh knew that HASHEM promised Noach that He wouldn’t bring another flood. He also knew that HASHEM pays back “measure for measure.” Therefore, Pharaoh determined that HASHEM would want to bring a flood to pay back the Egyptians for drowning the babies, but because of HASHEM’s promise to Noach, that couldn’t happen, so he felt protected from HASHEM’s wrath.
Clearly, Pharaoh understood the power of HASHEM. He realized that HASHEM watches over the world. He also understood that HASHEM acts with justice. Pharaoh had no problem with emunah, but he sure didn’t trust in HASHEM – he rebelled. He had emunah, but no bitachon.
Growing in emunah
Both emunah and bitachon are based on relating to the world in a deeper manner. Emunah is the understanding that HASHEM is involved in more than just the big picture issues: life and death, war, famine, disease. . . HASHEM is involved in the minutiae of my daily life. HASHEM is there with me, 24/7, 365, all day, every day, from morning to night.
Amazingly, I can have this understanding and yet lack a level of trust in HASHEM.
What I infer from this is that emunah is not "blind" faith. If it were, we'd be "dummies" or "zombies", just performing our activities without thinking through it at all. It seems that emunah requires at least some minimal understanding that G-d exists and is in control of all. Atheists, thus, have no emunah, based on this definition. Perhaps, this is why David in Tehilim (I think it's ch. 11 or 13?) calls them fools.
