The Mormon Church teaches that Joseph Smith saw God the Father and His Son. How do you reconcile this when the Bible says the Father cannot be seen?

These main points are important in addressing your question.

How do you reconcile this when the Bible says the Father cannot be seen?

• Jesus has seen the Father.
• Our way to the Father is through the Son.
• If we can not see the Father, that does not mean he has no body.
• A mortal man can not see God.
• There are very few recorded manifestations of God the Father, but there are some. He usually just introduces the Son.

Jesus has seen the Father

This verse addresses the comment that "the Bible is clear that God the Father cannot be seen".

Not that any man hath seen the Father, save he which is of God, he hath seen the Father. (KJV John 6:46)

No one has seen the Father except the one who is from God; only he has seen the Father. (NIV John 6:46)

That verse could reasonably be interpreted to mean that Jesus has seen the Father. Even if you don't agree that this scripture means Jesus saw the Father, it's not too much of a stretch to see how others might think Jesus saw the Father.

Our way to the Father is through the Son.

First, to answer this part of your question about seeing the Father:

Specifically it says, "God the Father and His Son, appeared to Joseph." I would like to know how it is that God the Father appeared to Smith since according to the Bible God the Father cannot be seen. I know that this was a vision but even the definition of the word vision is, "the faculty or state of being able to see." Also, Jesus Christ Himself said at John 1:18, "No one has seen God at any time. The only begotten Son, who is in the bosom of the Father, He has declared Him." Or at John 5:37, "And the Father who sent Me, He has born witness of Me, You have neither heard His voice at any time nor seen His form."

John 1:18 can be interpreted to mean that God the Father doesn't manifest himself to man, except that he does it through the Son. (There are other interpretations of this verse, but let this suffice for now.)

We read in the Old Testament about prophets seeing God. And as you wrote, these were via the Son:

It was not God the Father who was seen in the OT, but God the Son

This agrees with the theology of The Church of Jesus Christ of Latter-day Saints. As a general rule, scriptures about someone seeing or hearing God will be God the Son. Jesus is our intermediary with the Father. Although Jesus saw the Father (John 6:46), direct manifestations of God the Father to the rest of us are very very rare.

If we can not see the Father, that does not mean he has no body.

You noted that in John 5:37 Jesus said, "you have neither heard His voice at any time nor seen His form." Although they hadn't heard or seen the Father, that doesn't mean He can't be seen or heard.

To answer this part of your question:

So how does the LDS Church reconcile their teaching that the Father can be seen and He has a body of flesh and bones with what Jesus said and John 4:24 says, "God is spirit and those who worship Him must worship Him in spirit and truth."

Here is someone's explanation how this is possible. (From https://www.jefflindsay.com/LDSFAQ/FQ_Relationships.shtml#spirit)

In John 4, a woman is asking Christ about whether God is best worshipped on a Samaritan mountain or in Jerusalem. The context of John 4:24 shows that Christ's answer is about our spiritual communication with God, which is not restricted by place. He wasn't answering a question about God's physical nature, but about how we worship. In fact, the phrase "God is a spirit" may be a poor translation of the Greek, "pneuma ho theos," which really says "God is spirit." Some modern translations, like the New English Bible, recognize this and simply say "God is spirit." John 4:24 doesn't say that God is "only a spirit." It certainly doesn't say God is "an incorporeal, immaterial, formless spirit Being who is wholly other, comprising three persons of one substance." No, not even close.

...

We worship God in "spirit" because God is "spirit" and we, being spiritual beings also (but not spirits only), can communicate with Him "in spirit." But nothing in John 4:24 rules out the possibility that God has a body - or that Christ has a body, or that we have bodies. We all do. We are all spirits clothed in tangible bodies - and someday, that tangible body will be resurrected and made glorious - like Christ's body, according to Philippians 3:21, and presumably like the Father's body, in whose physical image we are created (Gen. 1:26,27, cf. Gen. 5:1).

The phrase "God is Spirit" should remind us of other similar phrases, such as "God is light" (1 John 1:5) and "God is love" (1 John 4:8). Are these passages defining God's physical nature or several of His many attributes? Is it not possible to be love and light and Spirit while still having material form? We humans are body and spirit - can it not be so with God as well? In fact, Paul writes that "he that is joined unto the Lord is one spirit" (1 Corinthians 6:17). Spirit and body are not antagonistic concepts, else how could we corporeal beings worship Him in spirit and truth? (But spirit and matter are incompatible in Neoplatonic philosophy, the Greek worldview of the fourth-century intellectuals who devised the post-Biblical creeds that gave us the definitions of the Trinity.)

