Cardinal and Ordinal Numbers: Halakhic Aspects (Column 401)

In the previous column, I discussed the distinction between quality and quantity. There I noted its connection to the mathematical distinction between cardinal and ordinal numbers, as well as to the physical distinction between extensive and intensive magnitudes. In this column I wish to consider some halakhic implications of these two kinds of counting, and the lomdut (conceptual) ramifications that branch out from this.

A dispute among the Rishonim about one who missed a day of the Omer count

At Tosafot s.v. “Zekher,” Menachot 66a, the view of Behag (Ba'al Halakhot Gedolot) is cited at the end regarding one who forgot to count one day of the Omer:

He also ruled in Halakhot Gedolot that if one interrupted for one day and did not count, he no longer counts, because it requires completeness (temimot). This is a great wonder and cannot be.

Thus, Behag and Tosafot disagree: according to Behag, one who forgot to count one day can no longer count; he has lost the mitzvah. It is commonly explained that his view is based on the verse commanding the Omer count, which says “seven complete weeks,” implying all the days. Tosafot reject this out of hand, saying it cannot be. Their explanation—like that of several other Rishonim (see, for example, Rosh, Pesachim, ch. 10, §41)—is that we recite a blessing every day before counting, which proves that each day is a mitzvah unto itself.

The usual explanation of the dispute is whether counting all the days of the Omer constitutes one general mitzvah or 49 separate mitzvot (one for each day). It is clear that with regard to enumerating the commandments there is only one mitzvah here, but the parameters of the mitzvah itself do not necessarily depend on the counting of mitzvot.

Practically speaking, we today follow the ruling of the Shulchan Aruch, sec. 489:9:

If one forgot to bless on one of the days, whether the first day or other days, he counts on the remaining days without a blessing.

In principle, he rules (out of doubt) to continue counting in order to fulfill the mitzvah, but out of doubt one does not recite a blessing.

What is the law of a minor who grew two hairs in the middle of the Omer count, or a convert who converted during the counting days? Seemingly, this too depends on the same dispute. During the days before he came of age/converted, he did not fulfill the mitzvah; therefore, according to Behag he lost that year’s mitzvah, and even if he continues to count he should count without a blessing. But according to Tosafot, he is obligated to continue counting with a blessing.

Halacha

Despite what was said—and as accepted among poskim and later authorities—judging by my best assessment, a minor who comes of age during the Omer count continues to count with a blessing according to all views (i.e., even according to Behag). The basis for my claim is that this person had been counting as a minor by virtue of the educational obligation (chinuch). True, as is known, the law of chinuch is rabbinic, and therefore a minor who counts does not fulfill a Torah-level mitzvah; nonetheless, in my view he should continue to count with a blessing.

Two explanations can be offered:

• He may continue to count with a blessing by virtue of chinuch. After all, when he counted under chinuch he also recited a blessing; if so, there is no reason that now, as an adult, he should count without a blessing. My assumption is that becoming an adult does not remove him from the framework of chinuch; it merely adds further obligations and does not exempt him from them. Admittedly, usually the law of chinuch loses practical significance once the child matures, because he moves into the category of those obligated on a Torah level. What, then, is different here?

This can be formulated in two ways:

1. Adults, too, are under a form of chinuch; but once they mature, a Torah obligation also applies, which overshadows chinuch. Therefore, when he lacks the Torah obligation (in this specific context), the chinuch obligation remains.
2. Once the child matures, the chinuch obligation lapses, since he is now obligated by Torah law. But in the case of a minor who matures in the middle of the count, because he still has not entered a Torah obligation in this particular mitzvah, specifically here the obligation to count by virtue of chinuch remains even after he matures.

• He continues to count with a blessing and thereby fulfills a Torah obligation even according to Behag.

Our concern here is with this latter claim, which I will now explain.

The nature of Sefirat HaOmer

We must consider whether Sefirat HaOmer is cardinal or ordinal. When I count the 15th day, am I counting how many days have passed since Pesach, or am I placing this day in the ordered series of Omer days up to Shavuot? One could hang this on whether the count faces forward (toward Shavuot) or backward (to Pesach), though that is not strictly necessary.

