Abarim Publications' online Biblical Greek Dictionary
The verb καθιζω (kathizo) means to set or settle down, emphasizing a newly achieved stationary position relative to a more common roaming range. Our verb consists of (1) the preposition κατα (kata), meaning down from, down upon, and (2) the verb ιζω (izo), meaning to set in the sense of to place something in a fixed place (of buildings or statues in their spot, masters in their office, bad guys in their ambush, armies in their position, people in the midst of some group or rowers on their bench, and so on).
The core-verb ιζω (izo) isn't used in the Bible and but our compound verb καθιζω (kathizo) occurs 48 times; see full concordance. The difference between the two is that the latter emphasizes a downward motion that is typical for whatever stops being freely up there and now settles in a lower, stationary position. This is why birds are said to "sit" on their branch, while they actually stand on it; the point that our verb makes is that perched birds are not flying freely.
In physics, complex dynamic systems are known to settle down when enough energy is extracted, and this settling down is usually upon some particular point or residual condition (like water that swirls around the sink until it settles calmly upon the stop in the drain). When this principle of "settling down of a complex system" befalls a society, the people will be able to diversify their activities and their society will become organized into different strata, which in turn are centered upon a government. This is the kind of rest that Lamech the Second expected his son Noah to bring about (Genesis 5:29), and the kind of rest that the presence of YHWH would give Israel (Exodus 33:14), and the kind of rest that Jesus promised his followers (Matthew 11:29). It's organizational rest; rest that yields treasures of fun and occupation, peace and prosperity. It's the rest that comes from knowledge and skill; the kind of rest that Cain would never know (Genesis 4:12). And it was what the Sabbath was for: not [only] for taking naps but to take inventory, to review and confirm control over one's vast and complex economy.
Our modern world is full of chairs, which is why we have a special verb that describes what we do on them: to sit. In the antique world, however, chairs were far less common and people reposed on the ground or perhaps an available boulder, and only very rarely on specifically manufactured furniture. Hence the ancients had no verb specifically for sitting, and to them a person was either on the move, or slumped into any of the many possible positions of repose, from lying flat down to sitting up against a wall.
In English the verb "to sit" serves as opposite of "to stand" or "to lay down", but our Greek verb rather makes a distinction between moving about and being stationary. It describes a being settled rather than a being seated, which is why the disciples could combine it with sorting fish (Matthew 13:48). Likewise, the tongues of fire didn't "sit" on the disciples' heads but stopped moving about and settled on them (Acts 2:3; and note that not the tongues - plural - but the fire - single - settled down). And Paul didn't "sit down" for eighteen months in Corinth but while being settled there, certainly enjoyed perambulatory liberties (Acts 18:11).
In antiquity, personal chairs were almost always instruments of symbolism rather than mere furniture: hence a king's throne was not a mere elaborate seat but rather the place where the entire nation was settled, and a judge's seat held the whole sway of justice and legal authority (Matthew 19:28, John 19:13, Acts 12:21). Moses had no chair that we know of, and the Pharisees certainly didn't sit in it (Matthew 23:2), and Jesus was probably much rather concerned with the refusal of the latter to further develop for a complex nation whatever legislation worked fine for the much simpler society of Moses.
From our verb καθιζω (kathizo), to settle down, come the following derivatives:
- Together with the preposition ανα (ana), meaning on or upon: the verb ανακαθιζω (anakathizo), which describes a settling down specifically in order to pay close attention to something. In the classics it's used to describe how a hare stops running to stand up and review his surroundings, or how Socrates, days before his death and just after dismissing his wailing wife Xanthippe, "sat down" specifically to rub his leg and explain to himself and his friend Crito how pleasure is related to pain. Quite strikingly, in the New Testament our verb is used solely to describe how dead people stop being dead and begin to pay attention to those around them, which implies that just before this they, or at least their minds, were roving about or otherwise dispersed (Luke 7:15 and Acts 9:40 only).
- Together with the preposition επι (epi), also meaning on or upon, but more in a physical sense rather than the causal sense of ανα (ana): the verb επικαθιζω (epikathizo), meaning to settle down upon. In the New Testament this verb is used only once, in Matthew 21:7, to describe how Jesus settled down upon the garments that the disciples had laid upon the colt.
- Together with the preposition παρα (para), meaning near or nearby: the verb παρακαθιζω (parakathizo), meaning to settle down near. In the classics this verb is also used to describe the installation of a co-judge or such an assistant of someone enthroned. In the New Testament, this verb is used only in Luke 10:39, as it describes how Mary of Bethany was settled down near the feet of Jesus.
- Together with the preposition συν (sun), meaning together or with: the verb συγκαθιζω (sugkathizo), meaning to settle down together (with), to jointly settle down. This magnificent verb describes the convention of a council or senate or such a body, and occurs in the New Testament only in Luke 22:55 and Ephesians 2:6.