These philosophies and more are expounded on the CompBio wiki.
I consider all of us as students of science. Every student in our group has a great deal of freedom to pursue projects of interest to them and are not asked to do things they don't want to do (except in pursuit of the larger goal of doing science, i.e., rigourous controls are necessary to do good science, for example). Unlike most other professions, the goal in our academic programme is to foster independent problem solving abilities. I'm also a strongly antiauthoritarian and the beauty of science is to never believe in yourself or your ideas too much and always be highly self critical and questioning. As such, our group is run as a structured anarchy ("Structured chaos", "complexity", or "edge of chaos" are all terms that describe some of the science we do, much like life itself, and we also study how models like these are among the most efficient and effective). I however expect, as a condition of working together, that students recognise that "with great freedom comes great responsibility" (made famous by who?). One of those responsibilities is to leave the group significantly more learnt (learned) and wiser, surpassing everyone's expectations, including their own as well those of their mentor(s). The fact that students in our group have done so is one of the reasons for their success.
As a mentor, I believe in fostering an environment where each student's dreams and potential can be fulfilled to the maximum extent possible. While I am passionate about doing great science I also put the interests of the people who work with me above my own. I value the intellectual and personal relationships I have with my students extremely highly and I consider myself highly fortunate to be part of a group that not only does great science, but makes it a pleasure to do so.
More generally, I see the reason to do great science as not only personal but also as an existential responsibility. I believe that "science is the greatest achievement so far of the human race and its long term best hope for it's survival and enlightenment." As organisms on this planet who consume more than they produce, I see this as a way to restore the equilibrium.
On a more personal level, a close knit group is almost like a family. Not everyone has to agree. Disagreements are encouraged, but we need to end up working together in the end to achieve our common goals. If you felt a sense of excitement and passion when you first read this and continue to feel it, then keep at it! The rest will follow. If you think you that you could use a reboot, then by all means use all means at your disposal in the group to reboot.
Finally, even though I use the word "science", I don't see it as being distinct from philosophy or art or other categorisations of fields of learning. Constantly attempting to falsify one's discoveries is science. Our niche is that we do computational science, i.e., computational experiments that are well designed and rigourously controlled in a computational laboratory. (For us, a set of one or more computers is a system that we call a laboratory; our group therefore is referred to as just that, a "group", not a "lab" or a "laboratory".)