I see the key difference is that in (1) the definition is a created effort that is a result of everyone in the group's efforts and that fits their understanding of the situation.
This presumes that (a) there are definitions that fit everyone's efforts, everyone contributes as well as each other, etc. and (b) that people are as capable of coming up with theories as each other. There are people out there who have come up with theories that I might never come up with, that still fit my ideas near perfectly. I see no reason not to build on their ideas rather than confine myself to what I might come up with locked in a room on my own without access to anyone elses thoughts.
Re: Define. Finite. Infinite - One
This presumes that (a) there are definitions that fit everyone's efforts, everyone contributes as well as each other, etc. and (b) that people are as capable of coming up with theories as each other. There are people out there who have come up with theories that I might never come up with, that still fit my ideas near perfectly. I see no reason not to build on their ideas rather than confine myself to what I might come up with locked in a room on my own without access to anyone elses thoughts.