Mormon Metaphysics & Theology

Peirce made some rather illuminating comments on propositions which I've found quite helpful for understanding certain issues. Hopefully some others might find these informative as well. It is important to understand that Peirce invokes three categories: firstness, secondness and thirdness in most of his philosophy. For simplicity with respect to logic we can consider this in terms of the number of necessary terms within the logic. Many logics historically only involved two terms. Peirce was innovative in showing that a three termed logic was important and it formed a significant part of his thought. Even in the 20th century many famous logicians oft times attempted to reduce to a two term logic what Peirce felt was irreducibly a three term logic.



In ordinary logical analysis such as is required in the algebraical or other purely formal treatment, it is sufficient to consider Category the Second as a two-sided element in the phenomenon, a Reaction, involving two objects which are differently related to one another, but having no general distinctive characters. In like manner Category the Third in the same analysis is regarded as a triadic element of the phenomenon without there being any reason for putting one of the triad of singulars which may be concerned in it as the First, rather than either of the others, nor any one as specially Second or Third. There are other purposes, however, for which it is necessary to conceive that in a reaction the first object [is distinguished] from the second by a general character common to all firsts, all seconds having their general character; and similarly in all triadic facts distinctive general characters are to be attributed to the First, the Second, and the Third of the three objects concerned. If two singulars A and B react upon one another, the action of A upon B and the action of B upon A are absolutely the same element of the phenomenon. Nevertheless, ordinary language makes the distinction of agent and patient, which, indeed, in the languages that are familiar to us is given great prominence; and this is the case with the majority of the languages of all families, as well as the Procrustean bed imposed by the grammarians allows us to make out their real character. But in all families, languages are found in which little or nothing is made of the distinction. In Gaelic, for example, the usual form of expression places what we should call the subject in an oblique case,-the genitive, in that language, but in some languages it is rather an ablative or an instrumental case. This distinction of agent and patient is sometimes useful even in philosophy. That is, a formal distinction is drawn between the action of A on B and the action of B on A although they are really the same fact. In the action of A on B, the patient B is conceived to be affected by A while the agent A is unaffected by B. A is modified in the action so far as to be in an active state; but this is conceived to be a certain Quality that the agent takes on during the action in which Quality the patient in no way participates, while the patient, on the other hand, takes on a relative character which can neither exist nor be conceived to exist except as correlative to an agent. That is the distinction of agent and patient. So in a triadic fact, say, for example

A gives B to C

We make no distinction in the ordinary logic of relations between the subject nominative, the direct object, and the indirect object. We say that the proposition has three logical subjects. We regard it as a mere affair that there are six ways of expressing this:

A gives B to C
A benefits C with B
B enriches C at expense of A
C receives B from A
C thanks A for B
B leaves A for C

These six sentences express one and the same indivisible phenomenon. Nevertheless, just as [in] conceiving of two reacting objects we may introduce the metaphysical distinction of agent and patient, so we may metaphysically distinguish the functions of the three objects denoted by the subject nominative, the direct object, and the indirect object. The subject nominative denotes that one of the three objects which in the triadic fact merely assumes a non-relative character of activity. The direct object is that object which in the triadic fact receives a character relative to that agent, being the patient of its action, while the indirect object receives a character which can neither exist nor be conceive( to exist without the cooperation of the other two. When I call Category th Third the Category of Representation in which there is a Represente Object, a Representamen, and an Interpretant, I recognize that distinction This mode of distinction is, indeed, germane to Thirdness, while it is alien to Secondness. That is to say, agent and patient as they are by themselves in their duality are not distinguished as agent and patient. The distinction lies in the mode of representing them in my mind, which is a Third. Thus there is an inherent Thirdness in this mode of distinction. But a triadic fact is in all cases an intellectual fact. Take giving for example. The mere transfer of an object which A sets down and C takes up does not constitute giving. There must be a transfer of ownership and ownership is a matter of Law, an intellectual fact. You now begin to see how the conception of representation is so peculiarly fit to typify the category of Thirdness. The object represented is supposed not to be affected by the representation. That is essential to the idea of representation. The Representamen is affected by [the] Object but is not otherwise modified in the operation of representation. It is either qualitatively the double of the object in the Icon, or it is a patient on which the object really acts, in the Index; or it is intellectually linked to the object in such a way as to be me tally excited by that object, in the Symbol.

