The material below is a transcription of recently-rediscovered rough notes that I prepared for a lecture that I delivered at University College London in May, 1984. Even though the notes below are hopelessly wordy, I have reproduced them almost word-for-word and almost entirely unedited. Furthermore, there are many things in these rough notes that I would say differently today or not at all. Nonetheless, it is possible that my original notes will be of interest to someone. But, bear in mind, that the notes below were extraordinarily rough -- even by the rough standards I used in 1984. Thank you.

But to return to my theme. In examining the details of the theory of logical relevancy, I had the nagging suspicion that there was something wrong with [Morgan's account of] the way in which [a person such as a trial judge or a trier of fact should] discount the force of evidence on the basis of the gener[a]lizations thought to be required to support [an] inference. That method of discounting was admirably simple.

In brief, [Morgan's recipe] told the trier to to estimate the probability of each supporting gener[a]lization and, to reach a final estimate about the probability of the fact in issue, to multiply all of the probabilities of all of the gener[a]lizations involved in the chain of inferences that happen to be involved in the inference about the final fact in issue. From one point of view, this seemed to make eminent sense. If, for example, evidence that defendant frequently carries a knife is offered to prove that defendant killed a person with a knife on a particular occasion, it might be said that 3 gener[a]lizations are required to support the proposed inference: (1) people who carry knives often intend to use them aga[i]nst other persons (under certain circumstances) and (2) people who intend to use knives against other persons often do use knives against other persons (under circ's) and (3)people who use knives against other persons (often) kill other persons. If this sequence of gener[a]lizations accurately describes the chain of inferences involved in the assessment of the probative force of the evidence of the knife on the question of killing (and it surely does not), Morgan instructs us that, to compute the force of the evidence, the trier must discount the probative force of the evidence by the uncertainty present in each gener[a]lization in each link of the chain of inferences. Thus, for example, if only 30% of persons carrying knives contemplate or intend using them against other persons, and if only 20% of the persons having this intent do use them against other persons, and if 40% of the persons using those knives in this way kill the other person, then the probability of of a killing, on the basis of the evidence of the knife, is only 30% x 20% x 40%, viz., [.024 or 2.4%].

It was apparent to me and it must be apparent to you that Morgan's picture of a chain of inferences presents many puzzles. Thus, for example, how does one know for sure how many links there are in the chain? (The number of links and their character clearly can have a decisive impact on the outcome of the trier's computations.) Also, for example, why did Morgan not speak about ... converging chains of evidence and their evaluation? (Perhaps because Morgan thought he was talking only about relevancy or, at least, only about the admissibility of separate pieces of evidence.) However, questions of this sort, while very important, were overshadowed by my nagging suspicion that Morgan's account [of] inferential chains was caught in some sort of a paradox. Using [Morgan's] scheme, it seemed to me that the same piece of evidence might simultaneously be considered as evidence favorable to a proposed inference (e.g., killing) and as unfavorable to the proposed inference. Thus, by a reasoning process I cannot fully re[c]ount [here, in London, today], I became convinced that the question is not, for example, how often people who frequently carry knives intend to attack other people but how much more likely [it is that] such people [people who carry knives]... attack other people than do people who do not habitually carry knives. To use a comfortable example, something is amiss with Morgan's analysis if the evidence is escape from jail and the issue is the guilt of the [escaping] defendant. If one believes the gener[a]lization that 10% of those who escape from jail are guilty and if one believes that no other links of inference are involved, then the evidence of defendant's escape establishes that the probability of defendant's guilt is 10% when the evidence of escape is considered by itself. But this is all wrong. After all, if it turns out that we believe that the greater the number of the people who escape from jail are innocent, the evidence not only does not favorably affect the [probability] of guilt but in fact decreases it. But if one uses Morgan's analysis, the evidence of escape is relevant and is admissible to show guilt. The paradox ... is that the same evidence is also favorably relevant to the [hypothesis] of non-guilt. Something is quite wrong here.

To make a long story very short, as a result of ruminations such as these, I became convinced that Morgan and ... similar writers had a vastly oversimplified theory of probability that could lead to very strange conclusions indeed. I sensed that Morgan was employing the product rule and that there was something wrong with the use of the product rule here. &&&