A FORTIORI LOGIC



Appendix 3 – A fortiori
discourse in the two Talmuds

There is a great need for someone to go through
all Talmudic literature, and in particular the two Talmuds, looking for all
sorts of reasoning in it, and more specifically for applications of the rabbinic
hermeneutic principles, and in particular for instances of a fortiori argument.
This is a massive job, of course, which ideally ought to be carried out in
relation to the original texts, in Hebrew and Aramaic. Many people need to get
involved in this project, which is really worthwhile. We can never hope to fully
and correctly understand and evaluate Talmudic logic without such thorough
empirical research. I have no intention to do this important work, for the
simple reason that I do not have the linguistic knowledge needed for it. But I
here try and do a small part of it, specifically in relation to a fortiori
argument and in English translation.


The Jerusalem Talmud

(JT) was the first to have been closed, ca. 400 CE. I have almost no personal
experience with this Talmud, but judging from what I have read about it, it is
shorter and less disputative, and so we may expect it to contain relatively
fewer a fortiori arguments. As Neusner wrote:

“The Yerushalmi speaks about the Mishnah in
essentially a single voice, about fundamentally few things…. [It] takes up a
program of inquiry that is not very complex or diverse. The Yerushalmi also
utilizes a single, rather limited repertoire of exegetical initiatives and
rhetorical choices, etc.” (Rabbinic Literature: An Essential Guide, p.
41.)


The Babylonian Talmud

(BT), closed ca. 600 CE, is the document that
will require the most research work. We can expect hundreds of a fortiori
arguments in it, to be listed and eventually analyzed. Blau reports that Schwarz[1]
estimates the statistics for the second hermeneutic rule, that of gezerah
shavah
, as follows:

“…in the Babylonian Talmud alone, there has to
be close to four hundred, in the Talmud Yerushalmi about one hundred and fifty
and in the Tosefta thirty. If one adds to that the gezerah shavah in
halakhic works and other sources, there would be, after deduction of the
numerous parallel passages, a total of six hundred” (p. 156).

I do not know if Schwarz made similar estimates
for the first hermeneutic rule, qal vachomer, in his book devoted to that
subject. But it is a fair guess offhand that the statistics are in the same
order of magnitude. Needless to say, we are not counting a fortiori arguments in
order to discover who has argued a fortiori the most often; there is no
competition to be won! The purpose of our counting them is to accurately
determine the number of cases we have to eventually list and analyze.

In any study of a fortiori argument in the
Talmud, we must of course distinguish the different sources of cases
found in it. The Talmud may be quoting a passage from the Torah (the Five Books
of Moses) or the Nakh (the rest of the Jewish Bible), or from the Mishna
(redacted ca. 220 CE)[2],
or from the Tosefta (compiled at about the same date or soon after)[3],
or a baraita (a statement the Gemara claims as Tannaic, not included in
the Mishna, though it may be in the Tosefta), or lastly the Gemara (which in
turn has many layers). I will not do this here, but obviously it has to be done
if we want to obtain an accurate picture of a fortiori use.

As regards English translations of the Talmuds,
we have, I think only five sets to choose from. The three most recent are The
Schottenstein Edition of the Talmud
Bavli as well as The
Schottenstein Edition of the Talmud
Yerushalmi (New York: ArtScroll,
various dates)[4],
The Steinsaltz Edition of the Talmud (New York: Random House, 1989-99)[5],
and The Talmud of Babylonia. An American Translation (Atlanta: Scholars
Press for Brown Judaic Studies, 1984-95)[6].
To my knowledge, these editions are not available in a form that allows computer
search, although the Steinsaltz edition is at least partly posted in the
author’s website[7].

An older translation is The Soncino Edition
of the Talmud
(London, 36 volumes, 1935-1952), edited by R. Isidore Epstein
(1894–1962). This is freely available online, thanks to

Halakhah.com (a Chabad project), in 63 pdf files[8].
This resource is potentially very useful, provided we take the trouble to merge
all these files into one document so as to avoid repetitive work; the single
file would of course need to be purged of all editorial content, such as
introductory material and footnotes.