If I am counting how many days have passed since Pesach—i.e., if the Omer count is cardinal rather than ordinal—there is no inherent bar to counting the 15th even if I did not count the 14th. Viewing the Omer as a cardinal count leads to the conclusion that there is a separate mitzvah each day. But if the Omer count is ordinal rather than cardinal—that is, I am arranging the days one after another—then there is no meaning to setting the 15th day in its place if I did not set the 14th day in its place. Unlike counting, ordering by its very definition is a matter defined over the whole chain. In an ordinal count we arrange the links one after another, and one cannot attach the 15th link if one did not place the 14th before it. Put differently, if we did not order the 14th day, then the 15th day is in fact the 14th in the chain; thus we have not placed it in the correct location on the time axis.

According to this proposal, the dispute between Behag and Tosafot and the other Rishonim hinges on the nature of the Omer count: is it ordinal or cardinal? How does this formulation differ from the more common one that ties the dispute to the parameters of “temimot” (completeness)? If Behag’s source is the verse, it is reasonable to assume that his view addresses the definition of the mitzvah of Sefirat HaOmer. But if his view rests on understanding the concept of “counting,” there is room to say that the problem is not in the mitzvah’s parameters but in the realization of the concept of “counting” in practice, irrespective of whether there is a mitzvah here. On this view, one who skipped a day is not “counting,” and consequently does not fulfill a mitzvah; but the issue lies in the act of counting, not in the mitzvah per se.

Implications: a minor and a convert

The practical difference between these two explanations concerns a minor who counted under chinuch until he grew two hairs. Such a person has indeed been counting from the start. True, his counting did not constitute fulfillment of a Torah mitzvah, but only by virtue of chinuch; however, in practice he performed the act of counting. If now, after maturing, he counts the 15th day, one cannot say he did not set it in its place, for in fact there has been a continuous act of counting from the beginning—even if in the early days the counting was not a mitzvah. His act of counting has been ongoing since the start; consequently, the later days also have the meaning of counting. He is placing them in their proper places, and the 15th day indeed falls into place after the 14th.

My claim, then, is that Behag does not intend to make a claim about the parameters of the mitzvah of Sefirat HaOmer—namely, that we are obligated to count all the days. I argue that even according to him we are separately obligated to count each and every day; however, the term “to count” means to order the days one after another. Any day you did not set after its predecessor, you did not fulfill the mitzvah of counting for that day; and therefore, if you forgot a day, you can no longer continue counting.

A proof for this understanding is the Rishonim’s question from the blessing. I noted that the disputants challenge Behag: how can there be an obligation to recite a blessing each day before counting? If the whole count is one mitzvah, we should bless only once at the beginning. Perhaps there are other ways to deflect this question, but on my proposal it vanishes of itself. We have seen that even Behag agrees the mitzvah is separate for each and every day; hence, it is not difficult for him that we bless before counting every day. He merely maintains that the term “to count” a day means to set it after the day before it. His conception is that this is an ordinal count and not a cardinal one, whereas Tosafot disagree and hold that it is a cardinal count.

By the way, a convert who converts in the middle of the Omer stands differently—unless we are speaking of a convert who already counted as a gentile from the beginning, in which case his law is like that of a minor who counted under chinuch. Admittedly, this too is open to discussion, for if his counting had no halakhic significance, there is room for an opponent to claim that at least on the halakhic level it is as if he did not count.

Implications: retroactive completion (bedi'avad)

Sefer HaChinuch, mitzvah 306, writes:

There are those who said that one who forgot and did not count one day can no longer count in that year, because they are all one mitzvah; and since he forgot one day, the entire reckoning is nullified for him. Our teachers in our generation did not agree to this view; rather, one who forgot one day should say, “Last night it was such-and-such,” without a blessing, and then continue to count the others together with all Israel.

So too in Biur Halacha, sec. 489:8, s.v. “sofer,” in the name of Mahari"tz Gi'at and Shibolei HaLeket.

The Acharonim were very perplexed by this view: yesterday’s mitzvah has been lost—it is “twisted and cannot be made straight.” What does mentioning it on the following day help?! But according to our approach, this view is quite understandable. Of course, yesterday’s mitzvah has been forfeited, for you were to count yesterday’s day in its time. However, in order to order today’s count, you must first set yesterday in its place; thus, as part of today’s mitzvah I first set yesterday. This does not repair the mitzvah I lost yesterday, but it enables me to fulfill the mitzvah of counting today. Once yesterday has been set in its place, today’s counting can be called “counting” (in the ordinal sense), and consequently there is also fulfillment of the mitzvah.

