We establish lower bounds for norms and CB-norms of elementary operators on B(H ). Our main result concerns the operator T a,b x = axb + bxa and we show T a,b a b , proving a conjecture of M. Mathieu. We also establish some other results and formulae for T a,b cb and T a,b for special cases.
Conflicts of norms and the revision of normative systems
✍ Scribed by Carlos E. Alchourrón
- Publisher
- Springer Netherlands
- Year
- 1991
- Tongue
- English
- Weight
- 589 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0167-5249
No coin nor oath required. For personal study only.
✦ Synopsis
REVISION OF NORMATIVE SYSTEMS
Normative systems, i.e., sets of norms, have two main practical functions: a) to evaluate human actions, and b) to guide people's behavior, l
The guidance and the evaluation based on a normative system may be good or bad. Ethics is supposed to be the discipline that supplies the criteria for judging the virtues and defects of normative systems. In this sense the theory of justice is the branch of ethics traditionally developed in order to single out the best normative system, i.e., the ethically optimal order, and also to detect the deficiencies of those systems that do not coincide with that optimum.
Although the substantial criteria for judging the features of normative systems stem from ethical considerations, logic, and more specifically normative logic, supplies a negative criterion for the adequacy of normative systems. For a logically inconsistent normative system is a bad one, independently of its ethical content.
An inconsistent normative system requires substantial modification in order to become useful as a guide for behavior. Some of its norms should be given up, and probably some of them should be replaced by opposite ones in order to preserve the practical functions of the system.
I believe that up to this point there is no controversy: Everyone will admit that inconsistent normative systems should, for the sake of practical usefulness, be changed in favor of consistent ones. Moreover, I think that it will be accepted without objections that the identification of the conditions under which a normative system is consistent or inconsistent is a logical and not an ethical enterprise.
In a recent, very stimulating paper 2 Risto Hilpinen has argued for 1 This paper was presented at a conference 'Rights and the Philosophy of Law' at the
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