A Social Pragmatic View on the Concept of Normative Consistency

Transcription

1 A Social Pragmatic View on the Concept of Normative Consistency Berislav Žarnić Faculty of Humanities and Social Sciences, University of Split A Workshop on Deontic Logic Angelo Sraffa Department of Legal Studies Università Commerciale Luigi Bocconi in collaboration with Thémis Centre d Etudes de Philosophie du droit, de Sociologie du droit et de Théorie du droit Milano, 12th February 2016

2 Overview 1 Von Wright s shift towards logical pragmatics 2 Translations: perfection properties and second-order norms 3 Diverse obligations and inconsistency

3 Deontic logic as modal logic Philosopher s recollection One day when I was walking along the banks of the River Cam I was at that time living in Cambridge (England) I was struck by the thought that the modal attributes possible, impossible and necessary are mutually related to one another in the same way as the quantifiers some, no and all. I soon found that the formal analogy between quantifiers and modal concepts extended beyond the patterns of interdefinability...i had made another accidental observation this time in the course of a discussion with friends namely that the normative notions of permission, prohibition, and obligation seemed to conform to the same pattern of mutual relatedness as quantifiers and basic modalities. Georg Henrik von Wright. Deontic logic: a personal view. (1999). Ratio Juris 12: Figure : Ludwig Wittgenstein and Georg Henrik von Wright (Photograph from April 1950.; taken in von Wright s garden while Wittgenstein was a guest at his house.)

4 Von Wright s Programmatic Statement Deontic logic as the study of rationality conditions in norm-giving activity Deontic logic, one could also say, is neither a logic of norms nor a logic of norm-propositions but a study of conditions which must be satisfied in rational norm-giving activity. It is strict logic because the conditions which it lays down are derived from logical relations between states in the ideal worlds which normative codes envisage. Georg Henrik von Wright (1993). A Pilgrim s Progress. In von Wright, G.H. The Tree of Knowledge and Other Essays, Leiden: Brill. Figure : Georg Henrik von Wright (June 14, 1916, Helsinki June 16, 2003, Helsinki) Photograph shows the River Cam in the background.

5 The turn towards logical pragmatics Here it will be proposed a semi-formal way of understanding and extending von Wright programmatic statement. standard deontic logic axiom set-theoretic approach property of a norm-set second-order norms obligation of the norm-giver g or norm-recipient r an example (D) Oφ Pφ Cn(N ) O 2 g(o r φ P r φ) The here proposed extension of the programmatic statement will include normative reasoning as another type of norm-related activity besides norm-giving activity. The here proposed application of the programmatic statement will discuss the second-order norms covering the norm-giver and the norm-recipient s relation to an inconsistent normative system.

6 Social Pragmatics of Deontic Logic The reasons why the term social pragmatics will be used are, inter alia, the following: the term pragmatics indicates the study of language-use: the norm-giver uses the language in building of a normative system, the norm-recipient uses a language-formulated (normative) system as the basis of her/his normative reasoning; the term social indicates that more than one language-user (or social role) is taken into account: the (role of) norm-giver, the (role of) norm-recipient. Social pragmatics of deontic logic studies the norms that apply to norm-related activities of social actor roles. These norms can be properly called second-order norms since they cover the activities that are related to a normative-system.

7 Connecting the two languages of deontic logic A simple formal explication for von Wright s programmatic statement can be obtained using the set-theoretic approach proposed by many philosophical logicians (e.g., Carlos Alchourrón and Eugenio Bulygin, or, more recently, John Broome), according to which the existence of an obligation-norm within a normative system is represented by the membership of its propositional content in the set that represents the normative system in question. In the set theoretic approach the basic idea is to represent the norm by the membership relation between its content φ and norm-set N : the expression it is obligatory that φ is explicated as φ N.

8 On set-theoretic approach This highly reduced model can be made more realistic by adding variables, such as those for the source, addressee and situation and taking as elementary the expression by the source s it is obligatory in the situation w upon actor i that φ. E.g., following Broome N would be treated as a three-place function which delivers norm-contents (requirements), N (s, i, w) L. The major point of divergence within the set-theoretic approach lies in the properties one is willing to assign to norm-sets. It is in accord with the approach proposed by von Wright to treat norm-sets as simple sets consisting just of sentences that correspond to contents of explicitly promulgated norms and to lay the question of their logical properties aside. In the approach proposed here it is not assumed that a norm-set is deductively closed (as Carlos Alchourrón and Eugenio Bulygin do), or closed under equivalence (as Broome does). The norm-set, as understood here, is just a set and the question of its desirable properties is solved by second-order norms addressed to different actor roles.