Still older is The
Rodkinson
Edition
of the
Babylonian
Talmud

(1903)[9].
This edition is freely available online thanks to the Internet Sacred Text
Archive[10],
in Kindle format[11].
I managed to convert this file into a Word file, from which I removed all
extraneous material (i.e. all Rodkinson’s introductions, synopses, footnotes,
etc.). This edition contains all of the tractates in the Orders (Sedarim) of
Moed (
Appointed Seasons: 12 tractates)
and Nezikin (Damages
: 10 tractates)[12].
Thus, four entire Orders are missing in it, namely:

Zeraim (Seeds: 11 tractates), Nashim (Women: 7
tractates), Kodashim (Holy Things: 11 tractates), Tohoroth (Cleannesses: 12
tractates). Clearly, the Rodkinson edition does not comprise the whole Talmud,
so that any information gathered from it is likely to be incomplete.

But my purpose here is to launch a pilot
study
, to show the way we may obtain the desired information and statistics.
I would have preferred to do this pilot study in relation to the Soncino
edition, which is not only more complete but also more generally respected; but
I decided to focus on the Rodkinson edition to save time and effort. This should
suffice to show the way, even if the results obtained will not be as thorough
and reliable. Anyway, even if Rodkinson’s translations are not universally
approved, this handicap hardly affects our study because it specifically focuses
on a fortiori argument.


Pilot study.

Ultimately, we need to actually list all passages of the Talmud that seem to
have a fortiori intent, and see whether they can indeed be cast in standard form
(whether valid or invalid). This can only be done exhaustively by going through
the whole Talmud page by page, which I do not propose to do here. Instead, I
propose to search for a number of key phrases which are usually, or even just
often, indicative of a fortiori discourse. This is why I needed a single
file, purged of all commentary. We cannot find key phrases and count instances
in the Rodkinson edition by means of an Index, because it does not have one.

I did in the past,
when I wrote Judaic Logic (1995), look
into the Index Volume of the Soncino edition (1952), and there found 137 entries
apparently indicative of a fortiori argument, which I tabulated as follows[13]:

Soncino BT index
entries

#

A fortiori

52

A minori ad
majus

31

Kal wa-homer

34

Deduction,
proofs by

2

Inference from
minor to major

8

Major, inference
from minor to

8

Minor, inference
from major to

2

Total count of a
fortiori references

137

Table A3.1

Research by means of search strings is bound to
give us a more accurate picture of a fortiori use. The problem with it, of
course, is that it allows for overlaps.

For example, we might count twice the single
argument “Aqiba then drew an a fortiori conclusion. He said: ‘If the soft
has so much power over the hard as to bore it (water over stone), how much
more
power will the Torah, the words of which are as hard as iron, have over
my heart, which is flesh and blood?’” – once for the phrase “a fortiori” and
once for “how much more.”
Such overlaps
can only be eliminated at a later stage, when each argument is listed and
examined closely. For the time being, we shall ignore this difficulty and aim
for a rough estimate.

Incidentally, it is important to keep in mind
when searching for such arguments that the relevant quantitative indicator has
to be in the putative conclusion – not in a premise. In the above example, for
instance, the relevant indicator is not the antecedent “so much” (which merely
refers to an unspecified, impressive quantity), but the consequent “how much
more” (which serves to signal a fortiori argument). Thus, an expression (such as
the “so much” used here) might be counted as indicative of a fortiori argument
and yet in fact not be so – because, though it would be indicative were it in
the conclusion, it is not in the conclusion.

The first step in our research is to think of
key phrases to search for. The expressions possibly indicative of a fortiori
discourse are of two kinds. The first groups includes idiomatic markers like
‘all the more’, ‘how much the less’, ‘so much more’, and so on. The second
groups descriptive markers such as ‘a fortiori’, ‘from minor to major’,
‘inference’, ‘argue’, ‘logical’ – to name just a few.

