"Tell me, Rabbi: is Judaism based on logic or faith?"
One of the great challenges for the Western Jew is to reconcile "Faith and Science", especially if he or she was raised in Uruguay, one of the most secular countries where the separation between Church and State was installed so "religiously" early on, at the beginning of the 20th century.
Are faith and reason two irreconcilable approaches or can they be complementary?
It depends on what one understands by "reason" and what one understands by "faith".
Faith and science are both based on axioms that are neither provable nor refutable. They are truths that are "self-evident" to those who regard them as such. It is based on such axioms that theories are constructed and will later be proven or disproven.
So both science and faith have unprovable aspects as well as logical aspects that can indeed complement each other.
Abraham and Moses are the two key figures in the foundation and consolidation of Judaism. Abraham rediscovered and spread Monotheism in the world and seven generations later, on Mount Sinai, Moses brought us the Divine Law, thus consolidating a process initiated through his ancestor Abraham. It was at the foot of Mount Sinai that the Jewish people was born; a nation whose definition as such and raison d'être is its commitment to live according to that law and to transmit and spread its teachings and values to all of mankind.
The path started by our patriarch Abraham was initiated by a logical process. “This complex and perfect world could not have created itself and implies a Creator,” he reasoned. Such was his conviction that he went out to challenge the powers at the forefront of the pagan and idolatrous culture prevalent at that time. This is one of the reasons why he is called Abraham Haivri, or Abraham "from the other side". In addition to the implication that he came from the "other side" of the Euphrates, it implies the idea that everyone was on one side of the ideological and religious divide, that of Polytheism and Paganism, whilst Abraham was —alone— on the other side, that of Monotheism.
It was, no doubt, a great achievement; but from there to knowing details about the Creator and His reason for creating us was beyond the reach of human logic. We cannot deduce by logic anything beyond the fact that the world has a Creator and that the Creator cannot have the limits that a created being has, for if He did, who created Him?
While G-d eventually reveals Himself to Abraham and enters into a covenant with him and his descendants, it was merely the beginning of a process.
It took seven generations —including 230 years of Egyptian slavery and the Exodus therefrom— before the conditions were right for G-d to reveal Himself to the Jewish people at Mount Sinai and transmit His wisdom and desire to us through Moses as documented in the Torah. According to our tradition, this happened exactly 3 333 years ago.
So we can understand the logical dimension of Judaism that was articulated by Abraham. When it comes to the supra-rational dimension revealed through Moses, which cannot be proven by logic, we accept it on the basis of faith.
Now, why should a rational being believe in something that cannot be proven or disproven?
The key to the answer can be found In the very formulation of the question. Faith —by definition— is not based on a "why". If there were a "why", there would be no need to resort to faith. People tend to say that "seeing is believing", but does that make sense? If I see something, there is no need to believe!
How, then, do I decide whether or not to believe in something?
There is a biblical story that I find very illustrative and helpful to understand the essence of the issue.
In the story of Samson and Delilah we read  about Delilah's attempts to get Samson to reveal to her the secret source cause of his superhuman strength. Her intention was to neutralize him and turn him over to the Philistines, her people of origin, enemies of the Jews living in Israel at the time.
On three separate occasions he lied to her when asked about it. The fourth time she asked him, he told her that he was consecrated as a Nazarite from birth and had therefore never cut his hair. If he were to cut his hair, thereby violating his status as a nazarite, he would lose the extraordinary strength that resulted from his status. Delilah informed the enemies that she already had the answer and that they should prepare to take him prisoner. While Samson slept she cut off his hair, and when he awoke he had indeed lost all of his Divinely endowed strength. The Philistines took him prisoner.
The Talmud  asks: Being that he had already lied to her on this same subject three time, how did Delilah know that this time Samson was telling her the truth?
The Talmud documents several opinions on the matter. The first answer quoted contains only three words: "Nikarin divrei emet", meaning: words of truth are recognized.
How simple and yet how powerful! The truth simply resonates differently. It does not need to be validated by external proof.
A contemporary example I use often in conversations about this subject is the certainty people have about the veracity of the atrocities that took place during the Holocaust.
How can we know for certain whether or not it is true that the totally incomprehensible and unimaginable atrocities we hear and read about actually occurred in the Nazi concentration and extermination camps?
When I ask the question, people are shocked. "What” You don't believe that six million Jews perished in the Holocaust?" they ask incredulously.
"Take it easy. I have no doubts about it," I reply. "My question is simply: on what do you base your certainty? How do you know it was so?"
The answer I usually get is that there is evidence, documentation, photos, etc. My next question is: "Did you investigate all the documentation and to verify that it is not forged? After all, Schindler's List looks like a documentary while in reality it was produced in Hollywood!"
"Well, Rabbi, how do you know, then, that it is true?"
"This is how it works for me.I did not see the events personally, but I saw the eyes that saw them. I heard first hand testimony from those who lived through it. I don't need documentation to prove the veracity of the events or the eyewitness accounts I heard. Nikarin divrei emet."
I often wonder: while this is a valid answer for all of us who heard about the Holocaust firsthand and saw the eyes that saw it, what about the next generation, who will not have that opportunity? How will they have that certainty? There will be those who will turn to archives and there will be those who will base their conviction on trusting the account they heard from someone who ‘saw the eyes that saw it’...
Something similar happens regarding our faith in the Giving of the Torah at Mt. Sinai. One who has doubts about the historical truth of the story, will not be helped much by all the documentation that exists. On the other hand, one who believes in the veracity of the story because he is sensitive to that recognizable and unmistakable ring of truth, does not need proof and nothing can refute or shake his faith in this regard.
In Judaism, both logic and its role and faith and its role are more complex, sophisticated and challenging than they appear at first glance. They are like the two wings of the bird that together allow it to fly. One without the other is incomplete and dysfunctional.
I invite you, dear reader, to dedicate some time this Shavuot to analyze how you handle these two components in your life, how much you know about them and how they work, and how to cultivate and develop them further.
As I write these lines I hear the sirens warning about the incoming bombs that are falling on our beloved Israel. I extend my prayerful wishes that this cruel threat be neutralized immediately so that tranquility and security may reign in our Holy Land and —consequently— in the entire world.
Looking forward to receiving the Torah once again with "joy and inwardness", as the Chabad salutation goes, perhaps as a result of employing the combination of faith and reason.
Judges, Ch. 16