1. 1. The Principle of Universalizability-an informal explication This work is concerned with the so-called Principle of Universalizability. As we shall understand it, this principle represents a claim that moral properties of things (persons, actions, state of affairs, situations) are essentially independent of their purely 'individual' or-as one often says -'numerical' aspects. l Thus, if a thing, x, is better than another thing, y, then this fact is not dependent on x's being x nor on y's being y. If a certain person, a, has a duty to help another person, b, then this duty does not arise as a consequence of their being a and b, respectively. And if in a certain situation, W, it ought to be the case that certain goods are transferred from one person to another, then this moral obligation does not depend on the individual identities of the persons involved. The Universalizability Principle may also be expressed in terms of similarities. Instead of saying that the moral properties of x are essentially independent of the individual aspects of x, we may say that any object which is exactly similar to x, which is precisely like x in all non-individual, 'qualitative' respects, must exhibit exactly similar moral properties. Thus, if two persons are exactly similar to each other, (if they are placed in exactly similar circumstances, have exactly similar information, preferences, character, etc. ), then they will have exactly similar rights and duties.

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1. Introduction.- 1. Introduction.- 1.1 The Principle of Universalizability-an informal explication.- 1.2 What our Universalizability Principle is not.- 1.3 The Universalizability Principle as a condition on a model.- 1.4 General outline.- I Theory of Universalistic Conditions.- 2. Questions.- 2.1 The concept of universalistic condition.- 2.2 Universalism and supervenience.- 2.3 Different universalistic conditions and their interrelations.- 2.4 Special status of (u) and (ur).- 3. Answers.- 3.1 The strongest plausible universalistic condition on C and D.- 3.2 Segerberg's proposal and the concept of alternative.- 3.3 The strongest plausible universalistic condition on R and D.- 3.4 Components of universalistic conditions.- 3.5 Normal universalistic conditions.- 3.6 Deep components of universalistic conditions.- 3.7 Proper universalistic conditions and the special status of (u) and (ur).- 3.8 The relation between (CR+) and (RR+) 56.- 3.9 Conclusions.- 4. Formalities.- II Universalizability and Automorphisms.- 5. Introductory Remarks.- 5.1 The concept of automorphism.- 5.2 The Universalizability Principle as a condition on automorphisms.- 6. Theory of Automorphisms.- 6.1 General axioms.- 6.2 Indiscernibility and identity.- 6.3 Automorphous permutations on individuals and minimal kinds.- 6.4 Extendibility and complex individuals.- 6.5 Indiscernibility and automorphisms.- 6.6 Entities.- 6.7 Pure entities.- 6.8 Purity and universal properties.- 7. Morality without Purity.- 7.1 Non-universalistic theories.- 7.2 D-homogeneous sets of individuals.- 7.3 D-homogeneity and complex individuals.- 7.4 A normality condition on moral theories.- 7.5 Maximal D-homogeneous sets.- 7.6 Classification of non-universalistic theories.- 7.7 Other normality conditions.- III Beyond Similarity.- 8. The Universalizability Dilemma.- 8.1 Presentation of the dilemma.- 8.2 A third way out: the condition (uu).- 8.3 (uu) and the extensions of Leibnizianism.- 9. Universal Aspects.- 9.1 Universality vs. individuality.- 9.2 Anti-Leibnizianism.- 10. Universality and Relevance.- 10.1 Definition of R and the first principle of relevance.- 10.2 The equivalence of (CR+) and (RR+).- 10.3 The second principle of relevance.- 11. Universality and Universalizability.- 11.1 The condition (uu).- 11.2 (uu), (u) and Leibnizianism.- 11.3 (uu) and (ur).- 12. Extensions of Leibnizianism.- 12.1 Absolute Leibnizianism.- 12.2 Radical Leibnizianism.- 12.3 (uu) and Leibnizian metaphysics.- 12.4 Critique of Absolute and Radical Leibnizianism.- IV Individuals Do Not Matter.- 13. Universalizability in Morals and Elsewhere.- 13.1 Propositional operations.- 13.2 Universalizability conditions and their common background.- 14. Intensions and Extensions.- 14.1 Intensional propositions.- 14.2 Intensional operations and the Principle of Extensionality.- 14.3 Proper and infinitary intensional operations.- 15. Universality and Intensions.- 15.1 Intensional propositions: universal and individual.- 15.2 Universalizable intensional operations. Universalizability of Ought.- 15.3 Individuals do not matter.- 15.4 Exact similarity: intensional and extensional.- 16. Leibnizianism Once Again.- 16.1 Individuals-do-not-matter and Leibnizianism. Are these two principles incompatible?.- 16.2 Discussion of the assumptions used in the derivation of incompatibility.- Appendix to Part IV.- Index of Names and Subjects.