With regard to the first kind, we need to decide
the order in which our search will proceed, so as to avoid unnecessary
repetition. For that purpose, I have developed the hierarchical arrangement
shown in the following diagram. The a fortiori phrases are there abbreviated,
using the first letters of the words constituting them; for example, ‘smms’
means ‘so much more so’. Note that for every expression with ‘more’, there is a
similar expression with ‘less’. The root of all these expressions is the top
one, the comparative ‘more’ (or ‘less’, as the case may be); from this we derive
‘much more’, ‘how much more’, ‘so much more’, and also ‘still more’ and ‘even
more’, and more specific verbal forms. A similar flowchart may be constructed
starting with the subsidiary root ‘the more’, from which we derive ‘much the
more’, ‘how much the more’, ‘so much the more’, and also ‘still more’ and ‘all
the more’, and less generic verbal forms.

Diagram A3.1 Hierarchy of a fortiori
expressions

In the above diagram, the most specific
expressions (e.g. smms) are on the right; the more generic (e.g. smm) are in the
middle, and the most vague (e.g. sm+) are on the left (examples of the latter
are ‘so much greater’ or ‘so much worse’). From this we see that the best way to
search through a given document, to ensure a minimum of misses or overlaps,
would be in the following order. First, we should look for derivatives of ‘the
more’, starting with the most specific ones and ending with the most generic
ones; second, we should look for derivatives of ‘more’, starting with the most
specific ones and ending with the most generic ones. The full orderly list and
the results obtained are given in the following table:

A fortiori wording

Count

A fortiori wording

Count

so much the more so

10

so much more so

0

so much the less so

1

so much less so

2

so much the more (residue)

152

so much more (residue)

11

so much the less (residue)

9

so much less (residue)

3

so much the (residue)

1

so much (residue)

6

how much the more so

0

how much more so

0

how much the less so

0

how much less so

0

how much the more (residue)

13

how much more (residue)

15

how much the less (residue)

0

how much less (residue)

4

how much the (residue)

0

how much (residue)

1

much the more so (residue)

0

much more so (residue)

1

much the less so (residue)

0

much less so (residue)

2

much the more (residue)

3

much more (residue)

2

much the less (residue)

0

much less (residue)

18

much the (residue)

0

as much as

2

still the more so

0

as little as

0

still the less so

0

much (residue)

4

still the more (residue)

0

still more so

3

still the less (residue)

0

still less so

1

still the same

1

still more (residue)

10

still the (residue)

0

still less (residue)

0

all the more so

2

still (residue)

?

all the less so

0

even more so

1

all the more (residue)

2

even less so

0

all the less (residue)

1

even more (residue)

15

all the same

3

even less (residue)

4

all the (residue)

0

even (residue)

?

none the less / nonetheless

18

more so (residue)

0

nevertheless

?

less so (residue)

0

the more so (residue)

8

no/not more

3

the less so (residue)

3

no/not less

0

the more (residue)

3

more (residue)

?

the less (residue)

1

less (residue)

?

Table A3.2

Please note well that this is almost raw data,
yet to be fully processed by detailed analysis case by case. However, I have
here made a small effort to narrow the field. As regards idioms that are almost
sure to signal a fortiori discourse, I looked at most cases briefly, in an
offhand manner, and eliminated obvious ‘duds’, by which I mean letter strings
that accidentally resemble a fortiori ones (for example: in ‘a children-teacher
who struck too much the children’, the string ‘much the’ is obviously not
intended as an a fortiori marker). As a general rule, in cases of doubt I
counted possible cases as actual cases, without taking the trouble to closely
examine the data further.