9 The translation function The basic idea has already been given and it can be easily extended to other deontic modalities if their interdefinability is presupposed. standard deontic logic Oφ Fφ Pφ Definition (More formally...) set-theoretic approach φ N φ N φ N Let L pl be the language of propositional logic. Function τ 1 translates formulas with first-order deontic modalities: τ 1 (φ) = φ if φ L pl τ 1 (Oφ) = φ N τ 1 (Fφ) = φ N τ 1 (Pφ) = φ N τ 1 ( φ) = τ 1 (φ) τ 1 ((φ ψ)) = (τ 1 (φ) τ 1 (ψ))

10 Reading postulates of deontic logic in terms of norm-set properties Examples (D) axiom, Oφ O φ, characterizes consistent norm-sets as shown by the translation: τ 1 (Oφ O φ) = φ N φ N adjunction axiom, (Oφ Oψ) O(φ ψ) characterizes norm-sets closed under conjunction as shown by the translation: τ 1 ((Oφ Oψ) O(φ ψ)) = ( φ N ψ N ) φ ψ N Comment. It may be thought that both consistency and closure under conjunction are desirable properties, i.e., the properties that any norm-set ought to have, but their desirability is relative to the actor s role. From the perspective of the norm-giver consistency is a property that ought to be achieved in the norm-giving activity, but closure under conjunction is not since it would involve an infinite sequence of communicative acts of adding still another conjunction for any pair of sentences already achieved in the process. From the perspective of the norm-recipient consistency of a norm-set is not a property that the norm-recipient ought to achieve in her/his normative reasoning since she/he ought to reason on the basis of the norm-set no matter whether it is consistent or not. On the other hand, closure under conjunction is the property related to the norm-recipient s reasoning since she/he ought to arrive at the minimal (non-redundant) conjunctive conclusion of her/his obligations.

11 Examples (K) axiom, O(φ ψ) (Oφ Oψ), in the presence of the necessitation rule characterizes deductively closed norm-sets as shown by the translation: τ 1 (O(φ ψ) (Oφ Oψ)) = φ ψ N ( φ N φ N ). 1 Extending the line of thought to the Roman Law principle (ultra posse nemo obligatur, impossibilium nulla obligatio) and introducing the operator Can r for doability or the recipient s ability to see to it that so-and-so is the case, Oφ Can r φ, it is clear that the priciple characterizes doable norm-sets as shown by the translation: τ 1 (Oφ Can r φ) = φ N Can r φ Comment. It is obligatory for the norm-recipient to draw deductive consequences of explicitly stated norms and not obligatory for the norm-giver to proclaim them. So, only from the norm-recipient perspective the deductive closure of N is its perfection property, i.e., she or he ought to relate to the deductively closed set, and not only to its deductive core. On the other hand, the Roman Law principle seems to allow for both interpretations: it is clear that the norm-giver ought to achieve a doable norm-set, but is disputable whether the norm-recipient is licensed to conclude that a norm is not binding if its content is not doable. 1 Alternatively, the rule if φ entails ψ, then Oφ Oψ vs. the property of closure under entailment.

12 Obligation-norms and permission norms Non-derivative character of permission Just as possibility is the negation of the necessity of the contradictory of a proposition, permission is the negation of the obligatoriness of the contradictory. Pp O p is a theorem of classical deontic logic. I think that this opinion is mistaken. The relation between permission and absence of prohibition is not a conceptual but a normative relation. One may be able to give good reasons why such things which are not prohibited by the norms of a certain code should be regarded as permitted by the code in question. But to declare the non-prohibited permitted is a normative act. One could have a meta-norm to the effect that the not-prohibited is permitted. The well-known principles Nulla poena sine lege and Nullum crimen sine lege may be thought of as versions of this meta-norm. Or at least as closely related to it. Georg Henrik von Wright (1991). Is There a Logic of Norms? Ratio Juris 4:

13 Permission If permission is not the absence of prohibition, what is it? Several answers have been discussed in the literature. An incomplete list follows with an additional proposal at the end. To give a permission is to remove an antecedently existing prohibition. Giving permission to an actor to see to it that something is the case means prohibiting any other actor to prevent her/him from doing so. To give a permission means to declare that something is optional. To give a permission for φ means to simultaneously introduce two permission-norms: Pφ and P φ. 2 Here the disputes on the meaning/s of permission will be set aside, and so it will be taken in the weakest non-derivative sense. In order to capture the concept of permission in non-derivative sense, the counter-set, N will be introduced in the model. 2 If the norm-giver proclaims Pφ, then her/his intending and not proclaiming Oφ would violate Gricean maxim of quantity, while the norm-recipient would be justified by the logic of cooperative communication to conclude that Oφ and therefore P φ.

