Bibliography

New Elements (Kaina stoiceia)

An affirmation is an act of an utterer of a proposition to an interpreter, and consists, in the first place, in the deliberate exercise, in uttering the proposition, of a force tending to determine a belief in it in the mind of the interpreter. Perhaps that is a sufficient definition of it; but it involves also a voluntary self-subjection to penalties in the event of the interpreter’s mind (and still more the general mind of society) subsequently becoming decidedly determined to the belief at once in the falsity of the proposition and in the additional proposition that the utterer believed the proposition to be false at the time he uttered it.

I have already defined an argument as a sign which separately monstrates what its intended interpretant is, and a proposition as a sign which separately indicates [what] its object is; and we have seen that the icon alone cannot be a proposition while the symbol alone can be an argument. [—] It will be observed that an argument is a symbol which separately monstrates (in any way) its purposed interpretant.

The man is a symbol. Different men, so far as they can have any ideas in common, are the same symbol. Judgment is the determination of the man-symbol to have whatever interpretant the judged proposition has. Assertion is the determination of the man-symbol to determining the interpreter, so far as he is interpreter, in the same way.

An axiom is a self-evident truth, the statement of which is superfluous to the conclusiveness of the reasoning, and which only serves to show a principle involved in the reasoning. It is generally a truth of observation; such as the assertion that something is true.

A belief in a proposition is a controlled and contented habit of acting in ways that will be productive of desired results only if the proposition is true.

A corollary, as I shall use the word, is an inference drawn in general terms without the use of any construction.

A definition is the logical analysis of a predicate in general terms. It has two branches, the one asserting that the definitum is applicable to whatever there may be to which the definition is applicable; the other (which ordinarily has several clauses), that the definition is applicable to whatever there may be to which the definitum is applicable. A definition does not assert that anything exists.

A diagram is an icon or schematic image embodying the meaning of a general predicate; and from the observation of this icon we are supposed to construct a new general predicate.

If the cause […] is a part of the causatum, in the sense that the causatum could not logically be without the cause, it is called an internal cause; otherwise, it is called an external cause. If the cause is of the nature of an individual thing or fact, and the other factor requisite to the necessitation of the causatum is a general principle, I would call the cause a minor, or individuating, or perhaps a physical cause. [—] The individuating external cause is called the efficient, or efficient cause; and the causatum is called the effect.

The purpose of every sign is to express “fact,” and by being joined with other signs, to approach as nearly as possible to determining an interpretant which would be the perfect Truth, the absolute Truth, and as such (at least, we may use this language) would be the very Universe. Aristotle gropes for a conception of perfection, or entelechy, which he never succeeds in making clear. We may adopt the word to mean the very fact, that is, the ideal sign which should be quite perfect, and so identical, – in such identity as a sign may have, – with the very matter denoted united with the very form signified by it. The entelechy of the Universe of being, then, the Universe qua fact, will be that Universe in its aspect as a sign, the “Truth” of being. The “Truth,” the fact that is not abstracted but complete, is the ultimate interpretant of every sign.

If the cause […] is a part of the causatum, in the sense that the causatum could not logically be without the cause, it is called an internal cause; otherwise, it is called an external cause. If the cause is of the nature of an individual thing or fact, and the other factor requisite to the necessitation of the causatum is a general principle, I would call the cause a minor, or individuating, or perhaps a physical cause. If, on the other hand, it is the general principle which is regarded as the cause and the individual fact to which it is applied is taken as the understood factor, I would call the cause major, or defining, or perhaps a psychical cause. [—] The defining external cause is called the final cause, or end.

If the cause […] is a part of the causatum, in the sense that the causatum could not logically be without the cause, it is called an internal cause; otherwise, it is called an external cause. If the cause is of the nature of an individual thing or fact, and the other factor requisite to the necessitation of the causatum is a general principle, I would call the cause a minor, or individuating, or perhaps a physical cause. If, on the other hand, it is the general principle which is regarded as the cause and the individual fact to which it is applied is taken as the understood factor, I would call the cause major, or defining, or perhaps a psychical cause. [—] The defining internal cause is called the formal cause, or form.

If the cause […] is a part of the causatum, in the sense that the causatum could not logically be without the cause, it is called an internal cause; otherwise, it is called an external cause. If the cause is of the nature of an individual thing or fact, and the other factor requisite to the necessitation of the causatum is a general principle, I would call the cause a minor, or individuating, or perhaps a physical cause. If, on the other hand, it is the general principle which is regarded as the cause and the individual fact to which it is applied is taken as the understood factor, I would call the cause major, or defining, or perhaps a psychical cause. [—] The defining internal cause is called the formal cause, or form.