As regards the search strings labeled ‘residue’,
my policy was to discount all cases but the most likely to be a fortiori
discourse. The statistics for such more generic words or phrases exclude the
counts for more specific phrases derived from them: whence the label ‘residue’.
For example, the count for ‘so much the’ excludes the counts for ‘so much the
more’ and ‘so much the less’, which in turn exclude the counts for ‘so much the
more so’ and ‘so much the less so’. This allows us to see more precisely the a
fortiori wording used, and also facilitates dealing with the vaguest residues.
To give an example: the count for ‘so much the more’ (152) excludes the more
specific cases of ‘so much the more so’ (10), and the more generic string ‘so
much the’ (1 instance) excludes the cases of ‘so much the more’ and of ‘so much
the less’.

Similarly with other word strings. Obviously,
the count of the residue of ‘all the’ must exclude cases falling under ‘all the
same’, as well as those under ‘all the more’ and ‘all the less’. The reason why
phrases with ‘the more’ (first column) must be counted before those with just
‘more’ (second column) is that the residue of ‘much’ excludes all cases with
‘much the’; and likewise, ‘still’ must exclude ‘still the’, and ‘more/less’ must
exclude ‘the more/less’.

The more vague the search string, the more
instances it in fact includes; but the method of residues here used allows us to
narrow the field somewhat. In the case of ‘so much the’, only one instance (“so
much the firmer”) was leftover, and this happened to indeed be a fortiori. In
the case of the residue ‘so much’, only 6 instances out of 75 qualified at first
glance as a fortiori (namely, those worded “in a so much larger degree” or “in
so much greater a degree”). For ‘how much’, out 80 remaining instances only 1
qualified (worded “how much severer”). For ‘much’, out of 234 instances only 4
qualified (worded “much better” or “a much greater”). For the residue ‘the
more’, out of 83 instances only 3 turned out to be apparently a fortiori (“I
enjoyed myself the more because I fulfilled two religious duties,” “the more
should it be allowed…,” “it applies the more to…”).

Note that all admitted cases involve a
comparison
(e.g. firmer, larger, greater, severer, better, more enjoyable).
In many cases, no potentially a fortiori instances were found (at least in my
offhand reading of them). Thus, to illustrate: none of the 99 instances of ‘no
less’ or ‘not less’ qualified; likewise, none of the residual 33 instances of
‘still the’ and none of the 1010 instances of ‘all the’ qualified (I looked). In
certain residual cases, I did not take the trouble to look at the individual
instances at all, expecting negligible results (i.e. close to zero). Thus, for
‘nevertheless’ (498 instances) ‘still’ (777), ‘even’ (3642), ‘more’ (1159) and
‘less’ (1949) – I put a question mark, and counted the results as zero. I should
explain that the work of individual verification, even done as roughly as I did
it, is extremely time consuming.

It is worth remarking that the ‘so’ of phrases
ending in ‘more/less so’ obviously refers to a previously given
predication. Phrases with ‘the more/less’ are intended as more emphatic
than those with just ‘more/less’; likewise, ‘so much’ is more emphatic
than just ‘much’; but these emphases are rhetorical: the logical weight is the
same. Similarly, ‘how much’ is a rhetorical question and therefore less
emphatic than ‘so much’; but their logical weight is the same. Looking at the
above list of commonly used expressions, it occurs to me that, from a purely
logical point of view, we could equally well use milder forms, like ‘a bit
more’, ‘quite a bit more’, ‘a little more’, ‘somewhat more’, or even ‘some more’
– for it is clear that the amount of ‘more’ is irrelevant here. Our habit
is to signal a fortiori intent by means of hyperbole (e.g. ‘all the more’), but
we could equally do so by understatement. However, looking for such milder
expressions in Rodkinson’s Talmud, I found no cases. Maybe some occur in the
Soncino Talmud.

Notice that I add in the above table a number of
search strings not included in the preceding diagram, namely: ‘still the same’
(1 out of 2 instances), ‘all the same’ (3/4), ‘none the less’ (18/18),
‘nevertheless’ (?/498), ‘as much/little as’ (2/114 and 0/0)[14],
and ‘no/not more/less’ (3/117 and 0/99)[15].
These are all expressions which may be (though evidently often are not)
indicative of a pari a fortiori argument (i.e. forms with an egalitarian
major premise, from which we can equally well reason from minor to major or from
major to minor). In any event, when we include these expressions in our listing,
we realize that there is a continuity in the wording, ranging from ‘all the
more’, through ‘much the more’ and ‘much the less’, to ‘all the same’ and ‘none
the less’ (and other expressions possibly indicative of a pari).