God is not like mortal man in many ways, for He is perfect, divine, immortal, infinitely wise and all knowing, etc. But He did create us in His image (Gen. 1:26,27). To say that He lacks a form or a body, based on John 4:24, would be to say that Christ cannot be God (or part of the Godhead) because He plainly taught that He does have a resurrected body and is not spirit alone. In Luke 24:39, His resurrection, He told his disciples: "Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have." When we resurrect, we will have a "spiritual" body (1 Cor. 15:44), though it will also have a component of tangible matter like Christ's resurrected body (compare Philipp. 3:21), and even mortal believers are said to be "spiritual" (Gal. 6:1) -- not because there is no tangible matter present, but because of the role played by the spirit. God is spirit, and so are we.

We are made in the image of God the Father. He has a human-like form, although holy and perfect, unlike us.

So God created man in his own image, in the image of God created he him; male and female created he them. (Genesis 1:27)

That wasn't just Adam and Eve. Evil men after the Fall were also made after the similitude of God.

Therewith bless we God, even the Father; and therewith curse we men, which are made after the similitude of God. (James 3:9)

We shouldn't worship man-made gods "which neither see, nor hear, nor eat, nor smell." (see Deuteronomy 4:28)

Jesus is also "in the form of God" (Phillipians 2:6) But not just human form. He was and is perfect in character as well. He is a perfect replica both physically and spiritually ("express image" in Hebrews 1:3). He told his disciples who wanted to see the Father that "he that hath seen me hath seen the Father" (John 14:9) because he was just like him. In a sense he was saying you're not going to see anything different by seeing the Father if you have seen me.

Some feel that having a body would make God lesser. Our bodies certainly are. But a resurrected, glorious, perfected body is different. God the Son has a perfect body and always will.

I am he that liveth, and was dead; and, behold, I am alive for evermore, Amen;... (Revelation 1:18).

Though the Son has a body, he is all knowing, all wise, all powerful, and perfect in every way. There is nothing that could change about him that would make him better, including getting rid of his body. He is perfect. God the Son is like God the Father.

Who, being in the form of God, thought it not robbery to be equal with God: (Philippians 2:6)

A mortal man can not see God.

It's also helpful to learn how to reconcile scriptures about seeing God (even God the Son) and seemingly contradictory scriptures that man can not see God. We understand that as a "man", or mortal, we can not see God. A change/transfiguration (even if temporary) needs to occur.

This is about Moses seeing God the Son: "But now mine own eyes have beheld God; but not my natural, but my spiritual eyes, for my natural eyes could not have beheld; for I should have withered and died in his presence; but his glory was upon me; and I beheld his face, for I was transfigured before him." (Moses 1:11)

There are very few recorded manifestations of God the Father, but there are some. He usually just introduces the Son.

• Adam and Eve spoke with God the Father in the garden (Gen 3:8-10)
• God the Father introduced His Son at Jesus's baptism (Matthew 3:17)
• God the Father introduced His Son when Jesus was transfigured (Matthew 17:6)
• Stephen saw the the Son alongside the Father( Acts 7:55-56)

To get this out of the way first, yes Joseph Smith indeed claims to have seen God the Father, and Jesus Christ, in what is called the First Vision:

Joseph Smith—History 1:17

17 [...] When the light rested upon me I saw two Personages, whose brightness and glory defy all description, standing above me in the air. One of them spake unto me, calling me by name and said, pointing to the other—This is My Beloved Son. Hear Him!

https://www.churchofjesuschrist.org/study/scriptures/pgp/js-h/1.p17#p17

How does this reconcile with what is written in John 1:18 and John 5:37?

