@Casey phil,
I like the existential context of the self you are conveying.
But this is your argument in propositional logic?
1.
S<--> L (The self is similar or comparable to life.)
2. (S <--> L) --> E (In common between the self and life is existence)
3. S --> L (Life is how the self can exist)
4. S <--> L (The self is close to what life is.)
5. L --> S (Life can be partially understood through the self.)
6. L --> ~S (To know what life is would be to live as life and then one could not live as the self.)
This is your statement without line #4 because it is redundant
1. S<--> L (The self is similar or comparable to life.)
2. (S <--> L) --> E (In common between the self and life is existence)
3. S --> L (Life is how the self can exist)
4. L --> S (Life can be partially understood through the self.)
5. L --> ~S (To know what life is would be to live as life and then one could not live as the self.)
To make it more coherent, you should propose first a single statement, something about life or self. That makes the syllogism doable. (i.e. 1. E or S)
Work on #3 and #4. It's almost a hypothetical syllogism (i.e. a-->b then b-->C) You could do it by changing the last variable in #4 (through the self) to either existence or some other variable.
If you work the problem, the argument logically concludes in ~L, or to not live as life, but I think thats not what you want to convey.