Of signs there are two different degenerate forms. But though I give them this disparaging name, they are of the greatest utility, and serve purposes that genuine signs could not. The more degenerate of the two forms (as I look upon it) is the icon. This is defined as a sign of which the character that fits it to become a sign of the sort that it is, is simply inherent in it as a quality of it.[—]

An icon is a sign fit to be used as such because it possesses the quality signified.

The other form of degenerate sign is to be termed an index. It is defined as a sign which is fit to serve as such by virtue of being in a real reaction with its object. For example, a weathercock is such a sign. It is fit to be taken as an index of the wind for the reason that it is physically connected with the wind. A weathercock conveys information; but this it does because in facing the very quarter from which the wind blows, it resembles the wind in this respect, and thus has an icon connected with it. In this respect it is not a pure index. A pure index simply forces attention to the object with which it reacts and puts the interpreter into mediate reaction with that object, but conveys no information. As an example, take an exclamation “Oh!” The letters attached to a geometrical figure are another case. Absolutely unexceptionable examples of degenerate forms must not be expected. All that is possible is to give examples which tend sufficiently in towards those forms to make the mean suggest what is meant. [—]

An index is a sign fit to be used as such because it is in real reaction with the object denoted.

Besides the logical depth and breadth, I have proposed (in 1867) the terms information and area to denote the total of fact (true or false) that in a given state of knowledge a sign embodies.

… every sign is intended to determine a sign of the same object with the same signification or meaning. Any sign, B, which a sign, A, is fitted so to determine, without violation of its, A’s, purpose, that is, in accordance with the ‘Truth,’ even though it, B, denotes but a part of the objects of the sign, A, and signifies but a part of its, A’s, characters, I call an interpretant of A.

A judgment is a mental act deliberately exercising a force tending to determine in the mind of the agent a belief in the proposition; to which should perhaps be added that the agent must be aware of his being liable to inconvenience in the event of the proposition’s proving false in any practical aspect.

The man is a symbol. Different men, so far as they can have any ideas in common, are the same symbol. Judgment is the determination of the man-symbol to have whatever interpretant the judged proposition has..

A proposition […] is not to be understood as the lingual expression of a judgment. It is, on the contrary, that sign of which the judgment is one replica and the lingual expression another. But a judgment is distinctly more than the mere mental replica of a proposition. It not merely expresses the proposition, but it goes further and accepts it.

Logic, for me, is the study of the essential conditions to which signs must conform in order to function as such. How the constitution of the human mind may compel men to think is not the question; and the appeal to language appears to me to be no better than an unsatisfactory method of ascertaining psychological facts that are of no relevancy to logic.

[—]

Logic is the study of the essential nature of signs.

The totality of the subjects, and also, indifferently, the totality of the real objects of a sign, is called the logical breadth.

The totality of the predicates of a sign, and also the totality of the characters it signifies, are indifferently each called its logical depth.

If the cause […] is a part of the causatum, in the sense that the causatum could not logically be without the cause, it is called an internal cause; otherwise, it is called an external cause. If the cause is of the nature of an individual thing or fact, and the other factor requisite to the necessitation of the causatum is a general principle, I would call the cause a minor, or individuating, or perhaps a physical cause. [—] The individuating internal cause is called the material cause. Thus the integrant parts of a subject or fact form its matter, or material cause.

A postulate is an initial hypothesis in general terms. It may be arbitrarily assumed provided that (the definitions being accepted) it does not conflict with any principle of substantive possibility or with any already adopted postulate. By a principle of substantive possibility, I mean, for example, that it would not be admissible to postulate that there was no relation whatever between two points, or to lay down the proposition that nothing whatever shall be true without exception. For though what this means involves no contradiction, it is in contradiction with the fact that it is itself asserted.

Of the two great tasks of humanity, Theory and Practice, the former sets out from a sign of a real object with which it is acquainted, passing from this, as its matter, to successive interpretants embodying more and more fully its form, wishing ultimately to reach a direct perception of the entelechy; while the latter, setting out from a sign signifying a character of which it has an idea, passes from this, as its form, to successive interpretants realizing more and more precisely its matter, hoping ultimately to be able to make a direct effort, producing the entelechy.

If a sign, B, only signifies characters that are elements (or the whole) of the meaning of another sign, A, then B is said to be a predicate (or essential part) of A.

