The Australian artist was responding to a letter from a fan who said she still felt "some communication" with family and friends who had died recently.
Cave replied: "If we love, we grieve... I feel the presence of my son, all around, but he may not be there."
Arthur died in the UK after falling from a cliff in Brighton.
Cave is best known as lead singer of Nick Cave and the Bad Seeds. He has been described as "one of the most intense and exciting live acts on the planet."
Cave posted the letter on The Red Hand Files, a website he uses to communicate with fans, earlier this week.
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One fan from the US wrote: "I have experienced the death of my father, my sister, and my first love in the past few years and feel that I have some communication with them, mostly through dreams. They are helping me.
"Are you and Susie feeling that your son Arthur is with you and communicating in some way?"
Cave thanked the fan for the "beautiful question", and shared his experience of dealing with grief.
Media captionArthur Cave was found at the bottom of the cliff at Ovingdean Gap in July
"Grief and love are forever intertwined. Grief is the terrible reminder of the depths of our love and, like love, grief is non-negotiable. There is a vastness to grief that overwhelms our minuscule selves."
"Within that whirling gyre all manner of madnesses exist; ghosts and spirits and dream visitations, and everything else that we, in our anguish, will into existence.
"These are precious gifts that are as valid and as real as we need them to be. They are the spirit guides that lead us out of the darkness."
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He added that he felt the presence of Arthur all the time.
"I hear him talk to me, parent me, guide me, though he may not be there.
"Dread grief trails bright phantoms in its wake. These spirits are ideas, essentially. They are our stunned imaginations reawakening after the calamity.
"Like ideas, these spirits speak of possibility. Follow your ideas, because on the other side of the idea is change and growth and redemption. Create your spirits. Call to them. Will them alive. Speak to them.
"It is their impossible and ghostly hands that draw us back to the world from which we were jettisoned; better now and unimaginably changed."
In September, Cave and his colleagues mourned the death of bandmate Conway Savage, who died aged 58.