Bibliography Record

By a Cut shall be understood to mean a self-returning linear separation (naturally represented by a fine-drawn or peculiarly colored line) which severs all that it encloses from the sheet of assertion on which it stands itself, or from any other area on which it stands itself. The whole space within the cut (but not comprising the cut itself) shall be termed the area of the cut.

A cut is not a graph-replica. A cut drawn upon the sheet of assertion severs the surface it encloses, called the area of the cut, from the sheet of assertion; so that the area of a cut is no part of the sheet of assertion.

An Argument is a Sign which, for its Interpretant, is a sign of law. Or we may say […] that an Argument is a Sign which is understood to represent its Object in its character as Sign.

An Argument is a sign whose interpretant represents its object as being an ulterior sign through a law, namely, the law that the passage from all such premisses to such conclusions tends to the truth. Manifestly, then, its object must be general; that is, the Argument must be a Symbol. As a Symbol it must, further, be a Legisign. Its Replica is a Dicent Sinsign.

A graph-replica is any individual instance of a graph. The sheet of assertion itself is a graph-replica; and so is any part of it, being called the blank.

By a Cut shall be understood to mean a self-returning linear separation (naturally represented by a fine-drawn or peculiarly colored line) which severs all that it encloses from the sheet of assertion on which it stands itself, or from any other area on which it stands itself.

A heavy dot scribed at the hook of a spot shall be understood as filling the corresponding blank of the rheme of the spot with an indefinite sign of an individual, so that when there is a dot attached to every hook, the result shall be a proposition which is particular in respect to every subject.

Two cuts one of which has the enclosure of the other on its area and has nothing else there constitute a double cut.

By a Cut shall be understood to mean a self-returning linear separation (naturally represented by a fine-drawn or peculiarly colored line) which severs all that it encloses from the sheet of assertion on which it stands itself, or from any other area on which it stands itself. The whole space within the cut (but not comprising the cut itself) shall be termed the area of the cut. Though the area of the cut is no part of the sheet of assertion, yet the cut together with its area and all that is on it, conceived as so severed from the sheet, shall, under the name of the enclosure of the cut, be considered as on the sheet of assertion or as on such other area as the cut may stand upon.

A cut drawn upon the sheet of assertion together with its area and whatever is scribed upon that area constitutes a graph-replica scribed upon the sheet of assertion, and is called the enclosure of the cut.

The graph which consists of all the graphs on the sheet of assertion, or which consists of all that are on any one area severed from the sheet, shall be termed the entire graph of the sheet of assertion or of that area, as the case may be.

All that is at any time scribed on the sheet of assertion is called the entire scribed graph.

Normative science has three widely separated divisions: i. Esthetics; ii. Ethics; iii. Logic.

Esthetics is the science of ideals, or of that which is objectively admirable without any ulterior reason. I am not well acquainted with this science; but it ought to repose on phenomenology.

Normative science has three widely separated divisions: i. Esthetics; ii. Ethics; iii. Logic.

… Ethics, or the science of right and wrong, must appeal to Esthetics for aid in determining the summum bonum. It is the theory of self-controlled, or deliberate, conduct.

A graph is the propositional expression in the System of Existential Graphs of any possible state of the universe. It is a Symbol, and, as such, general, and is accordingly to be distinguished from a graph-replica. A graph remains such though not actually asserted.

A graph is a legisign (i.e., a sign which is of the nature of a general type) which is one of a certain class of signs used in this system [of existential graphs].

A graph-replica is any individual instance of a graph.

The expression of a rheme in the system of existential graphs, as simple, that is without any expression, according to these conventions, of the analysis of its signification, and such as to occupy a superficial portion of the sheet or of any area shall be termed a spot. The word “spot” is to be used in the sense of a replica; and when it is desired to speak of the symbol of which it is the replica, this shall be termed a spot-graph. On the periphery of every spot, a certain place shall be appropriated to each blank of the rheme; and such a place shall be called a hook of the spot.

A spot is a graph any replica of which occupies a simple bounded portion of a surface, which portion has qualities distinguishing it from the replica of any other spot; and upon the boundary of the surface occupied by the spot are certain points, called the hooks of the spot, to each of which, if permitted, one extremity of one line of identity can be attached.

Science of Discovery is either, I. Mathematics; II. Philosophy; or III. Idioscopy.

Mathematics studies what is and what is not logically possible, without making itself responsible for its actual existence. Philosophy is positive science, in the sense of discovering what really is true; but it limits itself to so much of truth as can be inferred from common experience. Idioscopy embraces all the special sciences, which are principally occupied with the accumulation of new facts. [—]

Idioscopy has two wings: a. the Physical Sciences; and b. the Psychical, or Human Sciences.

Science of Discovery is either, I. Mathematics; II. Philosophy; or III. Idioscopy.

Mathematics studies what is and what is not logically possible, without making itself responsible for its actual existence. Philosophy is positive science, in the sense of discovering what really is true; but it limits itself to so much of truth as can be inferred from common experience. Idioscopy embraces all the special sciences, which are principally occupied with the accumulation of new facts. [—]

Idioscopy has two wings: a. the Physical Sciences; and b. the Psychical, or Human Sciences.

