What kind of relation is like identity but holds between a thing and itself (rather than between necessarily co-referring names, for example) by stipulation? Why, shmidentity, of course! The term “shmidentity” (actually “schmidentity,” but see infra on the spelling) was introduced by Saul Kripke in Naming and Necessity and, following his example, the “sh-“ or “shm-“ prefix is now often used in philosophy for properties or relations that resemble other properties or relations but have some feature that may be controversial in the case of the prototypes built in by stipulation.
The linguist David L. Gold, in a paper in the Jewish Language Review (volume 3, 1983) entitled “A Story about Pocahontas, Geronimo, and Sitting Bull in Yiddish,” refers to the fact that languages in decline (such as Yiddish) often become “ludic languages, that is, languages used largely for jocular purposes, often only for low comedy and vulgar humor” (113). Having made this claim he cites, without quoting, a responsum by him to a reader’s query in an earlier issue of the journal which I here excerpt:
Since Yiddish word-initial /š/ + consonant sounds “funny” to a sizable number of English ears, any Yiddish word containing it is automatically recategorized [as humorous] when entering English (e.g. shmir). Perhaps the fact that initial /šm/ is a pejorizer in Yiddish and EAE [Eastern Ashkenazic English]… has contributed to this feeling among English-speakers. (Volume 2, 1982, 302)
The use of the term “shmidentity,” therefore (and similar neologisms in the philosophy literature) is culturally insensitive, appealing to the ‘funny’-sounding phonemes of a language that translated Freud, Einstein, Shakespeare, and Emily Dickinson, among countless others, for a quick laugh now that that language has fallen on hard times and is forced to wear the fool’s motley. I recommend this usage be avoided in philosophy henceforth.
As for the spelling, “schmidentity” (the form used by Kripke himself) reflects the efforts of those who have sought to cast Yiddish as low German and transcribe it into Latin characters on the model of German spelling. It is, therefore, another blow to the dignity of Yiddish. Standard Yiddish Orthography romanizes /š/ as “sh.” If one must, therefore, continue to use this offensive neologism, I recommend that at least the spelling “shmidentity” be given.
This was to have been a footnote to a footnote to a footnote in my in-progress book. If anyone is interested, here is the tree of footnotes. This note on “shmidentity”  would have been a footnote to  a discussion of the title of Gold’s paper “A Story about Pocahontas, Geronimo, and Sitting Bull in Yiddish” and the question of whether the story, given in his paper, could really be said to be ‘about’ those figures. (I draw on Robin Jeshion’s views about the link between proper names and de re thought and talk and, obviously, on Kripke’s views about historical chains and reference.) This itself is a footnote to  a discussion of whether my Yiddish Batman meme commits the same kind of assault on the dignity of Yiddish that I here lay at the feet of “shmidentity.” (See this earlier post and the links to yet earlier posts it contains.) This, in turn, is a footnote to  the main text which is the commentary on my Yiddish Batman meme.