(with apologies to Simon F. for the resonance)
Once upon a time in the last millennium – as it happens, the first year of the first decade of the last century – a judge of the now-defunct judicial branch of the House of Lords decided to let a not-too-small cat out of the bag. He wrote:
“[A] case is only an authority for what it actually decides. I entirely deny that it can be quoted for a proposition that may seem to follow logically from it. Such a mode of reasoning assumes that the law is necessarily a logical code, whereas every lawyer must acknowledge that the law is not always logical at all.”
Quinn v. Leathem,  A.C. 495 at 506 (H.L.)
It is remarkable how often, over the past century plus, that judges in common law jurisdictions have found it necessary to repeat this reminder about an aspect of the process of common law legal analysis. Sometimes, though, one has to wonder whether the judge(s) meant to say what the written words assert.
The following recent-enough quotations from different reasons for judgment are accurate. I've not included the citations to protect the (perhaps) innocent. The 2nd and 3rd quoted paragraphs are contiguous paragraphs from one decision.
"I would add that there is an important difference between drawing an inference as to causation from circumstantial evidence, which is often done, and drawing an inference as to causation from no relevant evidence at all, which may be done only in the rare circumstances set out above. This is the difference alluded to … in …. when he distinguished between a logical inference and a legal one; the legal reference should not be resorted to unless the logical inference is impossible to establish with either direct or circumstantial evidence."
"Thus, at common law, according to the …. authorities, want of logic is not synonymous with error of law. So long as there is some basis for an inference – in other words, the particular inference is reasonably open – even if that inference appears to have been drawn as a result of illogical reasoning, there is no place for judicial review because no error of law has taken place.”
However, as I noted recently in … some doubt has been cast on the scope and operation of that principle by reference in later judgments to the need for findings or inferences of fact to be supported by “logical grounds” …
"In this case I am prepared to infer or conclude, on the balance of probabilities, that but for the Accident [the plaintiff] would not have the … pain that he does. There are times when such inferences are based on a “robust”, though nonetheless legitimate, exercise of fact finding … Here I do not consider that such an inference requires a particularly “robust” approach to fact finding; instead, I consider it to be both pragmatic and an exercise of “common sense”."
For what it is worth, a friend who knows the judge who wrote the last paragraph tells me that that judge would not have meant to say what the paragraph literally asserts: that "robust inferences" are not "common sense" inferences. The least of the reasons for that – apart from his knowledge of the particular judge – is that the Supreme Court of Canada has told us that robust inferences are common sense inferences. Borrowing, and paraphrasing, slightly, what a judge of the U.S. Supreme Court said about his bench, our Supreme Court, too, is infallible but only because it is final.
The context of the second excerpt shows the judge was casting doubt on the assertions that law's process of reasoning was allowed to be irrational, illogical, in the commonly understood meaning of those terms.
As to the first, excerpt, well … there is that creature called the Legal Fiction. In music, and real life, as Billy Preston pointed out years ago, "Nothin' from nothin' leaves 'nothin" (here). Law, however, isn't necessarily real, or life.
As we pass through law school, and then our legal careers, we are always told that law should strive for consistency; but not, of course, foolish consistency. Some years ago, a former Supreme Court of Canada Justice L'Hereux-Dubé, writing extra-judicially, wrote an article comparing the decision making processes of common law and civil law systems: "By Reason of Authority or By Authority of Reason" (1993) 27 UBC Law Rev. 1.
Addendum Feb 2/11
It's very kind of the SCC to make my point, I think, in a very recent (as of released today), very brief (3 paragraph) set of reasons. 2 of the paras. are by the majority, the 3rd is the dissent. This is text.
R. v. Bruce 2011 SCC 4
APPEAL from a judgment of the Alberta Court of Appeal (Berger, O’Brien and Bielby JJ.A.), 2010 ABCA 131, 477 A.R. 208, 483 W.A.C. 208,  A.J. No. 433 (QL), upholding the accused’s conviction. Appeal dismissed, Fish J. dissenting.
The judgment of LeBel, Deschamps, Abella, Charron, Rothstein and Cromwell JJ. was delivered by
 The Court is seized with an appeal as of right brought under s. 691(1)(a) of the Criminal Code, R.S.C. 1985, c. C-46, from a judgment of the Alberta Court of Appeal (2010 ABCA 131, 477 A.R. 208) rendered on April 22, 2010. A majority of the Court of Appeal dismissed an appeal from a judgment of the Alberta Provincial Court (Chrumka J.) declaring the appellant, Derek Dwight Bruce, guilty on counts of breaking and entering, committing assault causing bodily harm and possession of a weapon.
 I am of the view that the appeal fails. Although this appeal does not raise only issues of credibility, I agree with the majority of the Court of Appeal that the trial judge’s decision was reasonable, was supported by the evidence and that he had committed no error in the application of the relevant law to the facts. For these reasons, the appeal is dismissed.
The following are the reasons delivered by
Fish J. —
 With respect for those who are of a different view, I would allow the appeal and order a new trial, essentially on the ground that the decision of the trial judge rests on inferences that do not flow logically and reasonably from the evidence upon which they are made to rest, notably on the issue of identification ― the only real issue in this case.
Appeal dismissed, Fish J. dissenting.
So, here's the $64,000 question.
While the majority did not say "logically and reasonably" as did Fish J, I think we should assume that that is what they meant by stating that the trial judge's decision "was reasonable and was supported by the evidence" (my emphasis). Still, when the difference is over the something as basic as whether the conclusion is both reasonable and logical – implying that (at least for these judges) there's a difference, I'd like to know what they think the difference is in principal, and in the particular case.
For example – not referring to R. v. Bruce – if we start from the premise that the moon is made out of rancid green cheese, and cows come from Krypton so that they have super powers when exposed to the yellow sun, it may well be logical to conclude that the cow did not jump over the moon when the sun turned red. On the other hand, it is at least questionable whether the moon is made out of rancid green cheese.