Implications: “safeka deyoma”

As is known, in the Diaspora we treat festivals as if we had a calendrical doubt (safeka deyoma), celebrating two days “out of doubt.” Ba'al HaMaor at the end of tractate Pesachim wonders why we do not do the same for Sefirat HaOmer:

And regarding the Omer count there are those who ask… why do we not count two counts out of doubt, just as we observe two days of Yom Tov out of doubt? In sum, we should not be stringent with Sefirat HaOmer, which is only a remembrance nowadays… And if we were to count two counts out of doubt, the second count would extend into the first day of Atzeret (Shavuot), and one would come to treat a Torah Yom Tov lightly. Therefore, we have only the practice (of counting one).

He innovates that today Sefirat HaOmer is only a remembrance and not a Torah obligation, and therefore we are not stringent out of doubt. Admittedly, such stringency would cost us nothing, so it is not clear why not satisfy all opinions anyway. This could be explained by the rule that in a rabbinic doubt we are lenient, and there is thus no obligation. More difficult is what we would say according to the views that nowadays Sefirat HaOmer is indeed a Torah obligation.

Now, R. Shimon Shkop, in Sha'arei Yosher, Gate 1, ch. 5 (end of s.v. “However”), establishes a general principle about counts in general:

A number that is not determinate is not considered a number or a count.

That is, if you number something in an indeterminate way, you have not numbered it. On this basis he resolves Ba'al HaMaor’s question as follows:

It seems that if one is uncertain whether today is day 3 or day 4, he cannot count two counts out of doubt, for that is not considered counting at all. And I think I saw this law in some book.[1]

And according to our words, we can somewhat answer the Rishonim’s question why we do not always count two counts as we observe two days of Yom Tov; see Razah (Ba'al HaMaor)… for once we consider it a doubt, the entire mitzvah is nullified; and in the time when they were not expert in fixing the months, they would not fulfill the mitzvah of counting.

He argues that one cannot count two days out of doubt, because when you count you must know the number clearly; otherwise, there is no counting.

A great novelty emerges from his words. Today we have no real doubt, since the calendar is known to all; therefore, in our times there is recourse to count the correct day and not continue to count two days as if in doubt. But in the time when there was genuine doubt about the calendar, they truly could not count at all—and indeed he claims that in that period they did not fulfill the mitzvah of Sefirat HaOmer (which, according to Ba'al HaMaor, was a Torah obligation).[2] This is very difficult to say.

In any case, his view seems more reasonable if we assume the count is ordinal rather than cardinal. In a cardinal count, there appears to be no bar to counting out of doubt according to two possibilities: either 14 days have passed or 15 days. But ordering deals with setting the place of this very day; therefore, here one must know clearly whether it is the 14th or the 15th. This is not strictly necessary, of course.

However, R. Shimon’s words are difficult in light of several Rishonim. For example, at the beginning of that very Tosafot in Menachot it is ruled:

It seems that at doubtful nightfall (bein ha-shmashot) one may bless and need not wait until it is certainly night, since it is a rabbinic doubt.

We see from here that “counting with doubt” is still counting, not as R. Shimon assumed. So too in Ran at the end of Pesachim:

Therefore Tosafot said that since it is rabbinic, it is good to count on the first day at doubtful nightfall so that there will be perfectly “complete weeks,” but it is not proper to enter doubt ab initio. And as for “temimot,” we should not be more stringent about completeness nowadays, when it is rabbinic, than about counting when it was a Torah law; rather, whenever one counts at night, it is called “complete.”

It seems the Ran too accepts Tosafot’s law that one who counted during twilight has fulfilled [his obligation], but holds that one should not do so ab initio.

Indeed, R. Shimon himself challenges his principle from these sources (and adds more), and answers:

It may be said that the Sages originally instituted it that way because of “temimot.” And so the halacha implies from all the poskim: if he counted at twilight, he cannot bless again at night, lest he has already fulfilled [the mitzvah]; whereas according to what we said, out of doubt it would not be considered counting at all. All this still requires investigation.

He suggests that according to those views, this is how the enactment originally was—but he rejects this. If so, the question of Ba'al HaMaor returns: why do we not count two days out of doubt in the Diaspora?

