Abstracts
The present chapter is a small part of an effort to expose the logical structure of English criminal law. Our purpose here is to lay to rest some objections that might be raised against the project. A further aim is to show that, in particular cases, legal concepts actually respond well to logical analysis. We demonstrate this as regards the legal concept of proof beyond a reasonable doubt.
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Notes
- 1.
- 2.
A discipline’s identity is shaed by those methods of operation that are characteristic of it. Professional or administrative traits influence conditions of entry, issuance of qualifications and general management of the discipline’s infrastructure, including ways and means of the dissemination of results.
- 3.
The idea of disciplinary integrity is an ancient one. Aristotle refused admittance to “inappropriate” premisses, even if true. A statement is inappropriate in an argument when it belongs to a discipline different from the one represented by the argument’s conclusion. See On Sophistical Refutations 172a8 and Physics 223a 217–15, 263a4 -264a6.
- 4.
To mention just one example, informal logic has produced a vigorous research-programme in the past thirty-five years or so, but one could count on the fingers of one hand (with room left over) leading representatives of the mathematical mainstream who have paid it the slightest heed.
- 5.
A notable dissident is Jerry Fodor, for whom the name of cognitive science is an oxymoron. ([Fodor, 2000])
- 6.
As witness the displacement of astrology by astronomy and of alchemy by chemistry.
- 7.
Notwithstanding the widely held belief that all of biology is reducible to chemistry.
- 8.
An analytic discipline was thought to be one all of whose truths are so solely in virtue of the meanings of their contained terms. On the other hand, a synthetic ( priori discipline was taken to be one whose truths while not analytic (hence synthetic) are nevertheless knowable independently of sensory experience. Kant’s logic is examined in Tiles (2004).
- 9.
Transfinite arithmetic studies actual, rather than potential, infinities, conceived of as quite definite cardinal or ordinal numbers
- 10.
- 11.
The principle reason that one of the host disciplines – set theory – was shown to be inconsistent, and subsequent attempts to produce a consistent rehabilitation of sets were not credibly analytic.
- 12.
A more detailed treatment of the mathematicization of logic may be found in Gabbay and Woods (2004a).
- 13.
Hart and Honorϑ’s Causation in the Law also imported into legal studies, via the concepts of “family resemblance” and “open texture”, a rejection of essential definitions, occasioned by developments in ordinary language philosophy (Hart and Honorϑ, 1959). See also the entry on “indeterminacy” in Bix (2004, pp. 97–98).
- 14.
Its present-day form derives from Peirce (1955).
- 15.
All, in some versions.
- 16.
Defeasibility is a notion introduced to the philosophy of law by Hart HLA (1907–1992) in his lectures on Moral and Legal Reasoning in New College, Oxford in the academic year 1951–2.
- 17.
Bertrand Russell (1872–1970) was also a notable proponent of logicism. As it happens, however, Russell had a different understanding of this doctrine from Frege’s. While interesting, and important for the philosophy of mathematics, this is a point that need not occupy us here.
- 18.
- 19.
See also Bix (2004, pp. 77–78).
- 20.
See also Bix (2004, p. 50).
- 21.
See also Bix (2004, 26–27).
- 22.
In some accounts, ever.
- 23.
In some accounts, without the possibility of recovering their justifications.
- 24.
Something of an understatement, in the wake of the Columbia disaster.
- 25.
Reasoning is ampliative when its conclusions contain information not present in the premisses.
- 26.
Perhaps as further attestation to the law’s fondness for the tacit, only one of these nine shared concepts (viz., “precedent”; see also the entry on “analogy”) has an entry in Brian Bix’s A Dictionary of Legal Theory (Bix, 2004). True, one of the aims of that little book is to help adjust its readers to theoretical concepts imported from disciplines other than the law. Even so, these are striking omissions in any work carrying such a title. We might observe in passing that whereas Bix (2004) contains an entry on “rationality” (to which “reasonableness” is merely cross-referenced), it has nothing to do with the legal notions of the reasonable man and of reasonable doubt.
