So, cultivators of the art of reasoning found themselves long ago obliged to institute a speculative grammar which should study modes of signifying, in general. It is best regarded as separate from logic proper; for one of these days philologists may take it in hand, for which logicians will thank them.
An art of thinking ought also to recommend such forms of thinking as will most economically serve the purpose of Reason. [—] Since this is the general foundation of the art of putting propositions into effective forms, it has been called speculative rhetoric.
The sciences of speculative grammar, logic, and speculative rhetoric may be called the philosophical trivium.
“Exact” logic, in its widest sense, will (as I apprehend) consist of three parts. For it will be necessary, first of all, to study those properties of beliefs which belong to them as beliefs, irrespective of their stability. This will amount to what Duns Scotus called speculative grammar. For it must analyse an assertion into its essential elements, independently of the structure of the language in which it may happen to be expressed. It will also divide assertions into categories according to their essential differences. The second part will consider to what conditions an assertion must conform in order that it may correspond to the “reality,” that is, in order that the belief it expresses may be stable. This is what is more particularly understood by the word logic. It must consider, first, necessary, and second, probable reasoning. Thirdly, the general doctrine must embrace the study of those general conditions under which a problem presents itself for solution and those under which one question leads on to another. As this completes a triad of studies, or trivium, we might, not inappropriately, term the last study Speculative rhetoric. This division was proposed in 1867 by me, but I have often designated this third part as objective logic.
But besides being logical in the sense of demanding a logical analysis, our inquiry also relates to two as a conception of logic. The term “logic” is unscientifically by me employed in two distinct senses. In its narrower sense, it is the science of the necessary conditions of the attainment of truth. In its broader sense, it is the science of the necessary laws of thought, or, still better (thought always taking place by means of signs), it is general semeiotic, treating not merely of truth, but also of the general conditions of signs being signs (which Duns Scotus called grammatica speculativa), also of the laws of the evolution of thought, which since it coincides with the study of the necessary conditions of the transmission of meaning by signs from mind to mind, and from one state of mind to another, ought, for the sake of taking advantage of an old association of terms, be called rhetorica speculativa, but which I content myself with inaccurately calling objective logic, because that conveys the correct idea that it is like Hegel’s logic.
Logic is the science of the general necessary laws of Signs and especially of Symbols. As such, it has three departments. Obsistent logic, logic in the narrow sense, or Critical Logic, is the theory of the general conditions of the reference of Symbols and other Signs to their professed Objects, that is, it is the theory of the conditions of truth. Originalian logic, or Speculative Grammar, is the doctrine of the general conditions of symbols and other signs having the significant character. It is this department of general logic with which we are, at this moment, occupying ourselves. Transuasional logic, which I term Speculative Rhetoric, is substantially what goes by the name of methodology, or better, of methodeutic. It is the doctrine of the general conditions of the reference of Symbols and other Signs to the Interpretants which they aim to determine…
All this brings us close to Methodeutic, or Speculative Rhetoric. The practical want of a good treatment of this subject is acute.
In coming to Speculative Rhetoric, after the main conceptions of logic have been well settled, there can be no serious objection to relaxing the severity of our rule of excluding psychological matter, observations of how we think, and the like. The regulation has served its end; why should it be allowed now to hamper our endeavors to make methodeutic practically useful? But while the justice of this must be admitted, it is also to be borne in mind that there is a purely logical doctrine of how discovery must take place, which, however great or little is its importance, it is my plain task and duty here to explore.
That our thoughts are signs is an old and familiar doctrine. I show that it is only in so far as thoughts are signs, and particularly […] symbols, that they become subjects of logic; and further that the rules of logic are applicable to all symbols. Accordingly by regarding logic as a science of signs or formal semeiotic, and in the main as a science of symbols, or formal symbolic, we accurately cover its subject matter, and at the same time insure ourselves against all risk of being led astray into psychology. The word formal, in this connection, signifies that only the general conditions to which signs ought to conform are to be considered.
But those conditions may be distinguished into three kinds, leading to a corresponding distinction between three departments of logic, in its wider sense; or Formal Semeiotic. Namely the conditions are either, first, such as must be fulfilled in order that an object may be a sign at all; second, such as must be fulfilled in order that the sign may refer to the object to which it aims to refer, that is, may be true; and third, such as must be fulfilled in order that the sign may determine the interpretant it aims to determine, that is, may be pertinent. [—] The study of the third series of conditions will be found to coincide nearly with what is termed Methodeutic or Methodology; but I prefer to term it Speculative Rhetoric.
From an earlier/discarded draft
… a universal art of rhetoric, which shall be the general secret of rendering signs effective, including under the term “sign” every picture, diagram, natural cry, pointing finger, wink, knot in one’s handkerchief, memory, dream, fancy, concept, indication, token, symptom, letter, numeral, word, sentence, chapter, book, library, and in short whatever, be it in the physical universe, be it in the world of thought, that, whether embodying an idea of any kind (and permit us throughout to use this term to cover purposes and feelings), or being connected with some existing object, or referring to future events through a general rule, causes something else, its interpreting sign, to be determined to a corresponding relation to the same idea, existing thing, or law. Whether there can be such a universal art or not, there ought, at any rate to be (and indeed there is, if students do not wonderfully deceive themselves) a science to which should be referable the fundamental principles of everything like rhetoric, – a speculative rhetoric, the science of the essential conditions under which a sign may determine an interpretant sign of itself and of whatever it signifies, or may, as a sign, bring about a physical result. [—]
In the Roman schools, grammar, logic, and rhetoric were felt to be akin and to make up a rounded whole called the trivium. This feeling was just; for the three disciplines named correspond to the three essential branches of semeiotics, of which the first, called speculative grammar by Duns Scotus, studies the ways in which an object can be a sign; the second, the leading part of logic, best termed speculative critic, studies the ways in which a sign can be related to the object independent of it that it represents; while the third is the speculative rhetoric …
… I extend logic to embrace all the necessary principles of semeiotic, and I recognize a logic of icons, and a logic of indices, as well as a logic of symbols; and in this last I recognize three divisions: Stecheotic (or stoicheiology), which I formerly called Speculative Grammar; Critic, which I formerly called Logic; and Methodeutic, which I formerly called Speculative Rhetoric.