It is desirable that you should understand clearly the distinction between the Genuine and the Degenerate Index. The Genuine Index represents the duality between the representamen and its object. As a whole it stands for the object; but a part or element of it represents [it] as being the Representamen, by being an Icon or analogue of the object in some way; and by virtue of that duality, it conveys information about the object. The simplest example ol genuine index would be, say, a telescopic image of a double star. This is not icon simply, because an icon is a representamen which represents its obje solely by virtue of its similarity to it, as a drawing of a triangle represents mathematical triangle. But the mere appearance of the telescopic image of a double star does not proclaim itself to be similar to the star itself. It is because we have set the circles of the equatorial so that the field must by physical compulsion contain the image of that star that it represents that star, and by that means we know that the image must be an icon of the star, and information is conveyed. Such is the genuine or informational index.

A Degenerate Index is a representamen which represents a single object because it is factually connected with it, but which conveys no information whatever. Such, for example, are the letters attached to a geometrical or other diagram. A proper name is substantially the same thing; for although in this case the connection of the sign with its object happens to be a purely mental association, yet that circumstance is of no importance in the functioning of the representamen. The use of letters as indices is not confined to mathematics. Lawyers particularly often discuss cases in which A contracts with B to do something. These letters are convenient substitutes for relative pronouns. A relative, demonstrative, or personal pronoun comes very near to being a mere index, if it be not accurately so. It is far more correct so to define it than to say that a pronoun is a word placed instead of a noun. It would be nearer right to say that a common noun, when subject nominative, is a word put in place of a pronoun. A degenerate index may be called a Monstrative Index, in contradistinction to an Informational or Genuine Index.

A proposition is a symbol which like the informational index has a special part to represent the representamen, while the whole or another special part represents the object. The part which represents the representamen and which excites an icon in the imagination, is the Predicate. The part which indicates the object or set of objects of the representamen is called the Subject or Subjects, in grammar the subject nominative, and the objects, each of which can be replaced by a Proper Name or other Monstrative Index without the proposition's ceasing thereby to be a proposition. How much shall be embraced in the predicate and how many subjects shall be recognized depends, for the ordinary analyses of logic, upon what mode of analysis will answer the purpose in hand. If from a proposition we strike out a part and leave its place blank, this part being such that a monstrative index being put in its place, the symbol will again become a proposition, the part which remains after such erasure will be a predicate of the kind which I call a monad. Here are examples:

___ gives B to C
A gives ___ to C
A gives B to ___

If two blanks remain, I call the predicate a dyad. Such are

____ gives ____ to C
____ gives B to ____
A gives ____ to ____

If there are more than two blanks, I call the predicate a polyad. The entire proposition may be regarded as a predicate, the circumstances under which it is uttered, the person who utters it, and all the surroundings constituting a monstrative index which will be the subject. I term an entire proposition without a blank when it is considered as a predicate a medad, from mhden. Every proposition whatever has the Universe of Discourse for one of its subjects and all propositions have one Subject in common which we call the Truth. It is the aggregate of all realities, what the Hegelians call the Absolute.

Thus, to include more in the predicate than need be included is merely not to carry logical analysis as far as it might be carried: it does not affect its accuracy. But to include anything in a subject which might be separated from it and left in the predicate is a positive fault of analysis. To say for example that "All men" is the subject of the proposition "All men are mortal" is incorrect. The true analysis is that "Anything" is the subject and"___ is mortal or else not a man" is the predicate. So in "Some cat is blue-eyed" the subject is not "some cat" but "something," the predicate being "___ is a blue-eyed cat." "Something" means that sufficient knowledge would enable us to replace the "something" by a monstrative index and still keep the proposition true. "Anything" means that the interpreter of the proposition is free to replace the "anything" by such monstrative index as he will, and still the proposition will be true. Logicians confine themselves, apart [from] monstrative indices themselves, to "Anything" and "Something," two descriptions of what monstrative index may replace the subject, the one description vague, the other general. No others are required since such subjects, "All but one," "All but two," "Almost all," "Two thirds of the occasions that present themselves in experience," and the like are capable of logical analysis.

Everybody who has studied logic is aware that the only formal fallacies which ordinary logic detects are confusions between "Anything" and "Something." The same thing remains true in the logic of relatives except that we now meet with fallacies owing to confusions about the order of succession of "Anything" and "Something" as if one should carelessly substitute for the proposition "Every man is born of some woman" the proposition "There is some woman of whom every man is born."

"The Categories Defended" Essential Peirce 2:170-173