Abstract
In the foregoing we have already spoken of the formulation, within a formal system, of conditional norms, especially ‘commitment’ (Chapter VI, 7, 8, 9). In section VI.8 we have seen that the internal deontic implication cannot provide an adequate formulation of ‘commitment’. Also with regard to the external deontic implication, discussed in section VI.9, there were difficulties.
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Von Wright, 1956: Another pioneer was N. Rescher, 1958. After having been criticized by A.R. Anderson in 1959, Rescher amended his system in 1962. I agree with B. Hansson, 1969, in Hilpinen, 1971, p.136, that Rescher’s system is ‘extremely strong’. In Rescher’s system a conditional obligation e.g. strictly implies an unconditional obligation. Furthermore, the system is based on ‘P’ as single primitive deontic operator. ‘0(p/q)’ is defined as ‘-PO-p/q)’. Cf. section VII.7 concerning the difficulties with regard to an equivalence between 0(p/q) and -P(-p/q). For these reasons I favour Von Wright’s systems as a starting-point for a discussion on dyadic deontic logic. Cf. on Rescher, in addition to the authors already mentioned, Castaneda, 1959.
Von Wright, 1964; the article is included in Hilpinen, 1971. In more recent publications Von Wright has abandoned dyadic deontic logic; e.g. 1981, p.411: ‘I am less confident now than I used to be in the value of a dyadic deontic logic’. The reason for his abandonment appears to be the fact that there are more simple and conventional logical tools, which can be used to build a satisfactory theory of conditional norms, of which particularly external material implication. This matter will once more be considered by me at the close of this chapter.
Von Wright, 1964, in Hilpinen, 1971, p.105.
Von Wright, 1964, in Hilpinen, 1971, p.110.
Von Wright, 1964, in Hilpinen, 1971, p.116.
F0llesdal and Hilpinen, 1971, in Hilpinen, 1971, p.29 ff. The same concept can be found in Hansson, 1969, in Hilpinen, 1971, p.140; FH-71 expresses the fact that a (conditional) obligation can be overridden in (more) specific circumstances. Substantially the same concept was earlier expressed in a formal system, developed by R.M. Chisholm.
Hansson, 1969, in Hilpinen, 1971, p.140.
Hansson, 1969, in Hilpinen, 1971, p.140; the reference made is to Powers, 1967.
q-ideal worlds are sometimes defined as worlds in which q is true, and which in other respects resemble deontically perfect worlds as much as possible (Cf. F0llesdal and Hilpinen, in Hilpinen, 1971, p.30; Van Eck, 1981, p.7). The consequence to the latter is, however, that 0(p/p) becomes a trivial truth of logic. I do not presuppose in the text that q has to be true in q-ideal worlds, only that p has to be true in all worlds which are as deontically perfect as possible, as seen from a world in which q is true. This means that 0(-p/p) is a possibly valid conditional obligation, and not a logical contradiction.
This requirement is not accepted by all deontic logicians. N. Rescher, e.g. when speaking of conditional permission, rejects a theorem P(p/c) ⊃ P(p/c & d), because of the fact that ‘it establishes the prerequisite that, in stating the circumstance c in which an act p is permitted, our description must be so complete that no conceivable (conjunctive) modification of the circumstance c could possibly preclude the permittedness of p. But this is a task that is hopelessly cumbersome. In common life.... we are seldom (if ever) in a position to specify all the conceivable further modifications of these circumstances which would, if also realized, preclude the ,permitted, status of the act’ Rescher, 1962, p.5. More recently: (a.o.) Van Fraassen, 1972, p.420 (who reads 0(p/q) in a way which is incompatible with my requirement), Lindemans, 1982, p.263, Hansson, 1969, Van Eck, 1981, I agree with Anderson’s comment on Rescher, 1962: Tt is clear that when we say ‘p is permitted in the circumstance c’, we never (or at least very rarely) mean that c is a necessary condition for p’s being permitted. But surely we sometimes mean that c is sufficient condition for p’s being permitted .... In consulting a lawyer, for example, as to whether p is permitted to a person in our circumstances c, we expect him to give more than the prima-facie answer, and to go on to consider possible relevant special circumstances; and if he does tell us to go ahead with the project, we would feel that we were badly advised if it would turn out that by reason of special overriding considerations p was not permitted to us after all’.
J.A. van Eck, 1981. Cf. also Åqvist and Hoepelman 1981.
The description of WFFs means that the formulas of the standard system, such as Op, O(pvq) etc. are not WFF’s of W-64’ Because of the fact that unconditional norms can be formulated in W-64’ by writing a tautology on the right side of the dyadic symbol ‘/’ there is no need here for the formulas of the standard system.
Why S2 and not another system ? First, I need a formal reconstruction of the concept of (im)possibility. This compels me to a modal system. Second, weaker systems will not do: they do not contain the consistency postulate math (Cf. Hughes and Cresswell, 1972, p.230). If math, however, then ◊(◊(p & q) & -◊p). Likewise, then ◊(◊(p & q) & -◊p). Let us assume that these possibilities realize themselves. In that case, it follows from ax.l that -O(r/p&q) & O(-r/p&q). But, as -fa and -fa, the validity of O(r/p) & O(-r/p) & O(r/q) & O(-r/q) is not in conflict with the logic of W-64’ From this last conjunction it follows (by ax.2 and ax.3) O(r/p&q) & O(-r/p&q). Therefore, this last conjunction would be both contrary to and consistent with W-64’ This illustrates why weaker systems will not do. On the other hand, stronger systems do contain all the axioms (and theorems) of S2: we do not need them for the following.
Nevertheless, the definition of P(p/q) as -O(-p/q) is quite common among deontic logicians. See, e.g. F0llesdal and Hilpinen, 1971, p.27; Von Wright, 1968, p.25; van Eck, 1981, p.7.
By means of these two axioms ax.6.1 can be proven, by which axiom ax.6.1 becomes superfluous. The proof is as follows. From the assumed premiss ◊ q and ax.l we have-(O(p/q) & P(-p/q)), i.e. O(p/q) ⊃ -P(-p/q). From ax.2 we have by substitution and transposition -P(-p/q) ⊃ -O(-p/q). Therefore, by hypothetical syllogism, O(p/q) ⊃ -O(-p/q), and, by conditional proof, ◊q ⊃ (O/p/q)⊃-O(-p/q)).
Chisholm, 1963, p.33 ff.
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Soeteman, A. (1989). Conditional Norms. In: Logic in Law. Law and Philosophy Library, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7821-9_8
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