How do you, as a nonbeliever say you're sorry for the death of someone's spouse or children or whatever if you aren't going to say the "usual" I'll pray for you? Or some other god platitude?
I wrote to a neighbor who lost his wife, "Sorry for your loss, I hope you find peace, tranquility and purpose."
But if you are a nonbeliever, how you tell something like:" I hope find peace, tranquility and purpose." Great atheists don't believe in purpose. They are writers and atheists that don't believe something have a purpose and all ends with death. Do you believe that?
I have found that an expression of compassion and empathy is useful. But in reality there is nothing I can say that will make it easier for the bereaved. However actions of kindliness are always helpful. Platitudes are about as useful as "tits on a boar hog".
My son asked me about this when someone he cared about lost someone close to them. It is tough because so many things that people say are unintentionally hurtful. I suggested he focus on his friend- “I’m sorry for your loss.” And “what can I do to help?” (Said genuinely with desire to provide support) and to be available to listen and empathize.
"I am so sorry for your loss!" What follows that I have to think depends on what thei bereaved has expressed. Some are focussed on their loneliness. Some on worry about how their loved one may have suffered, and others feeling some guilt feelings for some friction in the relationship that didn't get resolved or feeling they didn't do enough before the death. Just listening sympathetically can be the most important part.