We know that we can't just DO whatever we want - neither according to halacha, nor according to [li-havdil] secular law. The halacha mandates punishments for serious infractions as does secular law.
What about beliefs? Can one freely speculate and believe or is he bound to a certain set of beliefs from which he may not stray??
The "frum" answer is that of course one may not think whatever he wants. There are certain uniform beliefs that every Jew must have and if one doesn't, then he is not part of the Jewish people. That is not [just] a "Bnei Brak" answer but that of the great "philosopher" and "rationalist" Rabbi Dr. Moshe the Son Of Maimon. [Reminds me of the probably apocryphal story of Yitzchak Rabin who was called up to the Torah in shul. The gabbai said "yaamod Yitzchak ben..." and he said "arbaim vi-shalosh". The gabbai said "lo - abba shelcha". Rabin said "ben shivim vi-echad"]. We are bound first and foremost to the 13 principles and in addition to believe in every word of the Torah, the reliability of Chazal etc. etc.
However, there is still room for "free thinking". When one is elevated above the basics of faith and climbs to the higher worlds of the secrets of the Torah and Kabbala, he can roam freely in his mind. When he does, he will find that all of the secrets of the Torah and the Universe fit in beautifully with our required beliefs.
The first type of faith is called אמונה מצטיירת - The faith that has a form and picture. The type of faith that one can explain to others. The second type is called אמונה מושכלת - The faith of [elevated] intellect, to which only the great Tzadikim are privy.
We are not on the level of אמונה מושכלת, but if you learn for many years, work on your middos, control your physical appetites etc. etc. you will get there. In he meantime - we have a taste from the writings of Tzadikim from all of the generations.
Bi-lashon Ha-rav:
למעלה ממנה עומדת האמונה המושכלת. בה יש דוקא חירות עליונה, והיא מתגלה רק לישרים הבאים בסוד ד'. וברית כרותה היא, שכשאדם שומר אמונים בכל תום באמונה המצטיירת, כשהוא נאמן הבית וההיכל של קדושת האמונה, יזכה לאור האמונה המושכלת, ששם הוא העולם המלא חירות, ויכיר וידע איך שכל הדברים מתאימים יחד, ואיך כל הדברים הנחקקים באמונה המצטיירת ומתבטאת גם-כן לפעמים, הם הם הינם הדברים עצמם שהם באמונה הרוממה המושכלת, בסוד ד' ליראיו ובריתו להודיעם.
