Furrowed Brow wrote: Now evolutionary theory lacks a formulas like Newton's. The simple formula I offered was not a special definition as defined by Walter Remine, because it attempts (poorly) to be a generic definition. Now my formula may fail as a useful equation, but it draws out some of the important components of what goes into survival of the fittest, and it does so without resorting to a special definition.
It seems to me that whatever values we wanted to put into the equation would either have to be the same every time we measured them or they would be different (more than likely). If they were different and we tried to give a general definition of fitness, fitness would be a different value every time resulting in a 'special definition' every time.... wouldn't it?
Furrowed Brow wrote: However there is more to survival of the fittest than tautology, as my simple formulation shows. For the concept survival of the fittest does include the concept of the gene, gene mutation, and environmental changes. These three facets of what is required to survive are empirical inputs into the concept...
...Polar bears in a warming artic circle may be one example. Whether polar bears survive the next 100 years is not tautological question. And whether Polar bear DNA is able to reproduce and mutate at a fast enough rate to cope with changing environment is also not a tautological question. If polar bears survive over the long term, and the ice pack continues to shrink, then if I made the prediction that survivors will display new hunting traits, will probably be smaller due to eking out their survival on less rich food sources, and that they may well lose the white fur in favour of a coat that suits the new terrain better, then these predictions about the survival of the polar best fitted to their environment are not tautological.
I agree, that is because special definitions for fitness have been given. In the examples given, the special definitions of fitness are:
1. reproduction and mutational rates ("whether Polar bear DNA is able to reproduce and mutate at a fast enough rate to cope with changing environment")
2. hunting traits ("survivors will display new hunting traits")
3. coat type (" they may well lose the white fur in favour of a coat that suits the new terrain better")
We could make a hundred more predictions on factors (environmental or otherwise) we think would affect polar bear fitness and still not be able to falsify natural selection. If the three factors above proved to be irrelevant to survival would natural selection be falsified? -- Of course not. Coat type may turn out to be the only factor involved in whether or not the polar bear survives. For a penguin in the same environment, fitness might be determined by toe length. If fitness is defined by short fur for better aerodynamics and also long fur to keep them warm, we then move into metaphysical definitions of fitness that are not falsifiable.