To put my point a bit differently I think your argument would disappear if you tried to define imagine/reason more precisely.
Humans certainly aren’t perfect at imagining. In fact if you ask most people to imagine a heavy object and a much heavier object falling they will predict the much heavier object hits first and I can give a host of other examples of the same thing. So certainly we can’t require perfection to count as imagining or reasoning.
Neither do we want to define reasoning in terms of speaking english sentences or anything similar. I mean we can imagine the possibility of intelligent alien blobs of gas that have no language at all (or at least that we can understand). Besides using this definition would just make the claims trivial.
The best approach I can think of to making these terms more precisce is by defining reasoning ability in terms of ability to respond in a survival enhancing way to a diverse set of conditions. However, when we try to define it this way it is far from clear that complexes of genes aren’t just as good at reasoning as people are.
Sure it’s weird that something like this might be the case but it’s damn weird that induction works at all so why not believe it can be captured in a large number of relatively simple heuristics.
Speaking as a mathematician (well a grad student) I can positively say I frequently see ‘by definition’ used in arguments and use it myself in a substantive valid fashion. Sure, definitions don’t support inductive inference but that doesn’t mean they are always trivial. Fermat’s last theorem follow by definition from the definition of the integers but it’s certainly not a trivial fact that it does so. While rarely quite so complex arguments about philosophy, politics and other things can sometimes benefit from the nonobvious manipulation of definitions.
Also the notion of something following ‘by definition’ is of incredible use of rebutting a great deal of misguided philosophy. Quite frequently in philosophy one will see an analysis of a concept like, life, knowledge, or morality claiming to be a explication of the term we use in everyday language. However, it can be very useful to point out that no matter what the theoretical virtues of reducing ‘moral good’ to ‘that which produces moral emotions in us’ it’s simply definitionally false. To the extent that we have a coherent notion of ‘moral good’ the sense that it refers to interpersonal facts that are more than mere feelings is inseperable from the concept. The word might change meaning but a theory which says there is nothing more to morality than moral feelings is by definition claiming that there are no moral facts not offering a materialist account of them.
Ironically in making this point I’m somewhat agreeing with Eliezer. The real benefit in using the definition like I did above was to combat the abuse of that definition in the original argument. Definitions are dangerous in arguments but not because people are inclined to say ‘by definition’ when they mean ‘damn right’ but because they let the presenter shift the flaw in their reasoning far away from the controversial results. Unless your used to evaluating complex mathematical arguments (and even then) a subtle flaw in a definition at the begining of an argument that has been forgotten by the time the conclusion is reached can be extremely misleading. Worse it harnesses the social awkwardness of being pedantic and insisting on details and rigor before the person has been allowed to get into the meat of their ideas to squash your ability to find the flaws (obviously these are side effects not purposeful choices)