This issue involves a host of verses in which God is said to be "seen" in some way, and these are variously set against the following:
John 1:18 No man hath seen God at any time.(cf. John 6:46)
Exodus 33:20 And he said, Thou canst not see my face; for there shall no man see me and live.
1 Tim. 6:16 Whom no man hath seen nor can see.
A general answer often given is that these verses indicate that God cannot be seen by men when in his full glory. God can be seen when in lesser form - as in the incarnation of Jesus Christ, or a theophany. These lesser forms are indicated, although their nature probably not fully understood by all of the writers, in Exod. 24:9,10, Amos 9:1, Gen. 26:2 and 32:30, John 14:9, and Ex. 33:11.
This response is basically correct, but requires some further elucidation. We shall analyze the relevant verses in a chronological order so that we can see, not a contradiction, but a paradox that is unraveled before our eyes.
Gen. 17:1, 26:2 -- Although these are the first places where it is said that God appears before someone, there is very little that can actually be drawn from it. God "appears" -- but in what form?
It is perhaps important to note that in both cases, it is Yahweh who appears before Abe and Isaac -- not Elohim, God's "majestic power" name. We'll get more into this shortly.
Gen. 32:30 -- Our next verse in this set is not really trouble to begin with, because it only reflects what Jacob thinks and says in the first place. Even so, we can draw something for this issue from it. First of all, the Hebrew term "face" has an idiomatic twist which refers to awareness and direct knowledge of presence, without the help or hindrance of a mediator -- one might say today, it is a "close encounter" of a personal kind.
Second, note that Jacob here says he sees not Yahweh, but Elohim.
Finally, most important to note here is Jacob's reaction. He clearly knows that the fact that his life was preserved is something unexpected. What we see being set up here is not a contradiction, but a paradox. Jacob knows that God cannot be seen, or the result is death; but something has happened that overruled that normal constraint. His reaction presupposes knowledge that God cannot be seen, and so he is aware of the "contradiction," which should give us pause.
What happened? Far be it for Jacob to know. But by the time of Exodus, someone gets a clue about an important distinction...
Ex. 24:9-11 -- Things are starting to develop here for our paradox. Once again, it seems that it was expected that something bad would happen (v. 11); and yet, there seems to be a sort of surprise that no harm came to the elders. But two factors now come to the fore. First, the Hebrew word here for see is chazah -- and has the connotation of gazing at, with mental perception, or having a vision.
The second factor is our key verse:
Ex. 33:18-23 -- This quote should actually be started as I have, at verse 18, for it is the keystone verse for my general "glory" explanation above. Note that Moses asks to see God's glory (v. 18) -- this word having the meaning of a radiance. Now recall again the Hebrew idiomatic use of "face" -- and connect this also with the face as the outward reaction ("radiance") of the inner person.
And now it becomes clear why we have explained things as we have: Jacob had not seen God's "face" in this idiomatic sense; nor had anyone else so far. At the same time, the Hebrew word here is different: ra'ah. This carries a simpler connotation of seeing and discerning by sight; or, it carries the idea of "taking heed unto" or considering. It is a general word used almost 1500 times in the OT, and merely establishes awareness without establishing the means whereby awareness is made.
Ra'ah is the word used in our first two Genesis quotes, and in the next quote:
Numbers 14:14 And they will tell it to the inhabitants of this land: for they have heard that thou LORD art among this people, that thou LORD art seen face to face, and that thy cloud standeth over them, and that thou goest before them, by day time in a pillar of a cloud, and in a pillar of fire by night.
Amos 9:1 -- Now here again, and in Numbers, note that it is Yahweh who is seen -- not the majestic Elohim.
Admittedly there are a couple of places where Elohim does appear to people (Gen. 35:9, 2 Chr. 1:7), but several things may be noted about this:
1) the rarity of the usage suggests that this is the result of the known process of scribes incorrectly substituting the divine name where it should not be, or else substituting Elohim intentionally as a form of "reverential evasion" associated with a hesitation to pronounce or write the divine name of Yahweh;
2) even without that, there is no indication that what was seen was God's glory, as opposed to some sort of other manifestation;
3) the general meaning of ra'ah can imply, but does not necessarily indicate, a physical appearance. Without further description of how the matters transpired, it is not possible to affirm that God has been "seen" in a way contrary to our verses above.
John 1:18 -- With the New Testament, the dichotomy between seeing Yahweh on the one hand, and not seeing Elohim on the other, remains. John, in mirroring the prologue of Genesis, clearly means to equate "God" here with the majestic Elohim.
The Greek word here (and in John 6:46), incidentally, is horao, and is used in the sense of understanding, as in Matthew 18:10: "Take heed that ye despise not one of these little ones; for I say unto you, That in heaven their angels do always behold the face of my Father which is in heaven."
John 14:7 -- I am frankly surprised to see this verse ever brought up in the discussion. Here "seeing" (also horao) God is equated with knowing Jesus. One might roughly equate this with a famous baseball figure saying, "You're looking at the next Babe Ruth":
Recall that in John 10:30, Jesus declares oneness in essence with the Father. This is not the same as saying that they are seeing God's literal glory.
1 Tim. 6:16 -- And so this cite too is now quite clear. The One who dwells in unapproachable light (God's radiant glory) can refer only to the majestic Elohim of the OT. And that this is so is made more clear by the fact that the word here is eido -- which, like ra'ah, is a "physical sight" word (cf. Matt. 2:12).
Our conclusion: The objection that asks whether or not God can be seen rests upon a lack of linguistic and theological knowledge.