The meaning of the Biblical word 'cleave' is relatively complex and this is exacerbated by the unfortunate fact that in English the word is capable of two almost entirely opposed meanings both of which were used by the KJV translators. Many Bible Dictionaries solve this problem simply by having two entries in their text. Of course the reader of the Bible is left to determine from context which of these two identical words is being used. For the purposes of clarity I will deal first with cleave meaning to split which occurs only in the Old Testament and then progress to the joining form of cleave which is used in both testaments.
Cleave meaning 'to split' is used to render three different Hebrew words. The commonest is bâqa‛ (H1234-11 occurrences) which is used of splitting wood, rocks or a passage for water. Shâsa‛ (H8156) is used twice: once of tearing an animal wing for sacrifice and once for describing how an animal hoof looks. Pâlach is used once, probably in a figurative sense in Job 16:13.
The definition of bâqa‛ is 'split, break open, break through or divide (Brown, Driver and Briggs 1996)'. This seems entirely consistent with the Biblical usage which is primarily of cutting wood, dividing ground or making a hole for water. The King James renders the word in a variety of ways: break (13), rend(8), rip(4) , divide(4), breach(2), tear(2), win(1), hatch(1).
Shâsa‛ is also defined as meaning to divide, part or split (Brown, Driver and Briggs 1996). However looking at the KJV renderings clovenfooted(4), rent(1), stayed(1) provides a rather more specialized meaning. The first usage of the word is even more suggestive:
Lev 1:17 And he shall cleave8156 it with the wings3671 thereof, but shall not3808 divide it asunder:914
Thus it would appear that means to tear, or split without the complete separation of both parts.
Pâlach is a rather obscure word that is never translated the same way twice (shred, cutteth, strike through, cleave, bring forth). Brown, Driver and Briggs and Strong both suggest a meaning of slice. The more modern translations render the word in verse in question as 'slash open' or 'pierce'.
The Biblical word cleave in the sense of join is an extremely eclectic term being a rendering of seven Hebrew, one Aramaic and three Greek words. Fortunately three of these words are closely related and form the majority of the instances of 'cleave' found in the Old Testament. The words are dâbaq (H1692), debaq(H1693) and dâbêq(H1695). The latter two are rare: debaq occurs once and is the Aramaic equivalent of dâbaq. dâbêq occurs twice and is the adjective form of the root dâbaq.
The meaning of dâbaq is given by both Strong and BDB as 'to cling or stick to'. It can also mean 'to be joined together' (Pual) or to pursue closely (Hiphil). Of the 60 occurrences in the Bible 35 of them are rendered 'cleave' or a derivative. Other renderings are: followed(9), keep(4), overtook(3), joined(2) and an assortment of individual renderings. The first use of dâbaq is in Gen 2:24 and speaks of the union of man and woman. The word is also used of sickness or evil's grip and of the relationship we should have to God.
Neh 10:29 renders châzaq (H2388) as 'cleaveth'. This is unique rendering. The verb means to strengthen or be strong and is usually rendered strong(48) , strengthened(42), repaired(39), hold(35) etc. As such cleave is here being used to denote the strengthening that comes from close association.
Psalm 41:8 gives another unusual use of cleave in the expression 'cleaveth fast'. This is a translation of yâtsaq which means 'to pour out' or to cast a metal. The word is generally rendered pour(26), cast(11), molton(6) and a variety of individual words. I suggest therefore the implication in Psalm 41 is that the sickness had 'welded' itself to the individual.
Sâphach (H5596) is another Hebrew word rendered 'cleave' and the meaning is far harder to discern. The word only occurs in six verses and is never rendered the same way twice. Brown, Driver and Briggs states the meaning is to join two things together or even to scab over. Examing the usages we find: someone driven from the priesthood asking to go back in (1Sa 2:36), someone being driven from the inheritance (1Sa 26:19), a group of refugees gathered in nettles (Job 30:7), an abnormal growth on the head (Is 3:17), strangers attaching themselve to Jacob (Is 14:1) and someone forcing alchohol on a nieghbor. I therefore suggest that this word appears to refer to some kind of abnormal or unnatural joining together.
A word which is also rendered 'cleave' which appears related to Sâphach semantically but not etymologically is lâvâh. Strong memorably translates this as 'to twine'. BDB adds that it can mean to borrow or to lend. It also occurs in Is 14:1 alongside Sâphach although there it is rendered joined. In Dan 11:34 where it is rendered 'shall cleave' the verse continues to say that it will be 'with flatteries'. I think lâvâh therefore points to the form of joining that occurs through an intricate web; be it of finance, social connections or words.
A simpler but beautifully graphic meaning of cleave is given by tsâphad (H6821). Appearing only in Lam 4:8: the word means to draw together, contract or shrivel. Anyone that has ever worn wet clothing will know the feeling and the picture in Lamentations of skin sticking in that manner will be suitably repulsing.
Cleave is a much less common New Testament word making the interpretation of it rather simpler. The commonest Greek word rendered cleave, kollaō (G2853), appears eleven times in total and rendered cleave on three of those occasions. The other occasions it is rendered join (6), company(1) or keep(1). It means to glue together (passively or reflexively). Thus is describes a bond between men (Acts 17:34), or dirt (Luke 10:11). It is also the relationship we should have with good (Rom 12:9).
Proskollaō (G4347) is clearly a related word which means 'glue upon', or 'join oneself to'. The two occasions it is used and translated 'cleave' both relate to a man joining to his wife; this makes it similar to the Hebrew word dâbaq. The word appears twice rendered as 'joined'. One of those again is a man to his wife the other a bond between cultists.
Interestingly the New Testament word expressing cleaving to the Lord is not the one relating man to wife. Instead it is prosmenō (G4357) which really means to remain in place. It is also rendered abide, continue(2) and stay. Thus we see the focus is not so much on the closeness of the join but on the permanency of it.
Scanning back over this paper the only real conclusion is that there is no conclusion. Cleave is a complex word which means to join or in the Old Testament may mean to separate. Usually in the Old Testament it will refer to objects being bound passively or reflexively although it is really impossible to tell without looking at the underlying original. In the New Testament it is rather simpler: if it relates to man and wife it means glue self unto, if it relates to man and God it means remain glued to otherwise it just means glue together.