1. In standard usage such things are called individuals.  However, I employ individual for a different kind of entity, so I will call such things particulars. 2. By an object that is contingently self-identical, I understand any object x such that x = x & (x = x). 3. Identity also relates haecceities to haecceities, particulars to particulars, and complexes to complexes. 4. [...] la identidad de cualquier modo es una unidad, ya sea que la unidad se refiere a pluralidad de cosas, ya sea que se refiera a una única cosa, considerada como dos, como resulta cuando se dice que la cosa es idéntica a sí misma.(Aristotle, Met., V, 9, 1018 a 7. Cited in N. Abbagano, Diccionario de Filosofía, Fondo de Cultura Económica, México, 1986, p. 640). [...identity is in any event a oneness, whether this oneness makes reference to a plurality of things, or whether it makes reference to a single thing considered as two, as happens when it is said that the thing is identical to itself.] 5. (13) and (*) are equivalent. (13) (x = x)z(z cont x & z cont x) (*) (x = x)z(z cont x) 6. S. Kripke, Naming and Necessity, Harvard University Press, Cambridge,  Massachusetts, 1980, p. 3. 7. By 'formal identity' I will understand the relation that is asserted to obtain between Hesperus and itself when one says Hesperus is Hesperus (or Hesperus = Hesperus).  By 'material identity'1 I will understand the relation that is asserted to obtain between Hesperus and Phosphorus when one says Hesperus is Phosphorus (or Hesperus = Phosphorus). Instead of 'formal identity' I will sometimes write 'self-identity'. 8. By the rule of Necessitation, together with the axiom that whatever follows logically from a necessary truth is itself necessarily true. 9. For "LPC=" read "Lower Predicate Calculus with Identity". 10. For Russellians such terms suffer from incomplete-symbolitis.  The therapy for this--available from an army of adepts--is radical paraphrasectomy.  For Fregeans such terms suffer from oratio oblicuaitis.  The therapy for this:  functions--and more functions.  Adepts abound wherever "exact" philosophy is purveyed. For Quine such terms suffer from acute reference failure.  The therapy for this: solitary confinement in a hyphenated context.  Adepts are few.  For Kripke such terms suffer from nonrigid designation.  Helpful as a diagnostic--alas! there is no cure--is the model structure.  Available wherever worlds are crunched. 11. From the standpoint of FOL ontology, no sense can be made of the difference between a necessary/contingent property and an essential/accidental one.  Broach this  topic with a Friend of FOL and you are sure to be greeted with the blankest of stares. 12. Of course, one may hold that (30) is both true and false. Those who would like to find out for themselves about dialethia, or dialethism (as such a doctrine is sometimes called), may wish to see something on this topic by its maximal leader*. 13. From (32) it follows that ¬(x = x); (32) [((x ex X) & ¬(x ex X) & (x = x))  (x ex X)] and from (32) and (A), that some particular contains x. (A) xyz((x ex Y)  (z cont x & z emb Y)) Therefore, from (32, B) it follows that x = x. (B) xyz((z cont x & z cont y)  x = y)) 14.  From (32) it follows that x ex X; (32) [(x ex X & ¬(x ex X) & ((x = x)  (x ex X)] from (32, C) that z(x ex Z); (C) x(y(x ex Y)  z(x ex Z)) and from (32, C, A) that z(z cont x). (A) xyz((x ex Y)  (z cont x & z emb Y)) From (32, C, B, A) it therefore follows that x = x & (x = x). (B) xyz((z cont x & z cont y) (x = y)) 15. Therefore, although the author of W is essentially an author*, it does not follow that the author of W is an author necessarily*. For this to follow, it would have to be so that the author of W is the author of W necessarily*, which he is not. 16. "To bifurcate reality is to separate off some aspect which in fact is relative and to treat it as though it were absolute. The resulting confusion is two-fold. (a) The reality thus substantialized proves inherently unsubstantial because our bifurcation has robbed it of just those connections which were essential to it. (b) There is now no locus nor basis for those correlative entities which are denied a foothold in this bifurcated and exclusive reality. Hence those connections which are the meat of a relative entity become the veriest poison of the absolute, appearance stands over against reality and we are in the heart of dialectical metaphysics. Precisely of this nature, as I shall argue, are the problems that surround the nature of substance, and fully remedial once we have surrendered that bifurcation which is their source and basis. (H. K.Wells, Process and Unreality, King's Crown Press, New York, 1950, pp. 67-68).