Faith and doubt are not opposites.  They belong together.  Without doubt, you cannot have faith.
That might seem contradictory if you define faith as saying “yes” to a set of propositions with your intellect.  And while thinking is a part of faith, what we do with our mind does not fully encompass everything that faith is.
Hokusai’s “Suspension Bridge on the Border…”

I’m going to borrow a phrase from Timothy Keller as a working definition of faith.  Faith is plunging ourselves into God’s grace.  Following Jesus involves relying upon him with our whole being: our heart and soul and will and body, in addition to our mind.
In a word, faith is about love.  Loving Jesus above everything else.  And when we love him we arrange our lives to be near him, to know him more fully, and even to be like him.
I’m getting a little ahead of myself here.  Let’s step back and look at today’s Gospel, and the close connection between faith and doubt will start to come into focus.

To Whom Can We Go?

Jesus has been teaching the crowds that he is the Bread of Life.  We can all have eternal life, but only by fully integrating him into our lives.  As he put it in today’s Gospel reading, we gain eternal life by eating his body and drinking his blood.  You might say, you are what you eat.
That was the last straw for many of the people who were following Jesus.  They did not say that this teaching was intellectually untenable.  They did not doubt with their minds.  They doubted with their hearts and wills.  What Jesus was suggesting was too hard.  He was asking too much.  So they walked away.
By contrast, Peter and another group of followers stayed.  Jesus asked them why they were staying, and Peter answered for them all.  
Because we know the end of the Gospel and say the Creeds week in and week out, we might hear only what Peter eventually says, “We have come to believe and know that you are the Holy One of God.”  (John 6:69)  But this is not all that Peter said, and what he said to preface this tells us a great deal about how faith and doubt are intertwined. 
Daumier’s “The Beggars 1845”

Peter said, “To whom can we go?”  (John 6:68)  
This is not a declaration of unshakable certainty.  Instead, Peter seems to be admitting that he has tried other ways to justify his life.  None of them have worked.  What Jesus teaches seems to be the only thing left before he gives up completely.  And he’s not ready to give up yet.
At the same time, he has his doubts.  This is not to say that he is still fact-checking Jesus or assessing the consistency of his various truth claims.  Instead, Peter is still a little shaky about his ability to follow through, to stick with Jesus when life starts to make his teachings feel even harder for him.
He understands why others have left.  What Jesus teaches is hard to get your heart around, much less your whole life around.  But Peter has already begun to see something, even if only dimly.  His choice is between eternal life and an emptiness that more closely resembles walking death than authentic living.
Doubting Peter
To put this a slightly different way, Peter is confident that he could pass a written test on Jesus’ lectures, but he wonders whether or not he could put that teaching fully into action in his own life.  Doubt is that agitation in the pit of our stomachs that can stop us in our tracks and even make us walk away from Jesus.  Faith often means taking the next steps precisely when we feel like throwing up.
Brash as he often seems, Peter wisely refused to assume an air of superiority over those for whom doubt proved too big an obstacle.  At some level, he sensed his own difficult moments ahead.  As it turns out, Peter would soon enough have one.  When the authorities arrested Jesus, Peter denied Jesus three times in order to save his own skin.  He too became one who left Jesus because his teaching had become too hard.
Honthorst’s “The Denial of St. Peter”

If doubt were the opposite of faith, this would be the end of the story.  Peter’s connection to Jesus would be lost.  Apparently, Judas thought in these terms.  When he betrayed Jesus, when doubt won the day, Judas saw suicide as the only option.
But Peter’s story reveals something very different about faith and doubt.  Peter’s capitulation to his doubts brought him to an even deeper place of faith.  Remember that Peter had said that Jesus’ words bring eternal life.  Well, he was almost right.  Only, eternal life does not come from Jesus’ words.  Jesus himself brings eternal life.
In other words, the point of following Jesus is not merely to internalize his teachings, but also to make a space for Jesus himself at the governing center of our lives.  And we do this in a very specific way.
Being the Beloved
To explain what I mean, I’m going to rush ahead in John’s Gospel to its very end.  After the resurrection, Jesus appeared to the disciples at the Sea of Tiberias.  There he spoke to Peter one-on-one.  Jesus asked Peter three times, “Do you love me?”  
Jesus was not trying to burden Peter with guilt or to grill him to insure his future reliability.  He was helping Peter to see that following Jesus is more than accepting his teaching as true the way we accept the accuracy of a biology professor’s lectures or even the soundness of a moral theologian’s argument.
If the teachings were the central point, we could learn our Bible lessons and go on our merry way without Jesus.  We could graduate from Jesus.  We could say, “Jesus is my Lord and Savior,” without making the least effort to know him more fully and to abide with him in all we do.
In other words, we can say that Jesus is the only Son of God and not love him.  And loving Jesus in response to his love for us is the whole point.
So, to return to the Sea of Tiberias, Jesus is asking Peter, “Do you finally see that I love you? Because if you do, you cannot help but love me.  Plunge yourself into the grace I have already offered you.”
Risking Mercy
Plunging into God’s grace is risky, doubt-inducing business.  In fact, we can only fully take that plunge when we arrive just where Peter finds himself after betraying Jesus: at a place of failure, at the place where doubt has gotten the best of us. 
Peter was finally ready at the Sea of Tiberius to learn about the essence of faith.  And this is it.  Trusting in Jesus does not mean that we bring him our accomplishments confident that he will find them acceptable.  On the contrary, putting our faith in Jesus means plunging our failures into his grace on the strength of his promise to redeem them.
No wonder faith involves doubt.  It’s risky business.  We put ourselves completely at Jesus’ mercy.  Paradoxically,  just when we have nothing to offer God to convince him that we are lovable, we are able to discover his love for us as a gift.  
When we hand him our failures, we see that we have not earned God’s love and that we are forever free from the pressure of winning God over.  God loves us because he has decided to love us once and for all.  And that love is the source of eternal life.
As it turns out, doubt is not the opposite of faith.  On the contrary, in the hands of the merciful God, doubt becomes the means to a deep, abiding faith.