- (Premise) If essentiality of origins doesn't hold, then every particle has a haecceity.
- (Premise) A haecceity of x is an intrinsic property of x.
- (Premise) A haecceity of x isn't a physical property of x or a function of any physical properties of x.
- (Premise) There is a particle each of whose intrinsic properties is a physical property or a function of physical properties.
- Therefore, there is a particle that lacks a haecceity. (2-4)
- Therefore, essentiality of origins holds. (1, 5)
I think the problematic premise is (4). But it is still somewhat plausible.