How about defining it as an instance of functional complexity? And treating the list of properties as following necessarily from this definition? Okay, this is very diamond-in-the-rough (or perhaps zirconium...) but here goes my thoughts on the matter: (Complexity) Many diverse parts (functional) acting for the sake of the whole I think I need to add something like "not as the instrument of another" or something like that. Given that they act together as one whole and given entropy, etc., the organism will need to posses more order than its surroundings (homeostasis). It will therefore need to take in energy (nutrition), which it will use to sustain its readiness to interact with its environment so as to preserve its own being (homeostasis again?), but which will eventually break down (death), so that in order for that life form to continue it will need to duplicate itself (reproduction), which, upon occurring, will involve both development (growth) to maturity and...
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For starters, the equation by McCulloch doesn't mean anything to me: what's dQ?
The equations aren't really important in that article. dX (where X in any variable) is essentially synonymous with delta_x, or change in X. dX means a small change in X. Technically, dX is an infinitesimally small change in X - this assumption is the basis of calculus. What that equation means in words is that if you add a small amount of heat energy to a closed system otherwise kept at constant temperature, you will likely contribute to it's disorder. This, if I hold an ice cube and put a lighter by it (adding the dQ), some of it will melt into water - thus ruining its order and increasing its entropy (corresponding to an increase in S on the other side of the equation).