- 27.
“Aleatory” derives from the Greek word for game.
- 28.
Bayesianism is named after Thomas Bayes (1702–1761), discoverer of the famous probability theorem that bears his name. There exists some scholarly disagreement as to how much of a Bayesian Bayes himself actually was. This is a question that need not detain us here.
- 29.
As with the statement that Philip Mountbatten is the First Lady of Great Britain.
- 30.
As with the claim made by some opponents of same-sex marriage that if the argument for same-sex marriage is sound, so too is an analogue of that argument on behalf of polygamy.
- 31.
In actual practice, courts are allowed “a great deal of freedom to ‘distinguish’ prior decisions as not being truly on point for an issue currently before the court.” (Bix, 2004, p. 163).
- 32.
In the Port Royal approach, the fallacy in question is one of deferring not to the merits of the case but rather to the rank or social status of one of the parties. The principal authors of the Port Royal Logique were Antoine Arnauld (1612–1694) and Pierre Nicole (1625–1695), although some scholars conjecture that Pascal contributed the sections on probability.
- 33.
As we show in Gabbay and Woods (2005) inference to the best explanation is just one form of Abductive reasoning, albeit it a common one. Even so, it seems the right form of it for reasoning to a verdict in criminal trials.
- 34.
Of course, over the decades quantum mechanics has acquired truly impressive levels of empirical confirmation. But at the time of its original conjecture there was nothing whatever in the physics of the day that lent it the slightest degree of confirmation. Here again we see the diachronic character of enquiry. What begins as an abduction may end up as a confirmed fact.
- 35.
“Epistemic” derives from a Greek word for knowledge.
- 36.
“Doxastic” derives from a Greek word for belief.
- 37.
In classical approaches to truth, any proposition that is alethically subpar is false. In many-valued approaches, an alethically subpar proposition has a less truth-like value than the proposition to which it is subpar. In truth-approximation approaches, one proposition is alethically subpar to a second when the former is less approximately true than the latter.
- 38.
This may appear to generate a very bad problem for criminal jurisprudence. If the standard in criminal trials is proof beyond a reasonable doubt, how can it be envisaged that an abductive conjecture, however confidently made, could rise to it? See Part IV below.
- 39.
- 40.
This proceeds not only from the abductive character of verdicts but also from the admissibility of testimony.
- 41.
For helpful criticisms and suggestions we thank Atocha Aliseda, S. Bradley Armstrong, Q.C., David Atkinson, Peter Bruza, Balakrishnan Chandrasekaran, Jonathan Cohen , Eveline Feteris, Martin Friedland, Q.C., Gilbert Harman , Jaakko Hintikka, Andrew Irvine , Erik Krabbe , Theo Kuipers, Neil MacCormick, Lorenzo Magnani, Sami Paavola, Jeanne Peijnenburg, Henry Prakken, Menno Rol, J.Roland M, Q.C., Cameron Shelley, Steve Uglow [DOV, PLEASE PUT IN THE OTHER UK LAWYERS ALPHABETICALLY], Johan van Benthem , Alexander van den Bosch, Jan Albert van Laar , Stephen Wexler and C.L. Woods, Research was supported by the Engineering and Physical Sciences Research Council of the United Kingdom, the Social Science and Humanities Research Council of Canada, Professor Nancy Gallini, Dean of Arts, University of British Columbia, Professor Christopher Nicol, Dean of Arts and Science, University of Lethbridge, and Professor [DOV PUT IN HEAD OF SCHOOL AT KINGS] We are most grateful for this assistance. For indispensable technical support we are also greatly indebted to Carol Woods in Vancouver and Jane Spurr in London.
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Gabbay, D.M., Woods, J. (2010). Logic and the Law: Crossing the Lines of Discipline. In: Gabbay, D., Canivez, P., Rahman, S., Thiercelin, A. (eds) Approaches to Legal Rationality. Logic, Epistemology, and the Unity of Science, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9588-6_9
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