Throw away this article
Modern technology has vastly increased the availability of regularly published Torah periodicals that address timely matters. While in times of old, rabbis certainly published divrei Torah, the costs of printing and distributing these divrei Torah were so high that once a person was given such a work, it tended to stay on that persons bookshelf, to be referred to, learned and examined. Such is no longer the case: many institutions or organizations distribute a weekly sheet with Torah articles, with the understanding that many people will not keep these sheets in their library. The critical halachic question is what to do with these weekly divrei Torah after you have read them? Can one throw them out? Can one dispose of them neatly? Must one bury them, as one must a Torah scroll? What is the proper procedure?
This halachic matter divided into four different categories:
(1) There are those divrei Torah sheets that explicitly quote verses of Torah in Hebrew. (2) There are those divrei Torah sheets that explicitly quote verses of Torah in English, and when they encounter the name of God, use an English translation of one of the seven un-erasable names. (3) There are those divrei Torah sheets that will quote whole verses of Torah, but when they encounter the name of G-d, they use the term Hashem, or G-d, or L-rd, thus avoiding even properly translating the name of G-d. (4) There are those divrei Torah sheets that address matters of interest to the community without quoting a verse of Torah or mentioning the name of G-d.
Each of these four categories have different halachic rules, and different ways to dispose of them. In the case of a dvar Torah sheet that quotes Torah verses in Hebrew, even if when the name of God is used, Hashem (written in Hebrew) is substituted and no full verses are thus cited, it is improper to dispose of this dvar Torah sheet in any denigrating manner (Rama and Shach, Yoreh Deah 276:10). If one of the seven names of G-G-d is explicitly used in Hebrew, of course it is improper to dispose of these divrei Torah sheets except in a geniza, or perhaps to burn or bury them in an very proper manner.
Indeed, as noted by the Talmud (Tractate Rosh Hashanah 18a and quoted by Rama Yoreh Deah 276:13) it is improper even to write the name of G-d in Hebrew on a piece of paper that is normally thrown out. (Shach YD 276:16 is more lenient on this matter, but even he is uncertain about this leniency, as noted in Nekudat Hakesef (on id.)). For more on this see Iggrot Moshe YD 2:134-135, and Minchat Yitzchak 1:17-18.)
In the case of the English dvar torah sheets that quote full verses of the Torah in English, and use various translations of the names of God that explicitly denote the Divine in English, halacha prohibits one from disposing of these sheets in an irreverent manner, such as simply discarding them in a garbage can full of rubbish; however, they need not be put in a geniza and can be disposed of in some other proper manner, such as burning in a dignified way, or even perhaps bundling them neatly together and putting them in a recycling bin or the like. The reason for this is that when the name of God is used in a language other than Hebrew, no technical prohibition against erasing it attaches, but yet it is improper to dispose of this material in an undignified manner. For more on this, see Minchat Yitzchak 1:17:(14). Of course, one cannot take such reading material into a bathroom of the like.
In the case of English divrai torah that use the term "Hashem" for God, and which do not quote full verses of the Torah even in English, the halacha is even more lenient, and their status is the same as any essay written about any torah topic which does not mention the name of God. In such a case, it is the better practice to dispose of these items in a dignified manner, but there is no requirement that they be placed in a geniza, and may even be disposed of in a paper recycling bin, or perhaps even a dignified manner in a garbage reserved for paper disposal. This is particularly so for modern photo offset material, which is printed by people with no intent that they be holy (even if the writer intended such, the copy machine operator certainly did not), and were intended to be used once or twice and then disposed of. This is quite a bit different than the English translation of a page of the Bible, when it rips out of a chumash, as that work is intended for permanent use. More generally, it is widely asserted that printed material has a lesser level of sanctity than handwritten material, particularly so when the printers are Gentiles. For more on this, see Michat Yitzchak 1:18(19-20), and Yabia Omer YD 4:21(4-6).
A related question is whether one can erase dvar torah pages when they are posted on the internet, and you are reading them "online." The question is whether directing the browser to the next web page, and thus causing whatever is on your screen to be deleted is called "erasing." The same question is posed when one downloads a dvar torah, and read it; can one delete the file from one's hard drive? It would appear to me that both of these activities are permissible to do, as the act of directing one's internet browser to the next web page is not called "erasing" that material; such is true, I think, even if the name of God, in Hebrew ,is actually on the screen. This is even more so true when one is merely overwriting a file. For a related question that elucidates on this principle, see Yabia Omer YD 4:20, and Iggrot Moshe YD 1:173.
In sum: Do not throw out this dvar torah sheet if you are reading it from a printed flyer. Keep it in your files if the topic interests you. Otherwise politely dispose of it in a dignified place, and not in a garbage. If you are reading it on the world wide web, when you are finished reading it browse on to the next torah topic, as there is much torah to learn, and you have finished reading this dvar halacha!
Rabbi Michael Broyde is a professor at the Emory University Law School and is the spiritual leader of the Young Israel of Toco Hills in Atlanta.