The System of Existential Graphs is a certain class of diagrams upon which it is permitted to operate certain transformations.
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.
The whole of this surface except certain parts which may be severed from it by “cuts” is termed the sheet of assertion.
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.
The sheet on which the graphs are written (called the sheet of assertion), as well as each portion of it, is a graph asserting that a recognized universe is definite (so that no assertion can be both true and false of it), individual (so that any assertion is either true or false of it), and real (so that what is true and what false of it is independent of any judgment of man or men, unless it be that of the creator of the universe, in case this is fictive); and any graph written upon this sheet is thereby asserted of that universe; and any multitude of graphs written disconnectedly upon the sheet are all asserted of the universe.
What we have to do […] is to form a perfectly consistent method of expressing any assertion diagrammatically. The diagram must then evidently be something that we can see and contemplate. Now what we see appears spread out as upon a sheet. Consequently our diagram must be drawn upon a sheet. We must appropriate a sheet to the purpose, and the diagram drawn or written on the sheet is to express an assertion. We can, then, approximately call this sheet our sheet of assertion.
A certain sheet, called the sheet of assertion, is appropriated to the drawing upon it of such graphs that whatever may be at any time drawn upon it, called the entire graph, shall be regarded as expressing an assertion by an imaginary person, called the graphist, concerning a universe, perfectly definite and entirely determinate, but the arbitrary creation of an imaginary mind, called the grapheus.
The matter which the Graph-instances are to determine, and which thereby becomes the Quasi-mind in which the Graphist and Interpreter are at one, being a Seme of The Truth, that is, of the widest Universe of Reality, and at the same time, a Pheme of all that is tacitly taken for granted between the Graphist and Interpreter, from the outset of their discussion, shall be a sheet, called the Phemic Sheet, upon which signs can be scribed and from which any that are already scribed in any manner (even though they be incised) can be erased.