[Avodah] Chazal are Infallible

[Zev Sero]

Micha Berger wrote:
> In vol 13, RJSO quoted Tosafos haRosh, who makes the argument about
> the shiur of pi rather than pi itself. [...] If you would like to
> pick up from that point rather than restart the debate from the
> beginning a third time, I would appreciate it.



> [JSO]
>> Tosefos HaRosh (Eruvin 14a) ... 
>> (A) How do we have a licence to record Pi as 3, i.e. as an 
>> appoximation. The Talmud anwers that the licence is from Scripture 
>> (i.e. Solomon's pool where it is also recorded approximately). 

OK, so you're proceeding on the assumption that the authors of this
gemara knew the correct value of pi, or something close to it.  At
least, they knew that it was bigger than 3, and that the mishna was
intentionally rounding it.  So let's see how your reading works.


> [RZS]
>> between 9.5*pi and 30.5). The Tosefos Harosh could learn the 
>> mishna very easily that way. But how can he learn the gemara that way?
> 
> I had this question as well when I first learned the sugya. But since (A)
> is the shita not only of the Tosefos HaRosh but also the Raavad, Meiri,
> Tashbatz and to my understanding the Rambam, GR"A (see Alef Kesav 117),
> Aruch HaShulchan, Chazon Ish and MB, I would suggest the following:

Really?  All these people comment on the gemara, and all understand
the gemara to actually know the correct value, and to be asking how
the mishna got the right to round it?  Where, exactly, does the Rambam,
for instance, comment on this gemara at all, let alone give this
explanation?  

Now I haven't seen the Tosfos HaRosh inside, so I have to take your
word for it that this is indeed what he says, and isn't simply
something you're reading into him, just as you're reading it into
the gemara.  But now you're telling me that *all* of these meforshim
explain the gemara that way, but somehow this explanation eluded our
Tosfos, who is left with a question, as well as all the other
meforshim on the page who don't even seem to have a question in the
first place?  That seems rather a lot for me to take on faith.


> [The Ramchal writes in Derech Tevunos that the derech of the Talmud is
> to be brief and many steps are unstated, and we have to fill them in
> for ourselves. So please treat the following in the same manner].

Seems like a license to make up whatever we like, and put it in the
mouth of the gemara.


> MENA HANI MILI [that X]
> We need to fill in for ourselves what X is, the Gemora does not
> specifically state what it is.
> X is: how do we have a licence to record Pi as 3?

How about, "hani mili" means exactly what it means EVERY OTHER TIME
the gemara uses those very words?  It ALWAYS means how does the
mishna know WHAT IT JUST SAID, not some hypothetical argument that
the gemara silently assumes the mishna is making.  If the gemara
understands the mishna to be saying something different than what
the words mean, it explains that first (and gives a reason or a
source), and THEN asks how the mishna knows it.  The mishna says
that anything with a circumference of 3 tefachim has a diameter
of 1 tefach, NOT that we merely "see" it as having such a diameter;
the gemara asks how the mishna knows that.



> ("3", after all, is a fairly close approximation (5%) and a nice round
> number that makes the presentation easier as we do in engineering
> texts today)

I'm not sure what you mean by this, so I'm leaving it in without
comment.  Is this meant to be an explanation of the gemara, or of
what the gemara is thinking about the mishna, or what?


> VEHA IKA SEFASO?
> The 10 cubit diameter is for the inner rim whereas the 30 cubit
> circumference is for the outer rim (Rashi).  Assuming that the
> width of each rim is a tefach which is one sixth of a cubit we
> then get approximately 2.903 (remember there are two rims).
> This gives us about 2.903 which is less accurate than 3 and is
> not the nice round number we were looking for.

So the gemara knows that pi is actually something greater than 3.1,
it's looking at this pasuk for confirmation that it's OK to round
it to 3, and it raises the objection that the pasuk seems to be
"rounding" to 2.903?  And therefore that should be the official
halachic approximation, because it's so much easier to work with
2.903 than with 3.142?  Really, how do you think this objector was
understanding the pasuk?  If you read the gemara straight, it's
obvious what the objector was thinking, but if we insist that the
amoraim understood that both the mishna and the pasuk were giving
rounded values, then please explain this makshan's hava amina.


> AMAR RAV PAPA
> The rim was of neglible width.
> 
> VEHA IKA MASHEHU?
> Even a neglible amount is a problem. 
> The problem is that we still get a number (say 2.988) that is less
> accurate than 3 and is not the nice round number we were looking for.

Huh?  We're taking it for granted that the pasuk is rounding, and
yet we cavil at a mashehu, that will cause what problem, exactly,
for our premise?  If the gemara understands the pasuk (as we do)
to be saying that the diameter of the yam was *approximately* 10
amot, and that the circumference was *approximately* 30 amot,
then what difference does it make that the thickness of the rim
was non-zero?  When we learn the pasuk, knowing as we do that
it's rounding the numbers, does it even occur to us to wonder
whether the measurements were taken on the inside or the outside?
The question seems ludicrous.  Only if we assume the pasuk's
numbers to be precise does the question of the thickness of the
rim, and of which surface was being measured, make any sense.



> KI KA CHASHIV
> Both the circumference and diameter are stated with respect to the inner
> rim and thus we get the nice round number 3 as an approximation of Pi.

As opposed to what, an ugly and unwieldy "round number" of slightly
less than 3?  Is that really the gemara's objection to the mishna,
that the mishna ought to have said that we approximate the true
value of pi to 2.903, or 2.999?  Why would it even occur to anybody
to do that?  Anyone who can work with a strange number like that,
can work with 3.1416 just as easily!



> The bottom line is that all these meforshim say that Chazal were well
> aware that 3 is an approximation and the question is only one of usage.

Which of these meforshim say that about *this gemara*, please?



> This also makes sense for a variety of reasons.  One of them is that
> the whole Mishna is talking about approximations, e.g. if the beam
> was made of reeds we view it as if it were made of metal, if round
> we view it as square, if it has a circumference of 3 [we view it
> as if] it has a diameter of 3.

[ZS: I assume that last figure is a typo for 1].

That is NOT what the mishna says.  That is explicitly NOT what it
says, and it's wrong of you to twist its words that way.  The mishna
is not giving approximations, but abstractions.  It's saying that we
don't care whether the beam could actually hold a physical brick,
but only whether it's big enough to hold one, so we abstract the
essential point -- its size -- from the accidents of its material
and shape.  We don't care about this notional brick's shape or
weight, any more than we care about who made it, or the colour of
the truck that delivered it, or how much it cost.   Then, after all
the "if it was...we view it as..." clauses, the mishna changes
language, and states as a *fact* that "any [beam] that has a
circumference of 3 tefachim has a diameter of 1 tefach";  NOT
"we view it as if it had" such a diameter.  Doesn't that change of
language seem significant to you?  How can you read it as simply
a continuation of the preceding list of "we view it"s?



> We are, I would say, forced to learn the Gemora like all the mefarshim.

As opposed to, say, our Tosfos?


-- 
Zev Sero               Something has gone seriously awry with this Court's
zev at sero.name          interpretation of the Constitution.
                       	                          - Clarence Thomas