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.
In consequence of every representamen being thus connected with three things, the ground, the object, and the interpretant, the science of semiotic has three branches. The first is called by Duns Scotus grammatica speculativa. We may term it pure grammar. It has for its task to ascertain what must be true of the representamen used by every scientific intelligence in order that they may embody any meaning. The second is logic proper. It is the science of what is quasi-necessarily true of the representamina of any scientific intelligence in order that they may hold good of any object, that is, may be true. Or say, logic proper is the formal science of the conditions of the truth of representations. The third, in imitation of Kant’s fashion of preserving old associations of words in finding nomenclature for new conceptions, I call pure rhetoric. Its task is to ascertain the laws by which in every scientific intelligence one sign gives birth to another, and especially one thought brings forth another.
There are three ways in which signs can be studied, first as to the general conditions of their having any meaning, which is the Grammatica Speculativa of Duns Scotus, second as to the condions of their truth, which is logic, and thirdly, as to the conditions of their transferring their meaning to other signs.
It is generally admitted that there is a doctrine which properly antecedes what we have called critic. It considers, for example, in what sense and how there can be any true proposition and false proposition, and what are the general conditions to which thought or signs of any kind must conform in order to assert anything. Kant, who first raised these questions to prominence, called this doctrine transcendentale Elementarlehre, and made it a large part of his Critic of the Pure Reason. But the Grammatica Speculativa of Scotus is an earlier and interesting attempt. The common German word is Erkenntnisstheorie, sometimes translated Epistemology.
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…
Logic, which began historically, and in each individual still begins, with the wish to distinguish good and bad reasonings, develops into a general theory of signs. Its three departments are the physiological, or Speculative Grammar; its classificatory part, judging particularly what reasoning is good and what bad, or Logical Critic; and finally, Methodeutic, or the principles of the production of valuable courses of research and exposition.
All thought being performed by means of signs, logic may be regarded as the science of the general laws of signs. It has three branches: (1) Speculative Grammar, or the general theory of the nature and meanings of signs, whether they be icons, indices, or symbols; (2) Critic, which classifies arguments and determines the validity and degree of force of each kind; (3) Methodeutic, which studies the methods that ought to be pursued in the investigation, in the exposition, and in the application of truth. Each division depends on that which precedes it.
… 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.