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"Now this is a revelation to me, and I hope you'll expound."

I'll do what I can.

"It was heretofore my assumption that one defining, and really inarguable, feature of what constitutes a species (at least a species that requires sexual reproduction, not a one-cell creature)is that cross-breeding of two identifiably seperate species would not result in fertile offspring, if offspring at all. I would call the goats in my example breeds, as a farmer would, not species. Holstein vs. Jersey...etc.

I'm assuming no one else has answered your question.

The definition of species is a difficult concept to pin down, simply because nature very seldom shows us a sharp demarcation between groups of related animals. If you view two highly disparate species it is very easy to differentiate between them. However since most differences between groups are in reality a continuum of morphological variation, seeing that demarcation is at times less than obvious. We are a species that needs to classify, whether it is a simple classification between those other organisms that eat us and those that we eat, as our ancestors had to develop, or the complex classification needed in formal logic. Unfortunately classification is necessarily discrete, where it becomes necessary for us to pigeonhole whatever objects we are classifying, in this case objects that are inherently difficult to place. In most cases the decision to place an organism into one or another taxonomic classification is more or less arbitrary.

When it comes down to it, this isn't very satisfying to our natural desire to view things in black and white, good and bad, friend or foe, so a number of different taxonomic 'schools of thought' have arisen in an attempt to make classification more satisfying. Most of these schools consider their method correct and every other method of classification overly restricting. This is why, along with the arbitrariness of any pigeonholing, it can become confusing to pin the species label on a specific population.

There is a 'working' definition of species that, although somewhat fluid, is fairly commonly used and is where most people get the idea of viable offspring being the main species property. It can be viewed from two different angles; what characterizes a single species and what differentiates two separate species.

A single species is a population where gene flow can occur between the extremes of morphology within the species. This is why dogs are still considered a single species even though you will not see a Great Dane breeding with a Tea cup Poodle. Genes from a Great Dane can still reach the TC Poodle through the intermediate sized dogs. Breed the Great Dane to a Standard Poodle, take the offspring of that pairing and breed it to a Miniature Poodle the offspring of which is bred to a Toy Poodle and that offspring is bred to a TC Poodle. Gene flow.

This causes problems with ring species however, such as in the Greenish Warbler species where there are a number of subspecies that will interbreed on occasion with their immediate neighbours, but the two subspecies physically (location) and genetically farthest from the parent species will not interbreed even though their ranges overlap. If the parent species were to become extinct, the question of whether or not the two end subspecies are actually different species would be settled. The gene flow would end. They would then be separate species because they no longer have a path for genes to flow along. If you were to take a gamete from a member of each of the two species and combine them they could still produce a viable zygote. This will never happen in nature however because they do not interbreed.

Creationist speciation on the other hand requires a cat to give birth to a dog, something that evolution has never claimed would or could happen.