To repeat, definitive statistics will only be
possible when each and every case is actually listed and examined in detail – a
massive job, which I will not here attempt to do. Having in the above table
dealt with idiomatic a fortiori indicators, we should next deal with the more
descriptive ones. The following table should, I think, cover most of the
potential ground.

A fortiori wording

Count

A fortiori wording

Count

a fortiori

147

it is sufficient

73

a minori (ad majus)

0

sufficient (residue)

365

a majori (ad minus)

0

it suffices

13

from minor (to major)

0

suffice (residue)

144

from major (to minor)

0

it is enough

0

kal vochomer

0

enough (residue)

171

inference(s)

60

it follows

19

infer(s), inferred, inferring

984

not follow

23

deduction(s)

19

analogy, analogies

166

deduce(s), deduced, deducing

467

analogous

32

proof

70

analogical, analogue

0

prove, proved, disproved

142

likewise

121

argument(s), argumentation(s)

70

similarly

23

argue(s), argued, arguing

27

general

261

logical

10

particular

255

other wording

?

N.B. These counts are raw data.

Table A3.3

Please note well that the statistics in this
table are even more unprocessed than those in the previous table. I just give
the raw numbers dished out by the search engine, without taking the trouble to
look at individual cases. The total for this table is 3662, and this is not
counting words indicative of inference like ‘therefore’ (1616), ‘hence’ (2270,
including 861 ‘whence’ and 42 ‘thence’), then (4729, including ‘thence’), etc.
Clearly, a lot of work is necessary to sort through all these.

I include ‘kal vochomer’ in this table, because
Rodkinson used this phrase in a note[16];
but as it turned out he did not use it in the text proper. Nor does his
translation, unlike the later Soncino translation, ever use the key phrases ‘a
minori/majori’, or ‘from minor/major’. His main descriptive term is, thus, ‘a
fortiori’; this may be used to signal a fortiori intent or to refer to an
already proposed a fortiori argument. In any event, use of this key phrase
cannot be indicative of anything other than assumed a fortiori discourse.

Nevertheless, many more a fortiori arguments
may
be found by means of the other key words listed in this table and others
like them. The word ‘infer’ presumably usually corresponds to the Hebrew word
din
, which is in rabbinic discourse often used to refer to a fortiori; the
same may apply to the words ‘deduce’, ‘prove’ and ‘argue’. Note that these words
often appear in a rhetorical negative question: ‘is it not an inference that…’,
‘can we not deduce that…’, ‘is it not logical that…’.[17]

Obviously, some of these inferences, deductions,
proofs or arguments must refer other hermeneutic principles, such as gezerah
shavah
and binyan av, since a fortiori is not the only form of
reasoning used in the Talmud. I do not at this time have a clear idea as to how
such other interpretative forms are actually worded in Rodkinson’s edition, or
anywhere else for that matter. Obviously, this question must eventually be
answered. When we do that, our

investigation
will expand from specific
concern with a fortiori argument to general concern with all the hermeneutic
principles. However, I am not disposed at the present time to look further into
this matter.

The main key phrases used by Rodkinson to refer
to a fortiori argument are now seen to be the descriptive phrase ‘a fortiori’
(147 instances), and the various idiomatic phrases ‘much the more/less’ (189),
‘much more/less’ (71), ‘even more/less’ (20), ‘still (the) more/less’ (15), ‘all
the more/less’ (8), among others (36)[18].
The overall result is that the number of a fortiori arguments in the Rodkinson
edition of the Talmud may be about 500 (a round number). This is ignoring
overlaps in the first and second tables (no doubt many), as well as all possibly
a fortiori intents in the remainder of the second table (maybe numerous);
perhaps these and those balance each other out somewhat. This is still a very
rough and uncertain tally, of course; but it is better than nothing – an
educated guess, let’s say. Moreover, keep in mind that Rodkinson’s edition
includes only two of the six orders of the Talmud – so the final count may be
three times this figure!

