53 (2016) 28 journal for constitutional theory and philosophy of law revus (2016) 28, 53–61 Juan Pablo Alonso* The logical structure of principles in Alexy’s theory A critical analysis This paper offers a critical analysis of the logical structure of principles proposed by Robert Alexy and, in particular, of their structure as optimisation commands. Its first part opens the question whether the optimisation element in the logical structure should be understood as part of modalisation, as part of the consequent, or as an independent element. In the second part, the author analyses possible forms of inter-definability of deontic operators. Finally, some questions are raised on the conditional structure pro- posed by Alexy for principles. Keywords: logic of principles, deontic modalisations, inter-definability, conditional norms 1 IntroductIon In this work, I intend to analyse the logical structure of principles proposed by Robert Alexy, in particular their structure as optimisation commands. In a paper on ideal ought published in German and Spanish, Alexy describes his proposal on the logical structure of principles as derived from the logical structure of norms.1 Alexy starts from what could today be labelled a standard logic of norms (that which accepts the classic deontic modalities of obligation – including “duty” or “command” – prohibition and permission).2 In Alexy’s view, rules express real or definitive commands. Principles, on the other hand, express ideal or prima facie requirements, or “pro tanto mandates”: the com- mand of principles applies once other opposed considerations are discarded.3 As to the logical structure of principles, Alexy presents it as a derivation of the deontic modality “Obligatory”, to which he adds one aspect: optimisation. While a rule of obligation imposes a plain and simple duty to do p (“Op”), a principle, according to Alexy, imposes the obligation to optimise p (“O Opt p”). *  jalonso@derecho.uba.ar | Professor of legal philosophy at the University of Buenos Aires. 1 Alexy 2010. 2 Alexy 2010: 42. A description of this standard logic of norms may be found in Echave, Urquijo and Guibourg 1995: 119 ff. 3 Alexy 2010: 43. 54 (2016) 28 journal for constitutional theory and philosophy of law Juan Pablo Alonso For Alexy, in this logical structure, p “would be an empirical object of optimisa- tion, that is, not a normative one”.4 Alexy holds that, alternatively, an optimisation mandate can be reconstruct- ed so that the object to be optimised is not empirical but normative. The struc- ture, in this case, would be “O Opt Op”. Following the author’s line of reasoning, this formulation is the counterpart of the “ideal obligation” (“Oip”). Between these two formulations, there is a relation of mutual implication in so far as “op- timisation commands and the ideal obligation are two sides of the same thing”:5 (1) O Opt Op ↔ Oip By contrast, between the first formulation and the ideal obligation there is a relation of simple implication, because the existence of an optimisation com- mand is a sufficient condition for the existence of an ideal obligation:6 (2) O Opt p → Oip Given the mutual implication of the formula “O Opt Op ↔ Oip”, the follow- ing implication is also valid for Alexy: (3) O Opt p → O Opt Op [by hypothetical syllogism in (2) and (1)] This Alexyan logic of principles is complemented by predicate logic and quantifiers.7 Accordingly, the complete logical structure of principles for Alexy derives from the logical structure of conditional norms, with the addition of “Opt” to the consequent, and hence the following ideal deontic modalities are obtained: “ideal obligation” (Oip), “ideal permission” (Pip) and “ideal prohibi- tion” (¬Pip). Let us examine two examples proposed by Alexy for this structure. (4) (x) (T1 x → Pi Rx) For every x, if x is an expression of an opinion (T1), then (→) it is prima facie permitted (Pi) to do x (R).8 (5) (x) (T2 x → ¬Pi Rx) For every x (x), whenever x is a restriction on the right to personal- ity (T2), then (→) it is not permitted (Pi) to do x (R).9 4 Alexy 2010: 45. 5 Alexy 2010: 47. 6 Alexy 2010: 55 7 Alexy (1989: 214 ff) already used this combination (standard deontic modalisations, predica- te logic, and quantifiers). 8 Alexy 2010: 50. 9 Alexy 2010: 50-51. 55The logical structure of principles in Alexy’s theory (2016) 28 journal for constitutional theory and philosophy of law I aim to probe Alexy’s proposal, in particular the logical functions attributed to “Opt” within the general logical structure. Specifically, I intend to analyse whether “Opt” should be understood (i) as part of modalisation, (ii) as part of the consequent, or (iii) as an independent element. The criticisms laid at the el- ement “Opt” will refer to the most basic formula “O Opt p”, although they could also be applied to the more complex formula “O Opt Op”. Likewise, I shall question the way in which the notions of ideal permission (Pip) and ideal prohibition (¬Pip) can be derived from the basic form “O Opt p”. Finally, some questions are raised on the conditional structure proposed by Alexy for principles. 