Abstract
This chapter offers a concise and elementary introduction to fundamental concepts in deductive and deontic reasoning.
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- 1.
The reader is not required to have any advanced technical background. Some basic knowledge on general philosophy, elementary set theory and propositional logic can be useful but not necessary.
- 2.
More on the concept of argument in Walton, chapter 3, part I, this volume, on “Legal Reasoning and Argumentation.”
- 3.
Indeed, if there is an argument from \(P_1, \dots , P_n\) into \(C_1, \dots , C_m\), it is usually the case that there are arguments for each conclusion in \(C_1, \dots , C_m\) from \(P_1, \dots , P_n\), and vice versa.
- 4.
As usual, \(\varGamma , \varGamma '\) and \(\varGamma , A\) are abbreviations, respectively, for \(\varGamma \cup \varGamma '\) and \(\varGamma \cup \{ A \}\).
- 5.
Sartor, Chapter 3, Part II, this volume, on “Defeasibility in Law.”
- 6.
See the next section for more details.
- 7.
But compare the interesting counterarguments offered by Alchourron and Martino (1990).
- 8.
- 9.
This is somehow a simplification. More on permissions in Section 4.1.1.
- 10.
The example is due to Sartor 2005, p. 453.
- 11.
If one knew that the action or state of affairs was not only permitted but obligatory, one would use the latter qualification, according to the Gricean principle of quantity, which requires that we provide all the relevant information we have (see Grice 1989).
- 12.
In deontic logic, when it is said that any A is facultative, this is equivalent to saying that A is indifferent.
- 13.
We use the expression normative proposition to mean any possible legal content: a rule, a principle, the connection between a factor and the outcome it favours, and so on.
- 14.
This issue has been famously addressed by von Jhering (1924), III, 35, who distinguished the purpose of a duty (the interest it is intended to serve, according to the point of view of the legal system, or of the legal community) from its various side effects (reflex-effects, Reflexwirkungen). Jhering considers, for instance, the case of a law prohibiting the import of certain goods, which was enacted by politicians having the aim of favouring a particular domestic producer (who had lobbied for this result). He argues that the fact the individual lawmakers had this aim in mind does not imply that the law confers a right on that manufacturer: from a legal perspective the manufacturer’s advantage is rather to be viewed as a side effect of that law.
- 15.
- 16.
Notice that, as we have argued at the end of Sect. 3.3 in regard to facultativeness, also here a better way for representing directed obligations would need to extend the language with actions.
- 17.
This section elaborates on parts of (Grossi and Rotolo 2011).
- 18.
No crime without law, that is, everything that is not explicitly prohibited should be considered as permitted.
- 19.
The problem of whether norms bear or not truth values is an old one in philosophy and was put forth in modern times by (Jørgensen 1937). The significance of the problem has recently been reemphasised in (Hansen et al. 2007), and a new approach to the problem emerged from the view of norms as “dynamic” operators—speech acts—modifying ideality orders.
- 20.
A preorder can always be associated with a given Boolean algebra in the following way:
$$\begin{aligned} a \preceq b&{\mathrm{IFF}}\,&a \sqcap b = a. \end{aligned}$$(35) - 21.
As is well-known, the idea that legal effects do not follow from norms by logic but, rather, by stipulation was notably defended in legal theory by Kelsen (1991).
- 22.
An interesting contribution is, for instance, offered by Lindahl and Odelstad (2008).
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Rotolo, A., Sartor, G. (2018). Deductive and Deontic Reasoning. In: Bongiovanni, G., Postema, G., Rotolo, A., Sartor, G., Valentini, C., Walton, D. (eds) Handbook of Legal Reasoning and Argumentation. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9452-0_10
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