It should be emphasized that this statistic lumps
together purely a fortiori arguments and a crescendo arguments. It is clear that
a future fuller study has to distinguish them, i.e. identify how many cases of
each of these two types there are. Moreover, each case must be classified as
either positive or negative, and subjectal or predicatal (copulative) or
antecedental or consequental (implicational), to be really understood. These
various moods should then be counted separately. All this additional precision
of course requires more detailed analysis of each individual case than here
done.


Regarding the dayo principle.

The key phrase ‘it is sufficient’ seems to be
our main indicator of appeals to the dayo principle here; surprisingly,
this occurs very rarely.
From the data
found through mechanical search for “it is sufficient” (73 instances) in the
Rodkinson edition of the Talmud, there appears to be only six passages
that explicitly appeal to the principle of dayo in some form, such
as “it is sufficient that the result derived from an inference be equivalent to
the law from which it is drawn,” or more briefly as “the rule of ‘It is
sufficient,’ etc.” The passages concerned are the following: In tract Baba Kama:
the Gemara concerning Mishna 2:1 (1 mention); the Mishna 2:5 (1 mention) and its
Gemara (5 mentions); the Gemara concerning Mishna 4:3 (1 mention). In tract Baba
Metzia, the Gemara concerning Mishna 3:6 (1 mention). In tract Baba Bathra, the
Gemara concerning Mishna 8:1 (2 mentions). And in tract Shebuoth, the Gemara
concerning Mishna 4:1 (1 mention).

One question to ask here is: do all these
applications concern the inference of a penalty from Biblical law? The answer is
clearly yes in cases 1-4, which all concern payment of damages. Case 6 concerns
legal liability through making an oath, and so can also be viewed as proper for
dayo application. Case 5 is open to debate: I have dealt with it in the
chapter on Adin Steinsaltz, in the section called ‘A recurring fallacy’ (18.2),
under the heading of ‘On Baba Batra 111a-b’, there pointing out that reference
to the dayo principle may be misplaced because while for the daughter the
proposed judgment is unfavorable, for the son it is favorable[19].
Thus, judging by the Rodkinson edition, in the 6 cases which explicitly appeal
to the dayo principle, it is used to limit a penalty or responsibility or
right. This accords with my theory of the intended scope of dayo.

This result, of course, does not exclude the
possibility that there are cases other than those here enumerated, where the
dayo
principle is appealed to explicitly but using other wording than “it is
sufficient,” or in a more tacit manner, which might yield a different conclusion
regarding the intended scope of the principle. To give an example, we saw in the
chapter ‘In the Talmud, continued’, in the section ‘Three additional Gemara
arguments’ (8.6), how the dayo principle (in both its versions) may be
very present in the background of a discussion without being explicitly
mentioned. Moreover, the Rodkinson edition is far from complete; so, some
dayo
applications may well be missed in it – for instance, the dayo
principle is appealed to in Zebachim 43b-44a, but the Rodkinson edition lacks
this tractate.

Note lastly that I have not here made an effort
to determine the standard form(s) of the six arguments relative to which dayo
was used. Cases 2 and 5, having been dealt with elsewhere, we know to be
positive subjectal; but the other four cases have yet to be classified. Since
the original dayo objections in the Mishna are of two sorts, applicable
respectively to purely a fortiori argument or to a crescendo argument, we cannot
predict how many of these two sorts occur in the Gemara. Furthermore, we should
look and see whether the language used in proportional differs from that in
non-proportional arguments. I leave these tasks to others.

We will end our pilot
study
here, without going into more detail or precision, having set an example of
methodology and structure of research, and anticipated and dealt with some of
the pitfalls that may be encountered.