14 Two-sets model Within the two-sets model the scope of perfection properties becomes wider. Besides perfection properties of individual sets, there are also perfection properties of the relation between them. Gaplessness is one these. Let L be the language in which the norm-system is expressed. Norm-system N, N is gapless iff N N = L. The operation corresponding to the introduction of permission-norm Pφ is the addition of φ to N, and for P φ is the addition of φ to N. Considering the case of Pφ, the reason for this is that φ is not in N if Pφ, and, since the system is gapless, φ must be put into N. So, there are two correspondences in a gapless system: 1. Oφ corresponds to φ N, and 2. Pφ corresponds to φ N. The same, mutatis mutandis, holds for the case of P φ.

15 Two types of inconsistency Relational (or external) inconsistency occurs if N N. An example: Pφ O φ is given in the picture below. Inner inconsistency occurs if {ψ, ψ} N for some ψ. An example: Oψ O ψ is given in the picture below. ψ ψ φ Norm-setA N Counter-set B N Figure : An example depicting a gapless but a doubly inconsistent normative system. It is externally inconsistent since the intersection is non-empty, and internally inconsistent since the norm-set contains a pair of contradictory sentences.

16 Relational perfections Let us assume that norm-system N, N actually has relational perfections that it ought to have: that it is gapless, N N = L, that it is externally consistent, N N =. The picture below depicts a norm-system having the two relational perfections. Norm-setA N Counter-set B N Figure : An example depicting a gapless and externally consistent system.

17 Extending the translation function If the two relational perfections present, translation function τ 1 will give descriptions of properties of the counter-set that correspond to deontic postulates. Definition Let L pl be the language of propositional logic. Function τ 1 translates formulas with first-order deontic modalities: τ 1 (φ) = φ τ 1 (Oφ) = φ N τ 1 (Fφ) = φ N τ 1 (Pφ) = φ N τ 1 (P φ) = φ N τ 1 ( φ) = τ 1 (φ) if φ L pl τ 1 ((φ ψ)) = (τ 1 (φ) τ 1 (ψ))

18 Reading postulates of deontic logic in terms of norm-set properties Examples (D) axiom, Oφ O φ, characterizes complete counter-sets as shown by the translation: τ 1 (Oφ O φ) = φ N φ N, adjunction axiom, (Oφ Oψ) O(φ ψ) characterizes counter-sets having at least one conjunct for any conjunction they contain as shown by the translation: τ 1 ((Oφ Oψ) O(φ ψ)) = φ ψ N ( φ N ψ N )

19 Correspondence of set properties in a gapless and externally consistent norm-system postulate of standard deontic logic norm-set property counter-set property (D) Oφ Pφ consistency completeness (2) (Oφ Oψ) O(φ ψ) (K) axiom together with necessitation rule closure under conjunction deductive closure having at least one conjunct for each conjunction contained closure under implicant (if φ entails ψ and ψ N, then φ N )

20 Social pragmatics of inconsistency Second-order norms with respect to an inconsistent system content revision norm-giver ought to revise the norm-system inconsistent norm-system logic revision norm-recipient ought to change the logic of normative reasoning Second-order norms, understood in prescriptive sense, also cover the relation towards an inconsistent normative system. The norm-giver ought to restore consistency by the revision of its content (by derogations, modifications,...). The norm-recipient ought to continue to reason on the basis of it, but it obviously cannot be done on the basis of classical logic where the principle ex contradictione quodlibet holds. Therefore, in absence of other remedies, the second-order norm for the recipient s dealing with an inconsistent system requires the shift to a inconsistency-tolerant logic. In other words, the norm-giver should revise the content and the norm-recipient should revise the logic of an inconsistent system.

21 Two types of revision The normative relation is different for each actor-role: the norm-giver ought to change the content of the norm-system so to remove inconsistency, the norm-recipient ought to change the logic of the reasoning based on the inconsistent norm-system. These second-order dynamic norms show the need of a notion of revision more general than that of AGM-revision. The generalized notion of revision must be wide enough to encompass the case where revision includes no contraction but, instead, takes the form of the change of logic. Since a presence of contradiction in a set of sentences need not imply the absurdity of its use in reasoning the two imperfections should be distinguished: the inconsistency, either internal {ψ, ψ} N or external N N, and the self-destruction under logic L, where either Cn L(N ) = L or Cn L(N {φ}) = L for some φ such that Pφ holds. 3 3 This means that φ N or, if φ = ψ, then ψ N.

