What we can do is keep the meaning of the word "fit" but see if we can find a new principle that relates fitness and evolution. What we want is a relationship that is both more reasonable on its face and more descriptive of what actually happens.
Let's start by looking back at that gedankenexperiment of the species interacting with its environment. We may not know how to pick the winners, but we can easily identify the losers. In any generation the losers are those who die before reaching sexual maturity, or those who select mates who are infertile, or those who have offspring who, by character or accident, die young. Those unlucky losers will not contribute to the gene pool of the future species.
That process is described by "the non-survival of the unfit". I think that nobody will argue against that as the precise statement of Natural Selection. It just sounds so negative.
But let's consider another group that are marginally better off. They just barely survive the rigors of childhood and manage to attain sexual maturity. By sheer luck they meet a fertile mate. They just manage to survive long enough to rear their children to the point that they, in turn, are sexually mature. They, and any members of the species who are marginally fitter or luckier, will contribute their genes to the next generation.
They are evolution's darlings, the ancestors of future generations. But what name can we give them? After all, keeping all those qualifications in mind isn't easy. What we need is a catch phrase like "the Fittest".
Whenever we get confused by words it helps to use diagrams.
Let us assume that we can describe the fitness of an individual to survive long enough to have offspring in terms of two qualities. We'll also assume that we can more-or-less measure these qualities on a scale represented by a number we'll call a "parameter". Actually, fitness may be described by three or more qualities, but it is easier to draw if we look at them two at a time.
The qualities will not be completely independent. In particular, for any value of one parameter there will be a range of values of the other parameter that will correspond to survival. As an example, an individual that is less well camouflaged can still survive if it can run faster. Figure EG0506a illustrates a case where darkness of coloration is plotted in one direction and fleetness of foot in the perpendicular direction.
If the coloration is too dark or too light the animal will have less camouflage and will be less likely to survive. If it is less well camouflaged but runs faster, it will be more likely to survive. But if all its development goes into speed it will be less likely to rear its children well, so the survival of the individual does not contribute to the next generation.
What we can say is that there will be a region in this "parameter space" that corresponds to survival. The boundary of this region is defined by the characteristics of the ecological niche; for instance a region with snowy winters will include an area in parameter space that represents white fur.
All those inside the boundary can pass on their characteristics to their offspring. If they happen to mate with another individual with similar characteristics their offspring will probably stay in the same neighborhood in parameter space. But if they happen to mate with an individual with different characteristics, or have recessive genes, their offspring may end up outside the boundary in parameter space. Then some of their offspring will contribute to the future gene pool, and others won't.
That's illustrated in Figure EG0506a where the children (gray) of surviving parents (black and white) may or may not survive depending on where they fall in parameter space.
Since mature males and females are likely to meet at random, we can expect that the entire region in parameter space that corresponds to survival will be more-or-less filled.
It is likely that somewhere within the region corresponding to survival is a sub-region that can be described as containing the individuals who are "the fittest", i.e., those most adapted to survive in the ecological niche. On the maps we've shown it is likely that those individuals are located in the central region rather than near an edge. But it certainly isn't obvious that one central region should contribute almost all of the future population.
We can represent the relative survival value of locations within the boundary graphically in Figure EG0506b.
Here the probability of survival of an individual in each sub-area of the map is plotted vertically. The higher the surface at a particular point the greater the likelihood that the descendants of that individual will be around for a while. The peak of the probability hill is the individual who is "the fittest".
"Survival of the Fittest" means that only those individuals located in a small region around "The Fittest" will make a significant contribution to future populations. That is simply not the case.
The likelihood that a range of individuals will contribute to future populations is measured by the volume below them (since this is the individual probability of survival times the population), so the total bulk of the hill represents the weighted probability of genetic material likely to be contributing to future populations. The volume immediately under a small region around the peak, i.e. "the fittest", is negligible compared to the total bulk of the hill.
This means that in comparison to the sum of the contributions of all those who are fit enough to make some contribution to the future gene pool, that individual who is "the fittest" can be completely ignored in considering the makeup of future populations. The individual probability of contributing to the future genetic stock of the species may be smaller for the "slightly less fit" than "the fittest", but there are so many more individuals who are not "the fittest" but are "fit enough" that they far outweigh "the fittest".
Thus it is not useful (i.e., it is bad science) to base the fundamental principle of evolution on "the fittest". That individual is not easily identifiable nor is the region around that individual obviously critical.