2 on the logIcAl functIon of “opt” I shall initially analyse the following three possible hypotheses: 1) “Opt” is an independent element; 2) “Opt” is part of a modalised action (or state of af- fairs); 3) “Opt” is part of a deontic modaliser. Hypothesis 1 Hypothesis 2 Hypothesis 3 O Opt p ¬O Opt p O ¬Opt p ¬O ¬Opt p O Opt ¬p ¬O Opt ¬p O ¬Opt ¬p ¬O ¬Opt ¬p O Opt p ¬O Opt p O ¬Opt p ¬O ¬Opt p . . . . O Opt p ¬O Opt p . . O Opt ¬p ¬O Opt ¬p . . Although Alexy does not accept expressly any of the said hypotheses, it seems that, since he accepts the implication “O Opt p → O Opt Op”, hypothesis 3 would be correct. This is so because Alexy states that his logic of principles de- rives from deontic logic, and some models of deontic logic do accept the theo- rem “Op → O Op”.10 Therefore, in this case it seems that Alexy holds that “Opt” is part of deontic modalisation, because, otherwise, the theorem would be “O Opt p → O O Opt p” if “Opt” was part of a modalised action or state of affairs, and Alexy does not hold this theorem to be valid. From a different, very intuitive point of view, it seems that hypothesis 2 is correct, given that optimisation (“Opt”) is an action that, much like any other action, could be subject to modalisation (normativisation). 10 For instance, the S4 deontic system proposed by Navarro and Rodríguez 2014: 31. 56 (2016) 28 journal for constitutional theory and philosophy of law Juan Pablo Alonso However, this reasoning would also imply the viability of hypothesis 1, be- cause both actions (optimisation and p) could be combined both with their ac- tion and with their omission, i.e., we could have a norm (specifically, a princi- ple) making the optimisation of the welfare of less favoured citizens obligatory (Opt p), another principle could make not optimising the welfare of wealthy citizens obligatory (¬Opt p), while a third one could make the optimisation of the non-welfare of those who have breached the most important rules of life in society obligatory (Opt ¬p). Option 1 entails the consequence that there would be no longer four,11 but eight basic normativisation forms. This does not seem to be Alexy’s view, since he proposes three ideal forms – ideal obligation (Oip), ideal prohibition (¬Pip), and ideal permission (Pip) – and it can safely be as- sumed that Alexy would accept the fourth: ideal permission to omit (Pi¬p). Based on these considerations, my first concern about the logical function of the element “Opt” is the following: it is not clear which is Alexy’s conception of this element, because it could be considered to be part of deontic modalisation, part of an action modalised, or to be an independent element. 3 the rules of trAnsformAtIon And Inference of the logIc of prIncIples Alexy notes that his logic of principles is part of deontic logic. One of the features of the latter is the existence of four basic modalisations, which are mu- tually inter-definable using the deontic operators obligatory (O), permitted (P) and prohibited (V):12 Obligatory p: Op ≡ ¬P¬p ≡ V¬p Prohibited p: O¬p ≡ ¬Pp ≡ Vp Permitted p: ¬O¬p ≡ Pp ≡ ¬Vp Permitted ¬p: ¬Op ≡ P¬p ≡ ¬V¬p Alexy shows how to pass from simple obligation to p (Op) to the obligation to optimise p (O Opt p), from there to the ideal obligation by implication (Oip), and from there to the obligation to optimise the norm “Op” (O Opt Op) by mu- tual implication (bi-conditional). 11 The four basic forms of normativisation are obligation (Op), prohibition (Vp ≡ O¬p), permis- sion to do (Pp ≡ ¬O¬p), and permission to omit (P¬p ≡ ¬Op). For further details, refer to section 3 below. 12 Echave, Urquijo and Guibourg 1995: 123. 57The logical structure of principles in Alexy’s theory (2016) 28 journal for constitutional theory and philosophy of law He also uses the notions of ideal permission (Pip is his notation) and ideal prohibition (¬Pip in his notation). He does not explain, however, either how this inter-definability between these ideal deontic modalisers works, or how to pass from the simple logical forms of deontic logic to ideal permission or ideal prohibition. To determine how inter-definability works, it is necessary to first provide an answer to the question posed above, because if optimisation “Opt” is an in- dependent element of the modaliser and of the modalised action (hypothesis 1 of section 2 above), then we would no longer have four basic forms, but eight – unless any (or some) of the eight forms should be eliminated under any given criterion. Nevertheless, regardless of which hypothesis in the previous section is cho- sen, there would still be doubt as to the sequence (rules of transformation and inference) to be followed so as to reach ideal permission and ideal prohibition. There are several options, and they are as follows: Option A | Keeping the above hypothesis 3 and following the inter-defina- bility rules of deontic logic: O Opt p → Oip (ideal obligation to p) O