A collection composed of any line of identity together with all others that are connected with it directly or through still others is termed a ligature. Thus ligatures often cross cuts, and, in that case, are not graphs.

The totality of all the lines of identity that join one another is termed a ligature. A ligature is not generally a graph, since it may be part in one area and part in another. It is said to lie within any cut which it is wholly within.

A heavily marked line without any sort of interruption (though its extremity may coincide with a point otherwise marked) shall, under the name of a line of identity, be a graph, subject to all the conventions relating to graphs, and asserting precisely the identity of the individuals denoted by its extremities.

The line of identity is a Graph any replica of which, also called a line of identity, is a heavy line with two ends and without other topical singularity (such as a point of branching or a node), not in contact with any other sign except at its extremities. Otherwise, its shape and length are matters of indifference. All lines of identity are replicas of the same graph.

Science of Discovery is either, I. Mathematics; II. Philosophy; or III. Idioscopy.

Mathematics studies what is and what is not logically possible, without making itself responsible for its actual existence. Philosophy is positive science, in the sense of discovering what really is true; but it limits itself to so much of truth as can be inferred from common experience. Idioscopy embraces all the special sciences, which are principally occupied with the accumulation of new facts.

The graph which consists of all the graphs on the sheet of assertion, or which consists of all that are on any one area severed from the sheet, shall be termed the entire graph of the sheet of assertion or of that area, as the case may be. Any part of the entire graph which is itself a graph shall be termed a partial graph of the sheet or of the area on which it is.

Science of Discovery is either, I. Mathematics; II. Philosophy; or III. Idioscopy.

Mathematics studies what is and what is not logically possible, without making itself responsible for its actual existence. Philosophy is positive science, in the sense of discovering what really is true; but it limits itself to so much of truth as can be inferred from common experience. Idioscopy embraces all the special sciences, which are principally occupied with the accumulation of new facts.
[—]
Philosophy is divided into a. Phenomenology; b. Normative Science; c. Metaphysics.

A graph is the propositional expression in the System of Existential Graphs of any possible state of the universe. It is a Symbol, and, as such, general, and is accordingly to be distinguished from a graph-replica. A graph remains such though not actually asserted. An expression, according to the conventions of this system, of an impossible state of things (conflicting with what is taken for granted at the outset or has been asserted by the graphist) is not a graph, but is termed The pseudograph, all such expressions being equivalent in their absurdity.

By a rim shall be understood an oval line making it, with its contents, the expression either of a rheme or a proper name of an ens rationis.

By “science of review” is meant the business of those who occupy themselves with arranging the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science. Such is the nature of Humboldt’s Kosmos, of Comte’s Philosophie positive, and of Spencer’s Synthetic Philosophy. The classification of the sciences belongs to this department.

The graphist may place replicas of graphs upon the sheet of assertion; but this act, called scribing a graph on the sheet of assertion, shall be understood to constitute the assertion of the truth of the graph scribed. (Since by §1 the conventions are only “supposed to be” agreed to, the assertions are mere pretence in studying logic. Still they may be regarded as actual assertions concerning a fictitious universe.) “Assertion” is not defined; but it is supposed to be permitted to scribe some graphs and not others.

A pair of cuts, one within the other but not within any other cut that that other is not within, shall be called a scroll. The outer cut of the pair shall be called the outloop, the inner cut the inloop, of the scroll. The area of the inloop shall be termed the inner close of the scroll; the area of the outloop, excluding the enclosure of the inloop (and not merely its area), shall be termed the outer close of the scroll.

A symbol for a single individual, which individual is more than once referred to, but is not identified as the object of a proper name, shall be termed a Selective.

It is agreed that a certain sheet, or blackboard, shall, under the name of The Sheet of Assertion, be considered as representing the universe of discourse, and as asserting whatever is taken for granted between the graphist and the interpreter to be true of that universe. The sheet of assertion is, therefore, a graph.

1. The System of Existential Graphs is a certain class of diagrams upon which it is permitted to operate certain transformations.

2. There is required a certain surface upon which it is practicable to scribe the diagrams and from which they can be erased in whole or in part.

3. The whole of this surface except certain parts which may be severed from it by “cuts” is termed the sheet of assertion.

The expression of a rheme in the system of existential graphs, as simple, that is without any expression, according to these conventions, of the analysis of its signification, and such as to occupy a superficial portion of the sheet or of any area shall be termed a spot. The word “spot” is to be used in the sense of a replica; and when it is desired to speak of the symbol of which it is the replica, this shall be termed a spot-graph.

A spot is a graph any replica of which occupies a simple bounded portion of a surface, which portion has qualities distinguishing it from the replica of any other spot; and upon the boundary of the surface occupied by the spot are certain points, called the hooks of the spot, to each of which, if permitted, one extremity of one line of identity can be attached.

…a point upon which three lines of identity abut is a graph expressing the relation of teridentity.