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Because from the records we have of human beings 2000 years ago, we know that the human form has changed very little since then.

I'm using "form" in the Aristotelian sense, as "substance" or "essence," not shape.

I don't think so. At any rate, human evolution is a very slow process, especially with the advent of technology, which has greatly reduced selective pressure on our species.

So how can I know with certainty that I am of the same species as Jesus? As Moses? As someone who lived 3000 years ago? 4000 years ago? 10,000 years ago? Etc.

Secondly, it seems to me to be plainly absurd to speak of the continual transformation (change in form) of species when the notion of the transformation of species assumes the existence of stable forms (species) that are universally apprehensible,

It assumes no such thing. Species are merely an artifical human construct that makes classification easier, nothing more.

The problem of universals is of paramount importance in philosophy, and is not so easily dismissed. The position you describe is the Nominalist position, which is incoherent.

We find an unequivocal affirmation of Nominalism in Positivism. For Hume, Stuart Mill, Spencer, and Taine there is strictly speaking no universal concept. The notion, to which we lend universality, is only a collection of individual perceptions, a collective sensation, "un nom compris" (Taine), "a term in habitual association with many other particular ideas" (Hume), "un savoir potentiel emmagasiné" (Ribot). The problem of the correspondence of the concept to reality is thus at once solved, or rather it is suppressed and replaced by the psycological question: What is the origin of the illusion that induces us to attribute a distinct nature to the general concept, though the latter is only an elaborated sensation? Kant distinctly affirms the existence within us of abstract and general notions and the distinction between them and sensations, but these doctrines are joined with a characteristic Phonmenalism which constitutes the most original form of modern Conceptualism. Universal and necessary representations have no contact with external things, sinct they are produced exclusively by the structual functions (a priori forms) of our mind. Time and space, in which we frame all sensible impressions,cannot be obtained from expierence, which is individual and contigent; they are schemata which arise from our mental organization. Consequently, we have no warrant for establishing a real correspondence between the world of reality. Science, which is only an elaboration of the data of sense in accordance with other structural determinations of the mind (the categories), becomes a subjective poem, which has value only for us and not for a world outside us

First of all, the rate of transformation is not constant. Sometimes it may even stop for periods.

The philosophical problem remains.

Second, the differences between pigeon and archaeopteryx are so different as to make the distinction unproblematic.

Of course. That's not the problem. The problem is, if species undergo constant transformation, how can we know this with certainty? How can this certain knowledge be reconciled with the subjectivism or anti-realism of Nominalism, which is ultimately solipsistic?

However, you are correct, that when two animals are very simlar, where you drawn the line between speices can be somewhat arbitrary.

But in fact, there are no actual species to draw a line between, only names that people attach to creatures that look alike, or what have you. Evolutionists here want to have their cake and eat it too.

I remember pressing curiosity on the problem of form/species fluctuation before. I hope he gives a better answer this time. :)

I'm told that Etienne Gilson's _From Aristotle to Darwin and Back Again_ quite admirably covers the philosophical difficulties. There are some notes of Gilson's points at this link. I have also found one philosophy of science professor who is engaging the problems an overly metaphysical kind of Darwinism poses for the essence or nature of a creature. See his weblog.

He touches a bit on nominalism, as well. One of the problems is that "species" is now an equivocal term having both an ontological and a biological sense. Curiosity seems to be using "species" in a biological sense, so I think trying to make it fit into its philosphical conception is a big bad category mistake.

Nominalism as a hard theory is definitely incoherent, but it seems to me that science has to proceed using some kind of pragmatically anti-realist or nominalist philosophy. Natural science is the attempt to build a model of nature, and that model must be both open to correction and amenable to scientific consensus. Practical nominalism, instead of "hard" nominalism, is a necessary practice to fit these requirements, so long as we don't get in the habit of being nominalistic everywhere else. (An old thread on Methodical realism might be relevant, or perhaps it contradicts me completely, I forget. Worth a read though.)

Biologically speaking, neo-Darwinism tends to be blind to the organism, generally treating it as an epiphenomenon generated as a byproduct of gene dispersal and duplication. This strikes me as an area with far more potential to attack, or simply to complement, Darwinian reductionism on biological grounds.

The problem of species classification is nothing else than an example of the problem of vague catagories. The difficulty in identifying the precise point where to draw the line between species is no different then the difficulty of drawing the line between red and orange on the rainbow. There are wavelengths of light that everyone will agree are red, and there are wagelengths of light everyone will agree are orange, and there are even wavelengths nearly everyone will agree are in between. But there are wavelengths on the borders of these three categories which are impossible to classify with any degree of certainty.

One does not have to resort to nominalism to resolve this problem. It is perfectly possible that the substance of red and orange exist, but it is impossible to determine, using empirical observation alone, where the precise boundary lies.

Likewise, "kinds" may exist as forms in the metaphysical, aristotelian sense, but physical measurement of the differences between groups of creatures cannot reveal the precisely where the boundary exists. Nevertheless, when the physical differences are large enough, we can can say with certainty that the kinds differ, much like we can say with certainty that certain wavelengths are red and not orange.

Similarly, the precise metaphysical boundaries of mankind cannot be known through biological observation. These boundaries may exist, but we simply cannot know them by merely measuring physical differences. Nevertheless, when we see that a population has no significant differences from the rest of humanity, then we can say with certainty that they are, indeed, our own kind.

This poses a problem in times where there exists a "borderline" homonid population. For instance, were Neanderthals human? They were extremely similar to us, but they also had a few significant differences. It's very difficult to say whether they were in fact true humans. I'm very glad I'm not living in the age where our kind coexisted with them, or even "archaic" homo sapiens for tha matter.