Opt ¬p → Vip (ideal prohibition to p) ¬O Opt p → Pi¬p (ideal permission to not p) ¬O Opt ¬p → Pip (ideal permission to p) Option B | Using the above hypothesis 2 and following the inter-definability rules of deontic logic: O Opt p → Oip (ideal obligation to p) O ¬Opt p → Vip (ideal prohibition to p) ¬O Opt p → Pi¬p (ideal permission to not p) ¬O ¬Opt p → Pip (ideal permission to p) It is clear that choosing either of the two options affects neither the ideal obligation or duty nor the ideal permission to omit (they remain equivalent). Albeit, in both options the content of ideal prohibition and ideal permission changes substantially. Indeed, as far as ideal prohibition is concerned, option a) establishes something such as “it is obligatory to optimise the non-welfare of those who committed murder”, while option b) establishes something such as “it is obligatory not to optimise the welfare of wealthy citizens”. As far as ideal permission is concerned, the results are similar. 58 (2016) 28 journal for constitutional theory and philosophy of law Juan Pablo Alonso Other options could also be proposed. For example: Option C | Using the Alexyan notion of normative (not factual) optimisa- tion and creating new inter-definability rules:13 O Opt Op ↔ Oip (ideal obligation to p) O Opt Vp ↔ Vip (ideal prohibition to p) O Opt P¬p ↔ Pi¬p (ideal permission to not p) O Opt Pp ↔ Pip (ideal permission to p) Indeed, more options are possible, although I understand that it is senseless to keep exploring this path. Based on the said considerations, my second question is: how does Alexy move the inter-definability of deontic logic to the logic of principles? More spe- cifically, which are the transformation and inference rules to pass from the pro- hibition to p (O¬p) to the ideal prohibition to p (¬Pip), and from the permis- sion to p (¬O¬p) to the ideal permission to p (Pip)? 4 the condItIonAl structure of prIncIples Many legal philosophers (e.g., Alexy, Atienza and Ruiz Manero, or Alchourrón and Bulygin)14 hold that the logical structure of principles is to a certain extent analogous to the logical structure of conditional norms. Other scholars claim that the logical structure of principles should be reconstructed with the schemes of preference logic15 or other semantic structures, but their view is not the majority view. Those who hold that there is a structural analogy between principles and conditional norms usually also claim that principles are a “weakened” version of norms. In this regard, there are three possible options: (i) weakening the an- tecedent, (ii) weakening the consequent, and (iii) weakening the connective be- tween them. Atienza and Ruiz Manero exemplify option (i), Alexy option (ii), and Alchourrón options (iii) and (i). Atienza and Ruiz Manero16 propose an elegant scheme to separate the dif- ferent types of principles and rules: 13 This option has been suggested by Hugo Zuleta. 14 See Alchourrón and Bulygin 2012: 118 ff. 15 See Navarro and Rodriguez 2014 and Alonso 2013. 16 Atienza and Ruiz Manero 1996. 59The logical structure of principles in Alexy’s theory (2016) 28 journal for constitutional theory and philosophy of law Antecedent (case) Consequent (solution) Rules action rules end rules closed closed closed open Principles strict sense directives open open closed open As is obvious, for Atienza and Ruiz Manero the central feature of the genus “principles” is that the case is open, that is, subject to further precision. This is what differentiates the genus “principles” from the genus “rules” (whose ante- cedent or case is closed). Clearly, the two Spanish authors choose to weaken the antecedent of the conditional, maintaining at the same time that for principles in the strict sense the solution is closed. Once the case is defined or specified, the solution is of the “Op” or “¬Pp” type, that is, a logical formula of standard, non-modified deontic logic.17 We shall see that Alexy’s proposal seems to be opposed to Atienza and Ruiz Manero’s, since for Alexy the case of principles in the strict sense is closed and the solution is open (or “weakened” or “prima facie”). Now, while Alchourrón does not state expressly his views on the structure of principles, his thesis on the defeasibility of norms is, in my opinion, applicable to the issues in hand.18 Alchourrón analyses different proposals to weaken the classic conditional connective (in any of its versions, such as material implications, generalised conditionals, etc.), replacing it with a connective that does not satisfy the law of strengthening the antecedent and modus ponens. For instance: (6) p > Oq According to Alchourrón’s analysis, the problem of weakening the connec- tive lies in the loss of inferential capacity. In other words, a connective that does not satisfy the strengthening of the antecedent and modus ponens is not useful to justify deductively any practical decision, i.e., a judicial sentence. Additionally, Alchourrón claims that those who use defeasible condi- tionals also hide the weakening of the antecedent in the common conditional. In other words, the use of defeasible conditionals mistakenly transfers to the connective a problem that in fact belongs to the antecedent of the conditional. 