Above I proposed that the basis of Behag’s view is that the count is ordinal and therefore must be continuous. If so, there is no need to assume that there is no counting out of doubt. The rule is that the order in the count must be continuous; consequently, if one is uncertain which day today is, he cannot count two days out of doubt, for after all he does not know with clarity the placement of the current day. But mere “counting with doubt” where there is no ordering problem—such as counting at twilight—can be a valid counting (I am placing the correct day in the correct place; it is only unclear whether the time for the mitzvah has arrived. That is merely a halakhic doubt, and we rule stringently). This, of course, resolves Ba'al HaMaor’s question, and the aforementioned Rishonim do not challenge it.[3]

Note: a parallel lomdus regarding fasts

Regarding a minor or a convert who becomes obligated in the middle of Sefirat HaOmer, I suggested that the demand for completeness and continuity does not deal with the parameters of the mitzvah, but with defining the very term employed by the mitzvah (“counting”). There is a similar conceptual phenomenon regarding the parameters of fasts, which I will note briefly. The poskim discuss whether one who ate in the middle of a fast—say, on Yom Kippur—must complete the fast, or has lost the mitzvah.

It is common to hinge this on whether the mitzvah to fast obligates each and every moment, or the day as a whole.[4] If the mitzvah applies to each moment, then even if he ate at one moment, it is reasonable that he should continue to fulfill the mitzvah during the remaining moments. But if the mitzvah applies to the day as a whole, once he ate he forfeited the fast and cannot complete it. Again, a question arises regarding a minor who grows two hairs on Yom Kippur: seemingly, whether he must fast the remaining time depends on this inquiry.

Here too one can deflect this in the same two ways. Assuming he fasted until now by virtue of chinuch, he can and should complete it; and this can be explained in two parallel formulations as above: (a) he may complete it by virtue of chinuch (in two sub-formulations as I gave above); (b) he may complete it by Torah law. This latter direction can also be explained here similarly to what we saw above.

The claim is that the requirement for a continuum of fasting moments does not stem from the parameters of the mitzvah of fasting, but from the definition of the term “fast.” The Torah did not define the mitzvah of Yom Kippur as a prohibition on eating, but as an obligation to “afflict yourselves” (“ve-initem et nafshoteichem”). My claim is that a fast is not simply refraining from eating. If a person does not eat for a single moment, he is not considered one who “fasted” for a moment—he merely did not eat. A fast exists only when a person refrains from eating over a continuous stretch of time. Therefore, from the very concept of “fast,” one can understand that the obligation is to fast over an entire day. But this does not mean there is only one mitzvah over the whole day. One can define it as a separate obligation to be fasting at each moment; however, by definition, “fasting” means refraining from eating over a whole stretch—in our case, twenty-four hours. Therefore, to be considered fasting at a given moment, I must be fasting during all the moments leading up to it and from it onward.

From this definition it follows that a minor who fasted during all the moments until he grew two hairs, by virtue of chinuch, is obligated to continue to fast during the remaining moments—even according to the view that one who ate at one moment no longer continues to fast. That now-adult individual will fulfill a Torah mitzvah at each moment he fasts from here on. Since he fasted up to the moment of maturity, refraining from eating at each subsequent moment counts as “fasting,” and thus there is fulfillment of a Torah mitzvah.

Beyond the halakhic implications of the distinction between cardinal and ordinal numbers, we have learned an important conceptual lesson: when we define a given law, we must clarify whether the definition operates only on the halakhic plane, or already at the conceptual plane. This can have ramifications—and at times it can turn the law on its head.

[1] It seems he is referring to Devar Avraham, sec. 34.

[2] One must discuss whether, after they learned when the court sanctified the month of Iyar, they could go back and count. Seemingly, this depends on the aforementioned dispute between Tosafot and Behag.

[3] Admittedly, Ba'al HaMaor himself apparently did not accept this; but it is a fairly sophisticated answer, and it is certainly possible he did not think of it. With non-trivial answers, it is not proper to build edifices on the fact that one Rishon or Acharon did not answer them. Therefore, I would not challenge R. Shimon himself from the fact that Ba'al HaMaor did not answer this way.

[4] I discussed this slippery issue in Gate Thirteen of my book Shtei Agalot.