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A mesorah would be quoting someone else who must have used the 13 principles and sevarah is what is logical, but the thirteen principles really are the essence of logic so they are not really two separate things.
All valid Rabbinic opinions do in a sense carry Biblical weight because the Torah commands that we follow their directives "Lo Sasur Min Hadavar...".
mesorah is tradition.
and I assume sevarah means reasoning. Though I am not sure.
1) rabbi yishmael's 13 rules are Not logic.
infact, rabbi dovid gottlieb, former prof philosophy and PhD in mathematical deduction, said they are not logical.
I wouldn't put it like that.. They are just rules. Applied logically.
This is a book on formal logic. I am familiar with the professor that wrote it.
Proo f and Disproof in Formal Logic: An Introduction for Programmers (Oxford Texts in Logic) (Paperback)
by Richa rd Bornat (Author)
Rules like this are the essence of logic. And they can be written using mathematical symbols.
A--->B A
-----------
B
an example would be that
I believe that when A happens, B happens.
I believe A,
So I conclude B
That is nothing like the 13 rules.
The 13 principles are ways of deriving the encoded meanings that the author (G-d) encoded into the Torah. For example, a general statement followed by an emumeration of particulars e.g.
Don't steal, don't steal apples, oranges, pears.
Has a different meaning to
Don't steal apples, oranges, pairs, don't steal.
The rule that these are different, is not "the essence of logic". It's not logic at all.
It's just a rule, applied logically.
2)
Secondly, not every tradition is derived from the 13 rules, infact I think you'd find that very few are.
I don't think you'd be able to use the 13 rules to conclude that potiphera's testicles were crushed.
Or the tradition that Cain and Abel had a twin sister.
Yes, there is a superfluous word there (Et - direct object marker). But no rule to get from that to the tradition that he had a twin. It is a hint to the tradition. But the source of the tradition is not the superfluous word.
3) Rabbinical fence laws are in gemara too, and not derived from those 13. neither are rabbinical mitzvot. You won't derive purim or chanukah from the 13 rules.
Infact. I reckon very few of the laws in gemara are derived from the 13..
I think the malbim had 613 rules, but you still won't get about potiphera's damage, or cain and abel's twin sisters.
Here is an application of rules.. perhaps not of the 13. But you see it is not going to get you creative traditions, fresh stories , that are blatantly not derived.
This is an example of something derived, by rules like rabbi yishmael's. It is quite different to what you suggest. The conclusions cannot be as open ended as you posit. It's just not the ball game that you think it is.
http://www.myjewishlearning.com/holidays/Passover/TO_Pesach_Seder/Matzah_368/matzahfirstnight/matzahfirstnighttexts.htmMekhilta, Pischa 8 (Lauterbach)
One verse says "Seven days you shall eat matzah" and one verse says
"Six day you shall eat matzah." How can both of these verses be
maintained? The seventh day was included (in the first verse) but then
excluded (from the second verse). That which is excluded from a more
inclusive statement is meant to teach us about the whole statement. So,
just as on the seventh day it is optional (r'shut), so on all of the
other days, it is optional. Does this mean that it is optional on the
first night also? The verse "In the first month, on the fourteenth day
in the evening, you shall eat matzah" (Exodus 12:18) fixes it as an
obligation (hovah) to eat matzah on the first night.