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(Note: In Rabbi Krinsky's own Lithuanian Ashkenazic dialect of Hebrew, his first name would be pronounced Yehudə or Yehudo.)
Krinsky was born into an Eastern European rabbinical family. He was apparently born in Minsk; the year of his birth is unknown, but his father, Rabbi Isaac Krinsky, died in the autumn of 1853, so this provides us with a terminus ante quem. In his youth, he studied both Torah and secular studies (what B. Z. Eisenstadt calls “hokhmā”). Later on, he moved to Slutzk, where he went into the timber business, and made a fortune. He became a philanthropist, supporting rabbis and Torah scholars. Later on, he moved (back?) to Minsk, where he began his major work of scholarship, the Mehōqeqē Yehudā. For Krinsky's (apparent) association with the movement known as Haskala, see below.
Only one work by Krinsky is known, though more might show up in the future. This one work is the five-volume Mehōqeqē Yehudā, a super-commentary on Abraham Ibn `Ezra's commentary on the Pentateuch and certain of the Megilloth. (The title, meaning The Lawgivers of Judah, is a reference to Krinsky's first name.) Krinsky worked on the Genesis volume from at least 1903 (the date of the first haskama, or rabbinic letter of approbation) until 1907, when it was published. The volume on Exodus was published in 1910. He continued to work on the remaining three volumes, but they did not get published until 1928, by which time Krinsky was probably no longer living.
The published Mehōqeqē Yehudā includes the Hebrew text of the Pentateuch, the Aramaic text of Targum Onqelos, and the commentaries of Rashi and Ibn `Ezra. Beneath these sources appear Krinsky's annotations. Krinsky's notes on Ibn `Ezra are divided into two columns. The first column is entitled Yahēl Ōr ("may light shine", an allusion to Krinsky's given name, YeHuda Leib), and it consists of straightforward explanations of Ibn `Ezra's words. The second column is entitled Qarnei Ōr ("beams of light", also a pun on Krinsky's name, based on its value in gematria); it consists of short essays relating to Ibn `Ezra's work. These essays often include quotes from one or more of the following three sources: (1) classical rabbinic literature; (2) other writings by Ibn `Ezra himself; and (3) reactions to Ibn `Ezra by other mediaeval Jewish writers. When the other writers criticize Ibn `Ezra, Krinsky tries to defend him. One of the most valuable aspects of the Qarnē Ōr is the extensive quoting from Ibn `Ezra's other works. The commentary of Ibn `Ezra on the Torah is a very concise and cryptic work; often, paragraphs that Ibn `Ezra has written in other works shed invaluable light on understanding these cryptic interpretations.
It is preceded by a short history of the Ibn Ezra's life and a bibliography of his works.
Attached to the Mehōqeqē Yehudā is a work Minchat Yehuda which brings Rashi's sources and clarifies the correct reading of the text.
Association with the Haskala (Jewish Enlightenment)
Krinsky's annotations in Mehoqeqei Yehuda make frequent reference to thinkers of the Haskala, such as Heinrich Graetz, S. D. Luzzatto, and especially Moses Mendelssohn. This raises the question of how strong Krinsky's own associations with the Haskala were. The study of Ibn `Ezra's writings was not particularly common among non-haskalic, Haredi Jews of nineteenth-century Eastern Europe, for Ibn `Ezra's commentary focusses on Hebrew grammar, and, to a lesser extent, the sciences. Thus, it would be reasonable to suspect that Krinsky was adhered to some form of the Haskala.
The haskama (letter of approbation) of Rabbi Eliezer Rabbinowitz, prefixed to the Genesis volume of Mehoqeqei Yehuda, refers to Krinsky as "God-fearing", an epithet that makes it clear that Krinsky was observant of Jewish law (halakha). This would place him firmly in the religious branch of the Haskala, rather than its secular branch. (This is clear also from other evidence, such as Krinsky's choice to publish Mehoqeqei Yehuda in the form of a traditional pentateuch for liturgical use in the synagogue.) And indeed, the haskamoth that Krinsky managed to obtain for his volume on Exodus were written by key figures of the Religious Haskala, including Abraham Berliner, A. E. Harkavy, and S. A. Poznanski, among others. (Conspicuously absent are the names of A. A. Kohut and D. Z. Hoffmann. One might have expected a haskama from Solomon Schechter, as well.)
There are also haskomos from major Haredi leaders such as R' Isser Zalman Meltzer who praises Krinsky for his attention to "Dikduk Ha'Lashon" (grammar) implying that the Haredi world was quite comfortable with his work. (Haskamah to Genesis - Note: the 1989 Reinman edition contains only the Haredi Haskamos.)
Criticism of Krinsky by others
The work Mehōqeqē has not been received well. The traditional world seems to have ignored it altogether, whereas the critical world has given it a number of bad reviews. Already in 1907, the year when Krinsky published the first volume, David Hertzog published a harsh review of it in ZDMG. Much later, in 1990, Arye (Leo) Prijs called Krinsky's work misleadingly incomplete, and cited a number of quotes from Hertzog's review, including them in the preface to Prijs's own book on Ibn `Ezra's commentary on the first three chapters of Genesis.
It must be remembered that despite the flaws for which Krinsky's work has been criticized, Mehoqeqei Yehuda remains to this day the only modern complete supercommentary on Ibn `Ezra's Pentateuch commentary. All the other attempts by moderns to produce a supercommentary on Ibn `Ezra's Pentateuch commentary have either been woefully minimal (such as Asher Weiser's annotations to the Mosad Ha-Rav Kook edition of Ibn `Ezra's commentary), or covered only a few chapters of Ibn `Ezra's commentary (such as the works by Prijs and Linetsky, each of which covers only the first few chapters of Genesis.)