I was listening to a podcast this week about Pascal's Pensées. In the discussion, one of the participants made a passing comment lumping the Buddhist idea of non-attachment and Stoicism together.
I've heard this before, and I think it is a misunderstanding of the idea of non-attachment.
Stoicism has the connotation of moderating emotion. Not getting too high. Not getting too low. It has the connotation of disengaging from the exterior world, because getting too caught up in things will always disappoint.
When the mystics tell us that we must become unattached to the things of the world, the ultimate goal is not to disengage from them entirely (although this may be needed for a time), but to engage with them fully without finding our life in them, without needing them for our happiness.
Take the situation of a wedding day. The Stoic is going to say: "Don't get too excited. This day is only a temporary high. The feeling of joy will soon pass, so don't let yourself get carried away." The Stoic will tell you to moderate your emotion. The mystic encouraging non-attachment will say: "Enjoy this day. Fully enter into it. It is one of the most meaningful and joyous days of your life. The immediate emotion of this day will pass, yes, but your ultimate well-being does not lie in temporary events or emotions, but in Something deeper within you."
The goal of non-attachment is to fully enter in to life, but without clinging, without looking to the things of the world for our ultimate well-being.