I think the most frustrating aspect of this whole conversation is that people seem to approach the question with a series of pat answers which in truth really don't answer the question as it was originally posed.
I fail to see how it hasn't.
I admit that the analogy that I originally presented was at best poor and at worse false and misleading, but it seem that people have chosen with unfailing regularity to quote it, ignoring the fact that I had already acknowledged, in the very first post, that it failed in several important aspects. However, the aspect that I was trying to emphasize with the analogy, the perception of the continuity of evolution (absent all of the creationist baggage that has now been attached to it), still stands and has not been answered adequately: how can we claim that the extant evidence that we have from the incomplete fossil record at this very moment (not the hypothesized evidence that we assume would be availible to us from a complete fossil record) presents eivdence for the continuity of evolution?
This is why it is not an epistemic problem. Epistemology deals with how one comes about knowledge, not how one comes about specific knowledge. But as I said above, I retract my previous statement to stop a derail of this thread.
I will, for the moment, assume that you only mean the
fossil record, and are not concerned about the mountain of other evidence which supports the continuity of evolution (see population and evolutionary genetics, the molecular genetics of mutations, ecology, etc). So your question becomes, in essence, "how do we fill the gaps".
This question is actually quite important, and one which I honestly would have assumed you would have had answered in the course of your three undergraduate degrees (I certainly did during mine). But that aside, we have to look at the various explanations we have for the fossil record.
On the one hand, when viewing the fossil record, we could assume that each fossil represents an organism which is un-causally linked to any other fossil. This is fine, it is just as good an assumption as any up to this point. However, we then have to question how these organisms came about, if they were not causally linked. The only assumption we can make is that these organisms just magically 'appeared' out of nowhere.
I hope you can see that such an assumption is absurd. We know that things do not "just appear out of nowhere". We also know that, thought selective breeding pressures, we can drastically change the form of an organism within recorded human history. See the banana, for example, or the more extreme breeds of dog. Thus, we know that selective pressures, acting on existing variation within a population, can lead to the changing of morphological characteristics.
Now we must re-evaluate our two possible assumptions with regard to the fossil record. Either the fossils are independent, and thus arose by "magically appearing out of nowhere", or there is a causal connection between the two. Since we know that selective pressures can lead to drastic morphological changes to an organism, we know that the changes we observe could be due to natural selection.
Armed with this, we then go about testing the theory, by forming a hypothesis and then testing it. For example, the hypothesis that there would be found 'intermediate forms' in the fossil record, even if they are rare. And, what do you know, but they
have been found. And ever since, nothing in the fossil record is inconsistant with evolutionary theory. This alone is evidential support for the theory. The fossil record does not falsify the theory, and follows the predictions made by the theory, thus it adds support to the theory.
Does that make sense?
People have answered variously with "intermediate forms" and "not enough time", which is strange because I dont think I implied that I was ever talking about a big jump in development, just a big jump in time (e.g., 1-2 million years when considering cetacean evloution, specifically the gap in the fossil record between Pakicetus and Ambulocetus or between Ambulocetus and Dalanistes). My point has mainly been that our claims to knowledge seem to far outstrip the current state of evidence, not that this discrepancy will never be resolved or that it even severly undermines evolution (both of which I don't believe). Thus, it seems that skeptics (as most of us are) would want to make conservative claims to knowledge based on the evidence.
Not true at all. The very fact that the current fossil record does not falsify the theory of evolution is support in and of itself for the theory. Furthermore, the sheer amount of evidence for evolution is so completely overwhelming, that to deny it is paramount to denying atomic theory.
In sum, I am not questioning the existence of evolution but rather the representation of evolution as continuous given the cureent extant evidence. Moreover, I am looking for a way to explain how the fossil record demonstrates the continutiy of evolution given its current fragmentary state.
Again, see 'intermediate forms'. These are entirely consistant with, and were predicted by, the theory of evolution. Furthermore, the theory of evolution predicts that like organisms will have like characteristics. Funnily enough this is exactly what we find. Moreover, the theory of evolution, coupled with current geological and physical theories, predicts that the fossil record will be patchy. To find otherwise would falsify a large amount of geological theory. A lack of evidence is not evidence for a lack of a theory.