As any debate coach knows, a course on formal logic does not help debaters much. I had a very bright, mathematically-oriented student who had just taken a formal logic course tell me such recently. As I have written before, part of the issue is that logic is not what is being done in economics, politics, and other social sciences; academics in these fields are not attempting to prove some fact absolutely follows from other facts (i.e., internal consistency from given or known facts); they are attempting to construct ideas that explain the world (i.e., external consistency).
I was struck recently to read how the Bank of England's advisory board works: the board members are presented with statistics, data, and other facts from the Bank's staff; then, the board members interpret these facts and debate each other about what the British economy is doing. The key act is interpreting -- putting the facts into one theory or framework to make sense of them, deciding which facts are noise and should be ignored -- not rising to proof. Obviously, each board member's prior experiences, opinions, and ideology probably have more to do with their interpretation than the specific set of facts presented in any given session. If the complexity of epicycles did not kill off the geocentric view of the solar system, then surely an economist is not going to abandon his pet theory so easily. Thomas Kuhn might have some things to say how what it would take.
There is a reason Toulmin's model is about the structure, not the content, of arguments: what counts as good reasons differ from field to field. It makes sense to talk about a research field as a discourse community: people talking to each other, in some sort of agreement about what constitutes evidence and good arguments. I do not want to get into whether discourse communities are successfully developing objective standards to evaluate evidence (I am sure it differs from community to community). My real point is that theory formation is at the heart of a research field. All arguments, evidence, and reasoning needs to be understood in terms of the eventual goal of building a theory. My own personal experience was trying to publish an article based on my thesis, which was about how California newspapers reported the new exit exam requirement for high schoolers. One rejection was very clear: the article did not advance theory, which was true. While the article certainly did reference mass communication theories to explain and interpret the reportage, it did not refine, clarify, or refute those theories, so it was not publication worthy.
I had all these thoughts jostling in my head when I was talking to my debater. It occurred to me that argumentation in debate is really about theory formation. In other words, arguing successfully is not about presenting sufficient evidence to back up your claims (otherwise, defensive arguments would win way more often that they do); arguing successfully is about presenting a coherent theory. Disadvantages are not done in by inconvenient brink problems here or there, so long as they seem to present a credible story. I would say, no one has lost a disadvantage because he did not prove the (highly improbable, totally speculative) internal link; he has lost it because it did not have a plausible, causal story. If the judge says, "A leads to B how?," the debater has lost. If the judge says, "A causing B seems pretty unlikely, but there's a risk...," the debater has most likely won. My point is that debate is not about analytical, deductive reasoning; debate is about synthetic, theory-building reasoning.