Abstract
The purpose of this paper is to improve on the logical and measure-theoretic foundations for the notion of probability in the law of evidence, which were given in my contributions Åqvist [ (1990) Logical analysis of epistemic modality: an explication of the Bolding–Ekelöf degrees of evidential strength. In: Klami HT (ed) Rätt och Sanning (Law and Truth. A symposium on legal proof-theory in Uppsala May 1989). Iustus Förlag, Uppsala, pp 43–54; (1992) Towards a logical theory of legal evidence: semantic analysis of the Bolding–Ekelöf degrees of evidential strength. In: Martino AA (ed) Expert systems in law. Elsevier Science Publishers BV, Amsterdam, North-Holland, pp 67–86]. The present approach agrees with the one adopted in those contributions in taking its main task to be that of providing a semantic analysis, or explication, of the so called Bolding–Ekelöf degrees of evidential strength (“proof-strength”) as applied to the establishment of matters of fact in law-courts. However, it differs from the one advocated in our earlier work on the subject in explicitly appealing to what is known as “Pro-et-Contra Argumentation”, after the famous Norwegian philosopher Arne Naess. It tries to bring out the logical form of that interesting kind of reasoning, at least in the context of the law of evidence. The formal techniques used here will be seen to be largely inspired by the important work done by Patrick Suppes, notably Suppes [(1957) Introduction to logic. van Nostrand, Princeton and (1972) Finite equal-interval measurement structures. Theoria 38:45–63].
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Notes
We regret the plethora of misprints in Åqvist (1992), trusting, however, that the reader will be able to correct them successfully.
A crucial distinction current among jurists and legal theorists is the one between factum probandum (“the [farthest] theme of proof”, “ultimate fact”, “fact immediately relevant to the issue”) and factum probans (“evidentiary fact”, “indicium”, “fact mediately relevant to the issue”)—see e.g. Ekelöf (1964, p. 48 f., esp. n.4), (1983, p. 10 f.). In the paper we make very little use of this admittedly highly important distinction, our interest being primarily focussed on the technical set-theoretical development of the Bolding–Ekelöf doctrine of “degrees of evidential strength”. A proper place for applying the factum probandum—factum probans distinction would then be in an empirical test of our present explication of this doctrine—a test that cannot be undertaken here.
As was observed already in Åqvist (1992, § 5), the present clause of the Theorem as well as Definition 7.3 below profit from the fact that W is assumed to be finite throughout our discussion (see Definition 3.1 ff.), which means that we don’t have to worry about infinite sums and suchlike. But in this context we ought to keep in mind the following remark made in Suppes (1957, §12.4, p. 280):
Since probability distributions appear to be so much simpler to define than finitely additive probability spaces, it might be thought that they should be the basic entities discussed in this section. Fields of sets could be dispensed with entirely, and the probability of any set would be obtained by summing over the probabilities of its individual elements. Unfortunately this simplicity disappears when infinite sets are considered, and many problems arise.
Our reason for sticking to the assumption that W always be finite is not only the simplicity mentioned by Suppes, but also what I have elsewhere [Åqvist (2005, § 1)] called the fundamentally finitistic nature of legal reasoning, which is obviously at stake here.
For the notion of a representation and uniqueness theorem required here, see Suppes (1972, §3).
An anonymous referee pointed out that my present claim is not entirely convincing at least as far as the Second Principle of Preponderance is concerned. He/She observes that the fact that the principle is violated in some cases constructed according to my theory “seems to be unfortunate”. This pertinent observation is then taken to be an issue for future research and possible improvement, and I fully agree with it.
References
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Åqvist, L. An interpretation of probability in the law of evidence based on pro-et-contra argumentation. Artif Intell Law 15, 391–410 (2007). https://doi.org/10.1007/s10506-007-9048-y
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DOI: https://doi.org/10.1007/s10506-007-9048-y