Non-circular Definition of Homology/Analogy

Well, I'd say homology would best be defined as:

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Significant similarity between two structures of two different species in which no functional explanation can suffice to explain.

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Basically, you have all these similarities in structure that have no explanation (pentadactyl limbs of tetrapods, for example). If you assume they were independently created, then the explanation is that the similarities is due to the whim of the creator, i.e, not much of an explanation at all.If you assume common ancestry, then these type of similarities are to be expected since form is constrained by descent from a common ancestor. So common ancestry predicts these type of non-functional similarities.I think this argument is not the best one to use off the bat since it requires a little bit of meditation on the subject before the "Ohh..I get it!" moment comes about.

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The "product" of evolution implicates that the similiarity in form that possesses no function might. This is why in the evolutionary context Gould named "exaptation" but I do not know of any comparable defintion for an IDist. This seems thinkable to me.

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Maybe you can reword this a little better, I think I get the gist of what you are saying but I'm not entirely sure.I believe some creationists argue that there really aren't such a thing as homologies as I've defined them: all the similarities are there because of functional contraints. For example, during development mammals develop pharangeal arches that seem to be homologous with a fish embryo's pharangeal arches. But, the pharangeal arch stage is essential for the development of individuals in both species as part of their "somatic program" so this would be considered a functional constraint.The burden is on the evolutionist, in this case, to show that it could have been different. But this case hardly applies to every case of homology. For instance, humans can be born with six fingers and function just fine in the world. This case might also come in criticism since I think that the mutation for six fingers, when homozygous, is lethal. So the creationist would say, again, that the five fingers are the result of a functional constraint.But to avoid all this we can just look at the amino acid sequences of organism's proteins. It is known for certain several spots in a functional protein's amino acid sequence can be substituted by another without any major deleterious effect on the protein's activity. Similarity in these spots are clearly homologous due to common ancestry (or the whim of the creator).

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Evolutionary theory successfully predicts the distribution of these similarities across different life forms. For example, it is a straightforward prediction of evolutionary theory that the genetic code of a mouse and rat will be more similar than the genetic code of a mouse and a nematode, because rat and mouse share a common ancestor more recently than rodent and nematode.

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How do you establish that a mouse and rat share a common ancestor more recently than either with a nematode? Here you are assuming common ancestry and hence your argument is backwards. You are saying that since a mouse and rat share a more recent common ancestor then they will share more homologies, but what you should say is that since they share more homologies this is evidence that they share a more recent common ancestor.Now, after you establish common ancestry through the comparison of several homologies you may make the prediction that more homologies will be found. But you can't forget what got you to establish more recent common ancestry in the first place: homologies.
[EDIT]
I may be misreading your argument here. It sounds like you assumed they had a common ancestor to begin with but I think that you may just be saying you assume this by virtue of it being your hypothesis.

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The distribution of similarity across species provides evidence that homology is a real thing in nature. Not just one protein, but all proteins, all physiological functions, all behaviours and all developmental processes are more similar between rat and mouse than they are between rat and nematode. The hypothesis that this vast array of similarities exists by virtue of being the result of descent with modification is then simply the most parsimonious explanation of the observed data.

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I would also quibble with this a bit. It's not the distribution of similarity that is evidence of evolution: it is the distribution of homologous (non-functional) similarities. Of course a mouse and a rat are going to share a lot of similarities in terms of anatomy, physiology, and behavior than if either one is compared to a nematode. This is because they have relatively similar niche.It's the non-functional similarities that are interesting. Edited by JustinC, : No reason given.Edited by JustinC, : No reason given.Edited by JustinC, : ambiguity

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It isn't as if the lack of a clear slam dunk argument for every homologous structures against a creationist ploy should be the basis for the scientific definition of a term.

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I accept your criticism and recognize that I'm using non-functional in a highly restrictive manner. When writing I was tacitly responding to the plethora of creationist critiques against using certain (seemingly homologous) features to infer common ancestry. That is, every so-called homology is a necessary functional constraint.For example, that fact that baleen whales develop teeth in the embryo just like toothed whales seems to me good evidence of common ancestry. But a staunch creationist would reply that the tooth whaled stage is necessary for the development of baleen and is therefore a necessity, yadda yadda yadda. I know the counter-argumnent is extremely frivilous and vacuous (especially considering their claim that creatures were created by an omnipotent being: why use the same developmental pathway?)So you are correct, the term used in science shouldn't be as restrictive as I proposed.