1. Jehovah HAS been seen, and heard, in the Old Testament (and New), numerous times

• Jacob Gen 28:13; 32:30; 35:1,9; 48:3
• Moses Ex 33:11
• Moses + 70 Elders Ex 24:9-11
• Abraham Gen 12:7 ; Acts 7:2
• Stephanus Acts 7:55-56 (notable because he sees God the Father, and the Son standing next to the Father)
• Salomon 2 Chr 7:12; 1 King 3:5; 1 Kng 9:2; 1 Kng 11:9
• Job Job 42:5
• Isaiah Is 6:1,5
• Isaac Gen 26:2,24
• Samuel 1 Sam 3:21
• Ezechiel Ez 1:26-28
• John Rev 4; Rev. 19:4
• Amos Am 9:1
• Micha 1 Kng 22:19

Some of those are less clear than others, but in summary the discrepancy is already in the Bible, with in my opinion more support for God can be seen than the other way around. What we see in the Old Testament more is the fear that seeing God (or an angel, in some cases) would lead to death. I just listed scriptures regarding seeing, if we include hearing there will be additional ones of course. Job has a lengthy conversation with God for example.

2. But Jehovah is God the Son, not God the Father

Maybe Jesus is saying here that, technically they always interacted with him, the Son, and not the Father, and that he is now revealing the Father to them. But to be honest, I find that not safisfactory because that would put a rather artificial divide here that doesn't really help his point.

3. Text and / or understanding incomplete?

How did Joseph interpret this in the Joseph Smith Translation? That might give a hint as to how he thought this discrepancy had to be resolved.

JST, John 1:19

19 And no man hath seen God at any time, except he hath borne record of the Son; for except it is through him no man can be saved.

https://www.churchofjesuschrist.org/study/scriptures/jst/jst-john/1.p19#p19

For John 5:37 I didn't find anything in the study helps.

4. Transfiguration

Moses 1:11

11 But now mine own eyes have beheld God; but not my natural, but my spiritual eyes, for my natural eyes could not have beheld; for I should have withered and died in his presence; but his glory was upon me; and I beheld his face, for I was transfigured before him.

https://www.churchofjesuschrist.org/study/scriptures/pgp/moses/1.p11#p11

But again, that would be a technicality that seems not like it would be the thing Jesus would bring up in John.

5. Just because something hasn't happened before, doesn't mean it can't happen. If the First Vision was indeed the first appearance of the Father, this would still be in line with John saying the Israelites hadn't seen or heard the Father, since this talks about the past.

6. John 5:37 Maybe it means none of you in particular? Seeing as he is talking to people claiming to be the ones to judge what is from God and what is not, when all they got is writings from prophets, instead of the prophets themselves, maybe it makes it clear that they really don't have authority at all to judge what is from God? Further support for saying he means them in particular is verse 38, which continues the train of thought with: "And ye have not his word abiding in you: for whom he hath sent, him ye believe not." You in particular have not his word in your heart, because otherwise you would believe me. "Heard his voice" in this sense could mean more abstractly that they don't obey his voice, which is in the scriptures, and the prophets.

How does the church resolve it in manuals etc.?

From the study manual from last year, "Come Follow me - New Testament 2019"

Can God be seen? January 21–27. John 1: We Have Found the Messiah John 1:18

The Old Testament records examples of people who saw God (see Genesis 32:30; Exodus 33:11; Isaiah 6:5). So why would John the Baptist say that “no man hath seen God at any time”? The Joseph Smith Translation of this verse (see John 1:18, footnote c) clarifies that God the Father does appear to men, and when He does, He bears record of His Son. For example, when He appeared to Joseph Smith in the Sacred Grove, He said to Joseph, “This is My Beloved Son. Hear Him!” (Joseph Smith—History 1:17; see also D&C 76:23). There are several other recorded instances where people saw God the Father in vision (see Acts 7:55–56; Revelation 4:2; 1 Nephi 1:8; D&C 137:1–3) or heard His voice bearing record of the Son (see Matthew 3:17; 17:5; 3 Nephi 11:6–7).

https://www.churchofjesuschrist.org/study/manual/come-follow-me-for-individuals-and-families-new-testament-2019/04.scripture_title5-p10#scripture_title5

Is God a spirit? February 11–17. John 2–4: “Ye Must Be Born Again” John 4:24

Some may be confused by Jesus’s statement that God is a spirit. The Joseph Smith Translation of this verse provides an important clarification: “For unto such hath God promised his Spirit” (in John 4:24, footnote a). Modern revelation also teaches that God has a body of flesh and bones (see D&C 130:22–23; see also Genesis 5:1–3; Hebrews 1:1–3). https://www.churchofjesuschrist.org/study/manual/come-follow-me-for-individuals-and-families-new-testament-2019/07.scripture_title4-p11#scripture_title4

In the same manual I don't find anything for John 5:37, but note this is an extremely condensed manual that can't be expected to have answers to everything.