Why does "p" in "aptitude search" mean not installed at all?

$ sudo aptitude search node

p   nodejs                                                                 - Node.js event-based server-side javascript engine  
p   nodejs:i386                                                            - Node.js event-based server-side javascript engine  
p   nodejs-dbg                                                             - Node.js event-based server-side javascript engine (debug)  
p   nodejs-dbg:i386                                                        - Node.js event-based server-side javascript engine (debug)  
p   nodejs-dev                                                             - Development files for Node.js  
p   nodejs-dev:i386                                                        - Development files for Node.js  

I know from man aptitude that:

The first character of each line indicates the current state of the package: the most common states are p, meaning that no trace of the package exists on the system, c, meaning that the package was deleted but its configuration files remain on the system, i, meaning that the package is installed, and v, meaning that the package is virtual.

i for "installed", c for "config", v for "virtual". That all makes sense.

Why does p mean "not installed at all, not even the configuration files" (note the lack of the letter "p" in that whole phrase!)?

I have to reread the man page every single time I see that p, because I always forget, and that really annoys me.

p is for : the package and all its configuration files were removed, or the package was never installed. According to aptitude documentation

[ http://algebraicthunk.net/~dburrows/projects/aptitude/doc/en/ch02s02s02.html ].

And p is for "purged" so it is absent from the system. I guess that is the meaning :)