"the relation in which" is correct and can be used in written English.
It is typically used to introduce or describe a specific relationship between two or more things or concepts. Here is an example: "The relation in which government policies and economic growth are intertwined is a complex and constantly evolving dynamic."
Or Lockwood (1989, p. 88): co-consciousness is "the relation in which two experiences stand, when there is an experience of which they are both parts".
For the Idealists, individualists neglected the spiritual nature of the social organism, which is neither mechanical nor biological, but instead depends upon the relation in which each person stands with every other.
The same human being can be first person 'I', second person 'you', and third person 'he' or 'she', depending on the relations in which he or she stands.
Since Twardowski accepts that among the parts of an object there are the relations in which that object is in, Twardowski's mereology is, strictly speaking, an atomless mereology: there are no simples (1894, §12, 74).
Notably, the contrasting conceptual folly has a metaphysical analogue, the insistence that "… things must be, before they can stand in the relations in which indeed alone their reality can become perceptible to us" (Micro, II, p. 583).
So to avoid violating this transitivity requirement, we simply have to stipulate in our criterion of personal identity that, if the relations in which identity consists may hold one-many, they must obtain uniquely for identity itself to obtain.
In a short essay published 1842, in which he sought to clarify the difference between his own approach to the philosophy of religion and Hegel's, Feuerbach suggested that this difference is most evident in the relations in which each of them stands to Schleiermacher, who famously defined religion as the feeling of utter dependence.
Returning to our earlier example of kin terms, the Whorfian orientation suggests we might ask whether or how young Chinese are or are not situated in their families differently than their American cousins, owing to the difference in the specificity of the relations in which they stand and speak with their kin.
In 1996, however, Yale University Press issued a new edition of "The Vinland Map and the Tartar Relation," in which the map was endorsed as a "major and authentic message from the Middle Ages".
By contrast, the most liberal choice would be to identify ξ with the universal relation, in which case (P.11ξ) would reduce to its consequent and assert the existence of an upper bound for any pair of entities x and y.
The psychological effects of this sort of self-policing were written about by Michel Foucault: "He who is subjected to a field of visibility, and who knows it, assumes responsibility for the constraints of power; he makes them play spontaneously upon himself; he inscribes in himself the power relation in which he simultaneously plays both roles; he becomes the principle of his own subjection".
