Everyone agrees that binah and daat are greater forms of knowledge than chachmah (see Shemos Rabbah 41:3 and Rashi to Shabbos 31a), but, the exact relationship between binah and daat is subject to dispute.
The Mishnah (Avos 3:17) states that daat depends on binah, and binah depends on daat. Rashi and Rabbi Ovadia Bartenura (1445-1515) explain that binah is the ability to derive a new idea from a lesson, and daat is the ability to understand the reasoning behind a lesson (see also Rashbatz). Accordingly, the Mishnah means if one can’t figure out the rationale behind a lesson, one can’t extrapolate anything further from it. Likewise, if one can’t extrapolate new ideas from a lesson, one can’t deduce the rationale behind it.
At face value, then, it seems that binah and daat go hand in hand. Some sources, though, assert that daat is superior to binah (see Maharsha to Kesubos 5a), while the Maharal [Chiddushei Aggados to Kiddushin 30a and Avodah Zarah 19b; see also Tiferes Yisrael ch. 56) maintains that binah is superior to daat.
The Torah reports that when Bezalel was charged with constructing the Tabernacle, G-d bestowed upon him chachmah, tevunah, and daat (Exodus 31:3). In this context, Rashi writes that chachmah is wisdom one hears (i.e., learns) from others, tevunah is the ability to understand something new based on information one has already acquired, and daat is knowledge gained by Holy Inspiration (ruach hakodesh).
Rashi’s source for the difference between chachmah and tevunah is the Sifrei (to Deuteronomy 1:13), and he cites the same explanation elsewhere (see Rashi to Deuteronomy 1:13 and Proverbs 1:5; see also Radak to I Kings 3:12).
The Talmud (Chagigah 12a) teaches that G-d created the world using 10 different qualities, the first three of which are chachmah, tevunah, and daat. In this context, Rashi writes that daat is reconciliation. Why does Rashi define daat differently than he does elsewhere?
Rabbi Shmuel Yaakov Burnstein (1946-2017) resolves this issue by explaining that “daat” encompasses both definitions since it really means a form of connection. Thus, the verb form of “daat” in the Bible is a euphemism for conjugal intimacy (Genesis 4:1) or familial connection (Ruth 2:1). Daat consists of connecting pieces together and coming out with a final resolution in which everything jives. Thus, “daat” can mean reconciliation as well as knowledge one has attained through Divine Inspiration, which is a form of connection.
Divine Inspiration essentially stems from a person connecting himself to G-d, and thereby becoming privy to certain details. Through Divine Inspiration, one can also see the bigger picture and have access to all the pieces that need to be reconciled. (See Nefesh HaChaim [1:6] which states that the fruit of the Eitz HaDaat Tov V’Ra had the ability to bring about the interconnectivity of good and evil. The Vilna Gaon [to Proverbs 2:5] similarly explains that daat is the dialectic reconciliation of contradictory ideas.)
If daat is the ability to connect two separate things, it also presumes the mechanism by which separation can occur. Indeed, the ritual separation between Shabbos and the workweek (Havdalah) is said in the Shemoneh Esrei berachah of knowledge. As the Rabbis said (Jerusalem Talmud, Brachos 5:2): If there is no daat, from where can there be havdalah (separation)?
Rabbi Chaim Friedlander (1923-1986) writes that daat represents the nexus of the intellectual and the emotional. When one connects one’s intellectual knowledge with one’s emotions, one fully internalizes the knowledge. Rabbi Avraham Bedersi HaPenini (13th century) also writes that daat is associated with emotions and feelings.
Interestingly, Rabbeinu Yonah (to Avos 3:17) writes that daat is the ability to independently think of new ideas. (Perhaps he understands that the connections denoted by “daat” refer to new connections forged between neurological synapses in the brain, which serve as the biological basis for acquiring new knowledge.)
Kabbalists (see Eitz Chaim, Shaar Ha’Amidah ch. 11) have long noted that these three forms of knowledge (chachmah, binah, and daat) correspond to the first three sefirot used to describe the ways we perceive G-d’s influence in the world: chesed, gevurah, and tiferet. Chesed refers to G-d’s kindness in bestowing upon us an unlimited influx of energy, gevurah denotes our perception of Him sometimes limiting His influence in the world based on our actions, and tiferet refers to the happy medium achieved when He balances chesed and gevurah.
By this model, chachmah refers to receiving knowledge from others, in accordance with what we have seen throughout this study. Binah, on the other hand, refers to intuiting knowledge based on what one already knows, with only limited input from outside. This sort of intuition is often times associated with womenfolk, who are said to be weaker in daat (Kiddushin 80b), but stronger in binah (Niddah 45b). Daat, then, refers to the balancing act of harmonizing received knowledge with intuited knowledge; it represents the final product that results from taking raw chachmah and processing it through binah. As Rabbi Shaul Levi Mortera (1596–1660) so succinctly writes, chachmah is acquired, binah is natural, and daat is a synthesis of those two possibilities.
Interestingly, Dr. Michael G. Samet (a brother of Ohr Somayach’s Mashgiach Rabbi Yehudah Samet) told me that he once pointed out to Yale professor Robert J. Sternberg that his Triarchic Theory of Intelligence closely resembles the three types of intelligence we have been discussing, and the latter was quite taken aback with this finding.