Rambam, in his Commentary to the Mishna (Sanhedrin 10), enumerates 13 "עיקרים" or "יסודות", which he holds are the core "principles" that every Jew is expected to believe. (Summary in English.)
But what are these "עיקרים"? Are they axioms in a mathematical sense; a set of statements with which all Jewish beliefs and truths will follow? This cannot be, for certain "עיקרים" follow logically from others. For instance the tenth יסוד (God knows the actions of humans and is not neglectful of them) is implied logically by the eleventh (God rewards those who obey the commands of the Torah and punishes those who violate its prohibitions). The fourth יסוד (God existed prior to all else) follows from the first (God exists; God is perfect in every way, eternal, and the cause of all that exists; all other beings depend upon God for their existence). Thus, these "עיקרים" cannot be the core of an axiomatic system.
Are they simply what Rambam felt were the most important beliefs in Judaism, regardless of their logical dependencies? This is hard to understand. Why then, would Rambam count the Resurrection as an עיקר (the thirteenth) when it is never explicitly mentioned in Tanach alongside God's unity (the second), which is explicitly stated in a verse that we say twice daily? In other words, it makes Rambam's identification of the "most important" beliefs seem somewhat arbitrary.
So, in light of the above, my question is: What are these 13 עיקרים? What identifying factor separates them from all other statements that are true according to the Jewish faith?
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