“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. Leatham,  A.C. 495, from the speech of Lord Halsbury, at 506
This past fall, we studied R. v. Morris,  2 S.C.R. 190 in Evidence. It was an interesting read - the majority and minority judgments each turn on neat little bits of formal logic.
The crux of the case (at the Supreme Court) was the admissibility of a newspaper clipping. Is a newspaper clipping about the heroin trade in Afghanistan relevant to prosecuting a conspiracy to import heroin from Hong Kong?
In the dissent, Lamer J. (as he then was) argues that the clipping was inadmissible, since it was more prejudicial than probative. The central argument is at p. 204:
Its sole relevancy is through proof of the accused's disposition, the reasoning being as follows: that, because persons who are traffickers are more likely to keep such information than not, people who keep such information are more likely to be traffickers than people who do not, and that a person who traffics is more likely to have committed the alleged offence than a person who does not. The ultimate purpose of placing the accused in the first category (people who keep such information for future reference) is to put him in a category of people the character of which indicates a propensity to commit the offences of which he was charged.
Lamer is saying that the clipping's only use is the impermissible inference - that because Morris had this interest, Morris is more likely to be a drug trafficker. In terms of formal logic, Morris was in the set of persons possessing clippings about the heroin trade. The set of persons having clippings about the heroin trade (at the very least) intersects with the set of persons interested in the heroin trade. The set of persons interested in the heroin trade is a superset of the set of persons involved in the heroin trade.
By my reading of his reasons, Lamer was saying that because this connection is so tenuous, the clipping is inadmissible - since it has so little value in proving anything but disposition.
By the definition of relevance in Paciocco and Stuesser's Law of Evidence, (4th ed), anything that, as a matter of logic and human experience is probative of a material issue is relevant. The impermissible inference is generally presented as an exception - that general character or likelihood to offend is not sufficiently strongly related to the specific crime an individual is charged with. However, interest in the Afghani heroin trade might have some circumstantial relevance to involvement in the heroin trade through Hong Kong.
Unfortunately, McIntyre J. is a great deal more subtle about the logical basis for allowing this evidence than Lamer is about the logical basis for excluding it. Fundamentally, McIntyre says that the clipping should be given very little or no weight, but that it is logically relevant - as well as a strong connection between him and other traffickers, he was informed about the heroin trade.
Although you may not be able to deduce Morris' participation in the heroin trade from the existence of the clipping, it is relevant - it places him in the set of persons who are informed about the heroin trade. Each piece of evidence provides a selection criterion for determining membership in a set of possible offenders. If the intersection of all these evidence-sets has one member, that should then be proof beyond a reasonable doubt of that member's guilt. All information that provides a valid selection function for a set of suspects is then relevant. The clipping then shows that Morris is part of that set of persons with some interest in the heroin trade. While this may not provide a significant narrowing of the set of suspects, it does place Morris in a particular set. Consequently, it's relevant - but given how unlikely it is to allow a decision between two possible suspects, it must be accorded very little weight indeed.
All that being said, I'm not sure that Lamer was wrong - if it is of little or no weight, does the minuscule probative value outweigh diminutive prejudicial effect? Is that prejudicial effect made worse by Morris' association with those with a stronger tie?