17 I should clarify that I do share some of the criticisms of Atienza and Ruiz Manero’s proposal mounted by Ratti 2013. I cannot, however, elaborate further on this matter in this work. 18 Alchourrón 1988. 60 (2016) 28 journal for constitutional theory and philosophy of law Juan Pablo Alonso Hence, Alchourrón proposes abandoning the use of defeasible conditionals (also called “prima facie conditionals”), keeping a strong connective (he pro- poses the generalised conditional “⇒”) that satisfies the strengthening of the antecedent and the deontic modus ponens, and adding a revision operator to the antecedent. The formula is as follows: (7) f(p) ⇒ Oq If p occurs, and no circumstances arise that may cause the revision of p (f(p)), then (strong conditional ⇒) it is obligatory to q (Oq). A revision is a function which affects the antecedent of the conditional, and which selects a certain subset of p cases (the most usual ones or those for which no exceptions have been verified). In my view, Alchourrón’s proposal is the best theory for the claim that there is a structural analogy between principles and conditional norms. In any event, the question of whether there is a best reconstruction of the logical structure of principles that draws no analogies with the logical structure of conditional norms (i.e., a structure as in preference logic) remains open. Alexy’s position seems to be opposite to that of Alchourrón, and of Atienza and Ruiz Manero. His paper on ideal ought (Alexy 2010) brings the following logical structure of principles: (x) (T1 x → Pi Rx) (x) (T2 x → ¬Pi Rx) As is evident, the connective used by Alexy is material implication (→), a connective that satisfies the strengthening of the antecedent and the deontic modus ponens. The antecedent, on the other hand, lacks revision functions or any other weakening mechanisms. Weakening, apparently, affects only the con- sequent. But the weakened consequent proposed by Alexy does not, in my view, solve the problems suggested in my above two objections. 5 conclusIons In my view, Alexy’s logical structure of principles is faced with the prob- lems I have outlined in the preceding paragraphs. First, the logical function of the “Opt” element is unclear; it could be considered to be part of deontic mo- dalisation, to be part of the action modalised, or to be an independent element. Second, it is unclear whether inter-definability governs deontic logic in Alexy’s 61The logical structure of principles in Alexy’s theory (2016) 28 journal for constitutional theory and philosophy of law principles. If so, what are the transformation rules and inference rules to pass from prohibition of p (O¬p) to ideal prohibition of p (¬Pip), and from permis- sion of p (¬O¬p) to ideal permission of p (Pip). Third, the logical structure that Alexy attributes to principles is the rejection of the position that weakens the antecedent of the conditional, the position which is, in my opinion, the strong- est and is held by those who claim that the structure of principles has saved the analogy with the structure of conditional rules. —Acknowledgments.— This article is the outcome of a research project which was car- ried out with Gabriela Scataglini, and funded by the School of Law of the University of Buenos Aires in the 2014-2016 biennium. DECyT 1403 “Implicit Legal Principles”. References Carlos ALCHOURRÓN, 1988: Condicionalidad y la representación de las normas jurídicas. In Carlos Alchourrón & Eugenio Bulygin, Análisis lógico y Derecho. Madrid: Centro de Estudios Constitucionales, 1991. 267-280. Carlos ALCHOURRÓN and Eugenio BULYGIN, 2012: Sistemas normativos. 2nd edition. Buenos Aires: Astrea. Robert ALEXY, 1989: Teoría de la argumentación jurídica. Spanish translation by Manuel Atienza and Isabel Espejo. Madrid: Centro de Estudios Constitucionales. Robert ALEXY, 2010: Deber Ideal. In Robert Alexy, La construcción de los Derechos Fundamentales. Spanish translation by Laura Clérico and Jan Sieckmann. Buenos Aires: Ad-Hoc, 2010. For the original, see Robert Alexy, Ideales Sollen. In Grundrechte, Prinzipien und Argumentation. Studien zur Rechtstheorie Robert Alexys. Eds. Clérico and Sieckmann. Baden-Baden: Ed. Nomos, 2009. Juan Pablo ALONSO, 2013: Principios implícitos y coherencia. DOXA. Cuadrenos de filosofía del de- recho (2013) 36. Manuel ATIENZA and Juan RUIZ MANERO, 1996: Las Piezas del Derecho. Barcelona: Ariel Derecho. Teresa ECHAVE, María Eugenia URQUIJO and Ricardo GUIBOURG, 1995: Lógica, proposición y norma. Buenos Aires: Astrea. Pablo NAVARRO and Jorge RODRÍGUEZ, 2014: Deontic Logic and Legal Systems. New York: Cambridge University Press. Giovanni Battista RATTI, 2013: Una nota sobre la forma lógica de los principios jurídicos. In Giovanni Battista Ratti, El gobierno de las nor- mas. Madrid: Marcial Pons.