[1]
In his Der Hermeneutische Analogie
in der Talmudischen Litteratur
, pp. 84, 87, 89.




[2]
See the Jewish Encyclopedia article
online:


www.jewishencyclopedia.com/articles/10879-mishnah
.




[3]
See the Jewish Encyclopedia article
online:


www.jewishencyclopedia.com/articles/14458-tosefta
.




[4]
These seem to be complete. See:


www.artscroll.com/Talmud1.htm
.




[5]
This refers to BT and apparently only
includes Bava Metzia, Ketubot, Ta’anit, and Sanhedrin. See:


www.steinsaltz.org/learning.php?pg=Talmud_-_Books&articleId=1424
.




[6]
This is translated (or edited?) by
Jacob Neusner, Tzvee Zahavy and others. Complete.




[7]
At:


www.steinsaltz.org/index.php
.
Since the search facility returns only 11 results for ‘fortiori’, I
assume the data base is far from exhaustive.




[8]
This is found at:


www.halakhah.com/indexrst.html
.
A Kindle edition is also available for a small price, at


www.talmudicbooks.blogspot.ch/2012/05/amazon-kindle-oral-torah-in-36-volumes.html
.




[9]
Michael Levi Rodkinson, previously
Frumkin, was a Jew who emigrated to America (1845-1904).




[11]
It is also available in eBook format
which can be read using Adobe Digital Editions (ADE) reader. I should
mention that, while the Kindle for PC reader has the advantage that its
search facility lists ‘all’ the matching cases at once, it has a maximum
limit of 100 hits; the ADE reader, on the other hand, has no maximum
limit, but it only takes you to the matching cases one at a time.




[12]
“Plus some additional material related
to these Orders;” namely: Ebel Rabbathi / Semahoth; Aboth of R. Nathan;
Derech Eretz Rabba and Eretz Zuta.




[13]
As I pointed out at the time, this
statistic cannot be taken at face value, “because the references are to
page numbers, which may contain more than one argument of the same type;
also, not having looked at them, I cannot guarantee that they are all
legitimate cases. I would suspect offhand, on the basis of my minimal
experience of Talmud study, that this list is incomplete (all the more
so if we include the Commentaries).”




[14]
The two apparent a pari in the
sentence: “Yea, thou hast occupied thyself as much as R. Hyya, but thou
hast not multiplied the Torah as much as he did” are perhaps more
implicit than explicit. Paraphrasing: If you occupied yourself with
Torah as much as he did, then if his credit is x, your credit would be x
(as much as his); and if you spread the Torah as much as he, then your
credit would be as much as his.




[15]
Wording: “not more rigorous” (2
instances of 3) or “no more than…” (1 instance of 17).




[16]
Rodkinson’s there (in Vol. 2, Part I)
says: “This is a case of where the peculiar Talmudical expression of Kal
Vochomer appears in the text. The literal translation is ‘light and
heavy’, i.e., from the lighter to the heavier or from minor to major. In
the Introduction to the Talmud by Prof. Dr. Mielziner an entire chapter
is devoted to the explanation of this term (pp. 130-141). However, no
general term can be found to express its meaning, and the expression
must be varied according to the demand of the text.” This remark is to
my mind rather strange, given that the Hebrew expression qal vachomer
has long been known to refer to a fortiori argument, and indeed
Rodkinson freely uses the expression a fortiori elsewhere!




[17]
Note that the 365 instances of
‘sufficient’ include 56 ‘not sufficient’ and 5 ‘insufficient’; the 144
instances of ‘suffice’ include 20 ‘not suffice’; and the 171 instances
of ‘enough’ include 15 ‘not enough’. Note also that besides the 19
instances of ‘it follows’ and the 7 of ‘not follow’, there are 281 other
‘follows’ and 82 other ‘follow’.




[18]
Note that here under ‘more/less’ I
include cases of ‘same’ and other comparatives.




[19]
This may be why the halakhah in this
case does not align with the dayo principle.