It is remarkable that while neither a pure icon nor a pure index can assert anything, an index which forces something to be an icon, as a weathercock does, or which forces us to regard it as an icon, as the legend under a portrait does, does make an assertion, and forms a proposition. This suggests the true definition of a proposition, which is a question in much dispute at this moment. A proposition is a sign which separately, or independently, indicates its object.

A proposition […] is not to be understood as the lingual expression of a judgment. It is, on the contrary, that sign of which the judgment is one replica and the lingual expression another.

…a geometrical figure drawn on paper may be an icon of a triangle or other geometrical form. If one meets a man whose language one does not know and resorts to imitative sounds and gestures, these approach the charac­ter of an icon. The reason they are not pure icons is that the purpose of them is emphasized. A pure icon is independent of any purpose. It serves as a sign solely and simply by exhibiting the quality it serves to signify. The relation to its object is a degenerate relation. It asserts nothing. If it conveys informa­tion, it is only in the sense in which the object that it is used to represent may be said to convey information. An icon can only be a fragment of a completer sign.

A weathercock conveys information; but this it does because in facing the very quarter from which the wind blows, it resembles the wind in this respect, and thus has an icon connected with it. In this respect it is not a pure index. A pure index simply forces attention to the object with which it reacts and puts the interpreter into mediate reaction with that object, but conveys no information. As an example, take an exclamation “Oh!” The letters attached to a geometrical figure are another case. Absolutely unexceptionable examples of degenerate forms must not be expected. All that is possible is to give examples which tend sufficiently in towards those forms to make the mean suggest what is meant.

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.

If a sign, A, only denotes real objects that are a part or the whole of the objects denoted by another sign, B, then A is said to be a subject (or substantial part) of B.

A symbol is defined as a sign which becomes such by virtue of the fact that it is interpreted as such. The signification of a complex symbol is determined by certain rules of syntax which are part of its meaning. A simple symbol is interpreted to signify what it does from some accidental circumstance or series of circumstances, which the history of any word illustrates. [–] A symbol is adapted to fulfill the function of a sign simply by the fact that it does fulfill it; that is, that it is so understood. It is, therefore, what it is understood to be. [—] Hardly any symbol directly signifies the characters it signifies; for whatever it signifies it signifies by its power of determining another sign signifying the same character.

A symbol is defined as a sign which is fit to serve as such simply because it will be so interpreted.

[—] A symbol is a sign fit to be used as such because it determines the interpretant sign.

…the most characteristic aspect of a symbol is its aspect as related to its interpretant; because a symbol is distinguished as a sign which becomes such by virtue of determining its interpretant. An interpretant of a symbol is an outgrowth of the symbol.

[—]

A symbol is essentially a purpose, that is to say, is a representation that seeks to make itself definite, or seeks to produce an interpretant more definite than itself. For its whole signification consists in its determining an interpretant; so that it is from its interpretant that it derives the actuality of its signification.

[—]

A symbol is an embryonic reality endowed with power of growth into the very truth, the very entelechy of reality. This appears mystical and mysterious simply because we insist on remaining blind to what is plain, that there can be no reality which has not the life of a symbol.

A theorem, as I shall use the word, is an inference obtained by constructing a diagram according to a general precept, and after modifying it as ingenuity may dictate, observing in it certain relations, and showing that they must subsist in every case, retranslating the proposition into general terms.

Of the two great tasks of humanity, Theory and Practice, the former sets out from a sign of a real object with which it is acquainted, passing from this, as its matter, to successive interpretants embodying more and more fully its form, wishing ultimately to reach a direct perception of the entelechy; while the latter, setting out from a sign signifying a character of which it has an idea, passes from this, as its form, to successive interpretants realizing more and more precisely its matter, hoping ultimately to be able to make a direct effort, producing the entelechy. But of these two movements, logic very properly prefers to take that of Theory as the primary one.

The purpose of every sign is to express “fact,” and by being joined with other signs, to approach as nearly as possible to determining an interpretant which would be the perfect Truth, the absolute Truth, and as such (at least, we may use this language) would be the very Universe. Aristotle gropes for a conception of perfection or entelechy, which he never succeeds in making clear. We may adopt the word to mean the very fact, that is, the ideal sign which should be quite perfect, and so identical, - in such identity as a sign may have, with the very matter denoted united with the very form signified by it. The entelechy of the Universe of being, then, the Universe qua fact, will be that Universe in its aspect as a sign, the “Truth” of being. The “Truth,” the fact that is not abstracted but complete, is the ultimate interpretant of every sign.