22 Is logic revision possible? It is not the norm-giver s duty to change the logic, this is the norm-recipient s duty. The norm-recipient s duty remains the duty to treat the norm-system as a logical object (with norm set closed under entailment and adjunction, and counter-set having corresponding properties). But can this be done? Is there a logic not self-destructive in the case of inconsistency and still conservative with respect to perfection properties of the norm-set and counter-set? The answer is affirmative. Dialetheic deontic logic of Graham Priest is both inconsistency-tolerant and preserves properties of the norm-set and counter-set.

23 Dialetheic deontic logic In Priest presented the system of dialetheic deontic logic, a logic with three values ({t}, {t, f}, {f}) and free from explosion principle. Graham Priest (2006). In contradiction : a study of the transconsistent. Expanded edition. (First edition published 1987 by Martinus Nijhoff Publishers). Oxford: Oxford University Press. The deontic operator O is receives two interpretations in a given possible world w: it has an extension ω + (w) L and anti-extension ω (w) L which are exhaustive ω + (w) ω (w) = L but not in general exclusive, i.e., it is allowed in the system that ω + (w) ω (w). It is obvious that Priest s extension corresponds to the norm-set, and anti-extension to the counter-set. The extension of O is closed under entailment, i.e., if α entails β and α ω + (w), the β ω + (w), and closed under adjunction, if α ω + (w) and β ω + (w), the (α β) ω + (w). The anti-extension is closed in the opposite direction, i.e. closed under implicant and having at least one conjunct for the conjunction contained. It is allowed for the extension to be inconsistent, i.e., α ω + (w) and α ω + (w). Since the DDL logic is free from self-destruction neither the fact of internal inconsistency, {α, α} ω + (w), nor the fact of external inconsistency, {α, α} ω + (w) {α} for some α such that α ω (w) do not imply ω + (w) = L or ω + (w) {α} = L, respectively.

24 Dialetheic deontic logic The informal reading for O is as follows:...if the world were such that all extant obligations were duly fulfilled, then it would be the case that α. The truth conditions are: t v w(oγ) iff γ ω + (w) f v w(oγ) iff γ ω (w) Operators P and F have standard definitions, O and O. E.g., t v w (Pφ) iff φ ω (w); f v w (Pφ) iff φ ω + (w).

25 Both...and not... instead of exclusionary either...or not... w = subsets of ω + (w) ω (w) valuation v w ω + (w) ω (w) ω + (w) ω (w) ω (w) ω + (w) Oφ Fφ Pφ P φ w 1 φ, φ {t} {t} {f} {f} w 2 φ φ {t} {t, f} {t, f} {f} w 3 φ, φ {t, f} {t, f} {t, f} {t, f} w 4 φ φ {t, f} {f} {t} {t, f} Table : Varieties of inconsistent normative systems. Firstly, note that the presence of contradictory sentences in ω (w) is not a sign of inconsistency, but the indication of the fact that φ is optional. The sufficient conditions for inconsistency are the presence of contradictory sentences in ω + (w) and ω + (w) ω (w). Secondly, note the absence of deontic explosion. In each of inconsistency types it is not the case that anything goes, not anything is permitted. In w 1 nothing is permitted with respect to φ. In w 2 it is only partially permitted that φ. In w 3 the inconsistency reaches its highest point and both φ and φ are simultaniously permitted and not permitted. In w 4 it is permitted that φ and permitted and not permitted that φ, and, so, φ is both optional and not optional.

26 Conclusion The programmatic statement put forward in von Wright s last works on deontic logic introduces the perspective of logical pragmatics. This perspective has been adopted here and extended so to include the role of norm-recipient as well as the role of norm-giver. Using the translation function from the language of deontic logic to the language of set-theoretical approach, the connection has been established between the deontic postulates, on one side, and the perfection properties of the norm-set and the counter-set, on the other side. In the study of conditions of rational norm-related activities it has been shown that diverse dynamic second-order norms related to the concept of the consistency norm-system hold: the norm-giver ought to restore classical consistency by revising an inconsistent system, the norm-recipient ought to preserve an inconsistent system by revision of its logic so that inconsistency does not imply destruction of the system. 4 4 The author acknowledges support from Università Commerciale Luigi Bocconi, Revus: Journal for Constitutional Theory and Philosophy of Law, and HRZZ research project: LogiCCom Logic, Concepts, and Communication.