Thought exercise: A malicious but trustworthy djinn appears to you. He tells you that one minute after your death, he's going to release magically faked evidence that you were a violent pedophilie.

All of your remaining friends and family will believe this, and the case will be so bad that your name will become associated around the world for the sheer heinousness and reprehensibility of the things you supposedly did. However the djinn is willing to bind himself to not doing this, but you have to pay him $1 right now.

If "nothing matters after you are gone", then you wouldn't even be willing to pay $1 to avoid this scenario.

While I’m alive, I would gladly pay $1 if it would avoid a traumatic experience for my friends and family (or even a stranger). I don’t see how this hypothetical changes that. In particular, it’s not about the memory of me, it’s about how that memory affects the lives of those who might care about me.

But you said that you don't care about things after being gone. So this clearly demarcates an exception to this.

You care about the wellbeing of your friends and family after your death, even though you're not "around to observe it". So there are at least some things that you value in life, that you still value after death.

Many people being value being respected in life. There's nothing particularly different about extending that value to being respected after death. At least not if you already assign valence to other values post-death.

There is a big difference between not being cause of hardship for your family and being remembered for the sake of being remembered. The former rises out of natural empathetical feelings you've towards your close ones which will be a cause for grief and depression till the end of your life, you get it's b repercussions in your life itself, unless you're a psychopath who don't have any regard for others suffering. Surely you can't just ignore it as 'nothing matters after I'm gone' as in being remembered, because being remembered for the sake of being remembered is merely just for the ego satisfaction from that recognition when you don't even have a working brain to enjoy it and unless you are one of those types that crave for attention and not being remembered affects your current state too emotionally. Trying to be billionaire to be remembered is just like trying to chase the moon.

Just because the results of it are non-observable (fair assumption) to the person leaving some sort of legacy behind them, doesn’t mean that doing so isn’t valuable to them. It is the satisfaction you get while still living, knowing that after you are gone, some (hopefully positive) remnants of you will still live on.

That may be what you believe, but it's a fringe belief. I point to every statue, every hospital named after someone, every estate still generating income for non profits, every example of suicidal selfless sacrifice in history as evidence.

There is such a thing as a-causal trade. Newcomb problem, prisoner's dilemma, that sort of things.

Few people really don't care what happens after they're gone. We almost always want something to linger on, be it descendants, a master works, or just the world.

But feeling you will be remembered can be important to people while alive.