Abstract
The paper is intended as a first, tentative, contribution to the clarification of the place that negation has in prescriptive discourse. In particular, the paper analyzes the ways in which rules may be said to be negated and the meanings they assume when they are so regarded. In so doing, the differences between external and internal negation of conditional rules are examined. The paper also deals with the effects of inconsistency between conditional rules, understood as the conjunction of a conditional rule and its corresponding conditional denial. The main result of the paper is that both rules negation and rules inconsistency are unclear concepts, casting their shadows over the very concept of rule.
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Notes
- 1.
For discussion, see Nárvaez (2010).
- 2.
Cf. Soeteman (1989, p. 132 ff.).
- 3.
Bulygin (1982).
- 4.
- 5.
It is interesting to observe that Soeteman’s (1989) classical treatment of the negation of normative expressions mainly deals with negation of categorical norms and the principle of prohibition, whereas I am here interested in conditional norms and I will not explore the mentioned principle. Moreover, his discussion of conditional norms—like Ross’s and von Wright’s—relies on the so called “insular conception” (which places conditions within the scope of deontic operators), whereas I shall resort to the so called “bridge conception” (which place conditions outside the scope of deontic operators).
- 6.
This is easily seen from the following truth-table:
p ⊃ q
&
p ⊃ ~q
≡
~ p
1 1 1
0
1 0 0
1
0
1 0 0
0
1 1 1
1
0
0 1 1
1
0 1 0
1
1
0 1 0
1
0 1 1
1
1
- 7.
- 8.
A third tenet is that their disjunction, in turn, is equivalent to the formulation of the so-called “conditional excluded middle”—“(p ⊃ q) ∨ (p ⊃ ~q)”—which allows one to derive, by disjunctive syllogism, the truth of a conditional by denying the other.
- 9.
- 10.
For discussion, see Alchourrón (1991).
- 11.
The formal representation of the corresponding propositional equivalence is as follows: ~(p ≡ q) ≡ (p ≡ ~ q). Cf. Quine (1961, p. 57).
- 12.
In standard deontic logic, “Non-obligatory q” (~ Oq), in fact, is equivalent to “Permitted non-q” (P ~ q).
- 13.
Alchourrón and Bulygin (1981).
- 14.
See Atienza (1992).
- 15.
Formally, enrichment is usually represented by the following sentence: “(p ⊃ q) ⊃ (p & r ⊃ q)”. In deontic logic, “(p ⊃ Oq) ⊃ (p & r ⊃ Oq).”
- 16.
“K” is for “consistency.
- 17.
Alchourrón-Bulygin (1971, pp. 101–102).
- 18.
For discussion, see Moreso (1996).
- 19.
Alchourrón and Bulygin (1971, p. 98 ff.).
- 20.
See Rodríguez (2002, p. 110).
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Acknowledgments
The author thanks Riccardo Guastini for his comments and observations on a previous version of the present paper.
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Ratti, G. (2015). Negating Rules. In: Araszkiewicz, M., Banaś, P., Gizbert-Studnicki, T., Płeszka, K. (eds) Problems of Normativity, Rules and Rule-Following. Law and Philosophy Library, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-09375-8_30
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