Is there really such a thing as a beneficial mutation?

I have avoided posting in this thread till now. But I will give a contrary view, though it won't help your YEC position.I think the term "beneficial mutation" is confusing, and should be avoided. Evolution can be explained without needing that term. I'll give some reasons for this.

1. Most evolutionists are neo-Darwinists. The neo-Darwinian account claims to avoid intentions. Yet the term "beneficial" is an intentional term. It seems to me that a neo-Darwinian should avoid the term "beneficial", and simply say that some mutations survive better into the next generation than do others.
   ​
2. Personally, I hold neo-Darwinism in some disdain. Perhaps that is partly because of the attempt of neo-Darwinism to deny intentionality. It is difficult to discuss biology without using intentional language. That's why we see biologists talking of "beneficial mutations". Dawkins' title "The Selfish Gene" uses intentional language. Biologists even coined the word "teleonomy" so as to allow the use of teleological language while denying teleology.
   ​
   However, even though I see the need for intentional language when discussing biology, I don't find the term "beneficial mutation" to be useful. That term suggests that there is an absolute benefit to a mutation. But in most cases, the benefit is relative. The mutation may offer benefits in a particular environmental niche, but be disadvantageous elsewhere. A mutation that gives bacteria resistance to penicillin is of benefit only in an environment where penicillin is in use, but it is deleterious elsewhere and selected against. The mutation that results in sickle cell is of benefit in a malaria ridden environment, but is deleterious elsewhere. Thus "beneficial mutation" is misleading, because it fails to mention the importance of relational aspects.
   ​
3. The idea that evolution proceeds by accumulating beneficial mutations is just silly. The driving force of evolution is change, including environmental change. If the environment to which an organism is adapted should disappear, then either the organism must change to exploiting a slightly different environment or it will go extinct. Mutations are enablers. A mutation may confer on an organism, the potential of being able to exploit a slighly different environment. A gene pool accumulates mutations, providing variation. That accumulation allows the possibility of change. But it is when change becomes necessity (adapt or go extinct), that the organisms will begin to make important use of some of the enabling possibilities that they have accumulated from past mutations.

You seem to be describing a Goldschmidt hopeful monster mutation. I have no problem calling that beneficial. But such cases are surely so rare as to not account for the evolution we see.

That's not necessarily a problem. If you use intentional language in discussing biology, you could be relying on the mind of a creator. Or you could be allowing that the biological system has some kind of primitive mind. The first is a problem, in that there is no actual evidence to support it.I don't see the problem in the second alternative, that the biology itself can produce something akin to a primitive mind. And that's roughly what WK's comment allows.The text in your first image is concerned that intentional analysis will "admit an external agent into the worldview", but I don't see that as a consequence of what I called the second alternative.We could say that the purpose of evolution is to produce humans. That's leads to classical teleological explanations, where we explain in terms of the "final purpose" - what is to be produced. That kind of intentional language is a problem for science, because science is about mechamisms rather than final purposes.With the alternative use of intentional language, we can observe that biological systems appear to be in a struggle for survival. But that could be simply an observation about the internal mechanisms of biology. Since the struggle may be unsuccessful (the species could go extinct), there is no reliance on final purpose as part of an explanation. But that use of intentional language does allow us to think of evolution as a kind of trial-and-error learning system, where a species experiments with recombinant DNA in the effort to enhance its odds of survival.