A rhema is somewhat closely analogous to a chemical atom or radicle with unsaturated bonds. A non-relative rhema is like a univalent radicle; it has but one unsaturated bond. A relative rhema is like a multivalent radicle. The blanks of a rhema can only be filled by terms, or, what is the same thing, by “something which” (or the like) followed by a rhema; or, two can be filled together by means of “itself” or the like. So, in chemistry, unsaturated bonds can only be saturated by joining two of them, which will usually, though not necessarily, belong to different radicles. If two univalent radicles are united, the result is a saturated compound. So, two non-relative rhemas being joined give a complete proposition.
Rhemata are very nearly what are ordinarily designated as Terms. Indeed, they are the same thing more accurately apprehended. A Rhema, or Term, is a Sign which is left to stand for whatever it may stand for.
From an early/discarded draft
A representamen is either a rhema, a proposition, or an argument. An argument is a representamen which separately shows what interpretant it is intended to determine. A proposition is a representamen which is not an argument, but which separately indicates what object it is intended to represent. A rhema is a simple representation without such separate parts.
…the word rhema is used in logic to denote any proposition and any blank form which would become a proposition if every one of its blanks were filled with a proper name.
A Rheme is a Sign which, for its Interpretant, is a Sign of qualitative Possibility, that is, is understood as representing such and such a kind of possible Object. Any rheme, perhaps, will afford some information; but it is not interpreted as doing so.
[—] Or we may say that a Rheme is a sign which is understood to represent its Object in its characters merely…
If parts of a proposition be erased so as to leave blanks in their places, and if these blanks are of such a nature that if each of them be filled by a proper name the result will be a proposition, then the blank form of proposition which was first produced by the erasures is termed a rheme. According as the number of blanks in a rheme is 0, 1, 2, 3, etc., it may be termed a medad (from μηδὲν, nothing), monad, dyad, triad, etc., rheme.
A rhema is either a proposition or a blank form that would become a proposition if all its blanks were filled with proper names.
An assertion fulfilling the condition having been obtained, let a number of the proper designations of individual subjects be omitted, so that the assertion becomes a mere blank form for an assertion which can be reconverted into an assertion by filling all the blanks with proper names. I term such a blank form a rheme. If the number of blanks it contains is zero, it may nevertheless be regarded as a rheme, and under this aspect, I term it a medad. A medad is, therefore, merely an assertion regarded in a certain way, namely as subject to the inquiry, How many blanks has it? If the number of blanks is one, I term the rheme a monad. If the number of blanks exceeds one, I term it a Relative Rheme. If the number of blanks is two, I term the rheme a Dyad, or Dyadic Relative. If the number of blanks exceeds two, I term it a Polyad, or Plural Relative, etc.
Each rhema is equivalent to a blank form such that of all its blanks are filled with proper names, it becomes a proposition, or symbol capable of assertion.
Let a heavy dot or dash be used in place of a noun which has been erased from a proposition. A blank form of proposition produced by such erasures as can be filled, each with a proper name, to make a proposition again, is called a rhema, or, relatively to the proposition of which it is conceived to be a part, the predicate of that proposition.
A rheme is a sign whose proper interpretant ignores all difference between the sign and its object (and a fortiori all difference between the sign and its interpretant)
In regard to its relation to its signified interpretant, a sign is either a Rheme, a Dicent, or an Argument. This corresponds to the old division Term, Proposition, & Argument, modified so as to be applicable to signs generally. [—] A rheme is any sign that is not true nor false, like almost any single word except ‘yes’ and ‘no’, which are almost peculiar to modern languages. [—] A rheme is defined as a sign which is represented in its signified interpretant as if it were a character or mark (or as being so).
Another case is where a sign fully interpreted in its definition, the very creation of the new sign, not now bringing about an actual event, as with the dicisign, but merely imparting to the definition a certain capacity, or contingent power, that of being properly applied to designate whatever the definitum may designate. A sign whose whole purport can be so interpreted or conveyed is termed a rheme.
If from a propositional symbol we erase one or more of the parts which separately denote its objects, the remainder is what is called a rhema; but I shall take the liberty of calling it a term. [—] On the whole, it appears to me that the only difference between my rhema and the “term” of other logicians is that the latter contains no explicit recognition of its own fragmentary nature. But this is as much as to say that logically their meaning is the same; and it is for that reason that I venture to use the old, familiar word “term” to denote the rhema.
In their relations to their Triadic, i.e. intended or adaptational Interpretants, Signs may, 1st, determine those interpretants, merely in the sense that, if the Interpretants represent the Objects as the Signs themselves do they are such Interpretants as are intended. Such is an ideal statuette, and exclamation of surprise, a noun, whether common or proper. 2nd, Signs may be adapted to compelling or tending to compel the determination of their intended interpretants, such is a portrait with the name of the person represented under it, such is a weather-cock in a good breeze. 3rd, Signs may be adapted to determining a particular interpretant logically. Names: Rheme, Dicisign, Argument.
Take any proposition and erase certain parts of it, so that it is no longer a proposition but only a blank form which after every blank had been filled by a proper name would become a proposition, however nonsensical. Such a blank form of proposition which can be converted into a proposition by filling every blank with a proper name has been called by the writer a rheme. There may be any integer non-negative number of blanks, so that the term rheme is extended even to a full proposition, when it is looked upon as having a number of blanks which happens to be zero
A rheme is a blank form of proposition, such that when each blank is filled with a proper name, the result is a proposition. The valency of a rheme is the number of proper names that have to be inserted in it to make a complete proposition.
By a rheme, or predicate, will here be meant a blank form of proposition which might have resulted by striking out certain parts of a proposition, and leaving a blank in the place of each, the parts stricken out being such that if each blank were filled with a proper name, a proposition (however nonsensical) would thereby be recomposed.
When a blank form is such that the result of determining each blank in it to express a proper name is to reconvert it into a proposition, however silly, that blank form is termed a rheme or predicate.
A rhema is an indispensible part of speech in every language. Every verb is a rhema.