Q&A: Counting
Counting
Question
And one more question, Rabbi. You explained the difference between quantity and quality: in the first case one counts with cardinal counting, and in the second with ordinal counting.
It’s true that quality can only be counted with ordinal counting, but surely quantity (or quantities) can also be arranged and counted with ordinal counting, no? I can arrange however many books I have on the table.
Answer
If you are arranging quantities, then you have attached qualitative measures to them. For example, you arrange my books so that first there is a single book, after it A Good Measure on the Hermeneutical Principles (2 volumes), after that the trilogy (3 volumes), and after that the quartet (4 volumes). Then each group of books in the sequence has both a quantity of books and a quality that places it in the series. The trilogy has a quantity of three books, and its quality is that it is third in the series.
Mathematicians do not distinguish between ordinal and cardinal numbers when it comes to finite numbers (the difference exists only with infinities—cardinals and ordinals). But that is only because there is a one-to-one correspondence between them. I am speaking about the philosophical meaning of numbering, and that is different even when there is a correspondence (as in the case of the chain of books I described).
Discussion on Answer
Indeed.
Rabbi, in column 193 you wrote that there are halakhic decisors who say it is forbidden to measure time but permitted to measure temperature (and from that you distinguished between cardinal and ordinal counting, etc.). What is the source? Which decisors? I want to see what they wrote. Thanks!
https://www.yeshiva.org.il/midrash/20570
Thanks.
1) Isn’t it true that your approach can be said only according to Igrot Moshe following Rashi’s view, that the prohibition of measuring stems from the prohibition of buying and selling? Otherwise (if it stems from the rationale of weekday-like activity, as in Tosafot), there would be no room for your distinction, right?
2) I still didn’t find there any decisor who holds both that measuring time is forbidden and measuring temperature is permitted (which is where you actually found room to distinguish between cardinal and ordinal).
That rabbi who gave the lecture saw a contradiction between the prohibition on measuring time and the permission to measure temperature. It may be that he was challenging one person with another, but that doesn’t matter. My goal was not to reconcile the rulings but to use this in order to sharpen the idea that distinguishes between cardinal and ordinal.
It is true that this is naturally explained in light of Rashi’s approach, that the prohibition is because of buying and selling (and that is indeed how I explained it in the lecture). But this distinction exists in any case, regardless of the explanation. Even if the prohibition is due to weekday-like activity, one still has to discuss which kind of measuring is considered a weekday activity and why.
“Even if the prohibition is due to weekday-like activity, one still has to discuss which kind of measuring is considered a weekday activity and why”
Maybe that too can be discussed by means of your very distinction, and one could say that cardinal counting is weekday activity (perhaps because it is used for material and mundane matters), while ordinal counting is “holy” (because it is more abstract, and ordinal counting implies hierarchy and ascent; these are signs of sanctification…). What do you think?
Exactly. But more simply: weekday-like activity is also connected to commerce. Commerce is done on weekdays.
Just making sure: you agree that your distinction is helpful both for Rashi’s view and for Tosafot’s view, right?
Yes. That’s what I wrote.
Very precise—I understood, thank you very much. Just to make sure I understood correctly: a quantitative dimension can be counted only with cardinal counting (and vice versa, meaning that if I am counting cardinally that is a sign that it is quantitative), and a qualitative dimension can be counted only with ordinal counting (and vice versa, meaning that if I am counting ordinally that is a sign that it is qualitative), right?