The term "ri" is mentioned quite frequently in Tenrikyo. Since it is used in a wide array of contexts, it is very difficult to give a simple summary of its range of meanings.
The Chinese character used to write ri includes the meaning of preparing and polishing a jewel. Polishing a jewel harnesses its innate qualities and gives a smooth consistency to its surface. Thus, ri has come to generally refer to settling, reaching, or achieving a level of consistency with something; it is a word that can be rendered into English as "reason," "truth," "logic," or "(unchanging) principle."
In Tenrikyo, ri is often used in a similar way. We can see this in expressions such as "To have something happen in such a way reflects one truth (thread of reasoning/logic)" or "One becomes angry or upset because one upholds one's own truth (reasoning) without trying to understand the truth of another."
However, there is a use of ri that is unique to Tenrikyo. Its primary definition refers to the providence of God the Parent--who created the world, human beings, and everything else--as well as the fundamental principles of existence and of the cosmos that also include the path that human beings ought to follow. It refers to the manifestation of God the Parent's miraculous protection that guides and settles everything in this world out of God's profound parental love. It can be said that this meaning is contained in phrases like "the truth of heaven," which appears, for example, in the following words of God: "Sincerity alone is the truth of heaven. Because it is the truth of heaven, I accept it at once and give a return at once: this is the one truth" (Kakisage).
Among the beginning verses of the Ofudesaki, we read:
This is a world constructed on reason (ri). So I shall press upon you everything with the reason in verse.
"Ri"--rendered here as "reason"--that appears in this verse also has the same meaning and describes how the world is built with God the Parent's providence and how all things fall under the governance and protection of the truth of heaven at any given moment. The verse goes on to say that God will inform us of any error through verse if we human beings do anything that deviates from the truth of heaven.
In addition to referring to the principles of heaven that are maintained by God the Parent's miraculous protection and God the Parent's providence itself, "ri" also refers to God's profound intention embodied in God's providence and protection. Expressions such as "settle truth in the mind" and "in accord with the truth" reflect this usage.
Among Oyasama's instructions that relate to the Service, She once said: "These are the songs of truth (ri). So you must dance to the truth. You should not just dance. You must dance the truth" (The Life of Oyasama, Foundress of Tenrikyo, p. 71). Ri--rendered here as "truth"--can be said to refer to God the Parent's intention, the teachings, and the profound implications embodied in the words and expressions comprising the songs of the Service.
When "ri" is rendered as "truth," as in "the truth of a thing lent, a thing borrowed," it can be said that this refers to the connotations or implications of what God the Parent has taught to us. Further, "ri" is also used to refer to what lies at the basis of all matters and phenomena--the universal principles that maintain the essence of all things. Expressions such as "receiving the truth of Jiba" or "receiving the truth of the Parent" and concepts such as "truth of the Sazuke" and "truth of a church name" can be said to refer to God the Parent's protection that maintains the fundamental forces, workings, virtue, merit, or effectiveness of these "truths." The expression "keep truth in mind" cautions us against our tendency of treating matters lightly due to our selfish human thinking and closing our eyes to God the Parent's profound intention that is embodied in the true significance of everything that occurs around us.
The expression "uphold truth" (ri o tateru) is used to describe a consistent and methodical course that is in accord with God the Parent's intention. The practice of making a donation as a sign of our sincerity and out of our wish to receive God the Parent's protection and grace to assist us before proceeding with a matter developed from this ideal of following a course that is in accordance with the divine intention. Donations in this case are frequently referred as ri-date or a donation that helps "uphold truth."