To prompt you, in this short course, to any thoughts that may hereafter prove of much value to you will draw upon such abilities as mine for all that they can render. Were I dealing with a special science the case would be different. A lecturer upon electricity, for example, if he lays down a general principle, at once shows you an experiment to illustrate it. If the experiment does not fully prove the principle,
Ladies and Gentlemen:
Let us take up the subject of necessary reasoning, mathematical reasoning, with a view to making out what its elementary steps are and how they are put together.
In order to do this it is necessary to replace the confused syntax of ordinary language by a system in which the meaning of every form is exactly defined, which is free from forms that cast a tinge of passion or of any kind of subjective feeling on the facts, and which has no more forms than are requisite in order to express every kind of fact or truth
so analytically as to in such a way as to enable us to carry the dissection of reasoning to its smallest steps. I shall Let us devote this evening's hour to forming such a system of expression.
Before beginning, let us distinctly recognize
the purpose which this system of expression is designed to fulfil. It is intended to enable us to separate reasoning into its smallest steps so that each one may be examined by itself. Observe, then, that it is not the purpose of this system of expression to facilitate reasoning and to enable one to reach his conclusions by [or "in"] the speediest manner. Were that our object, we should seek a system of expression which should reduce many steps to one; while our object is to subdivide one step into as many as possible. Our system is intended to facilitate the study of reasoning but not to facilitate reasoning itself. Its character is quite contrary to that purpose.
Let the blackboard represent the universe. As thus significant we will call it the sheet of assertion.
Let whatever I write upon the black board or sheet of assertion go toward making the representation
of the universe more determinate. Thus, I write
A pear is ripe
That represents that there is a pear and a ripe pear in the universe.
Necessary reasoning can never
ascertain answer questions of fact. It has to assume its premisses to be true. Therefore, in order to avoid the possibility of questioning what is written on the board, let us say that it is not the real universe that is represented by the board, but a universe existing in my imagination, concerning which you have no source information except my testimony. By the universe I mean the entire collection of things, or subjects of force, to which I imagine there are in the universe all that is going to be written on the board will relate. Logicians call such a collection of things, or subjects of force, to
which the whole of a discussion relates, the universe of discourse.
The system of expression which I have thus begun to describe will be found to be a system of diagrams. The mathematicians call a diagram that is composed mainly of spots of different kinds and lines, a graph. This system is called a system of existential graphs. In this system, the spots
are may be conveniently differentiated from one another by words written in them. The consequence is that a sign of this system is party drawn and partly written. For brevity, I always say it is scribed. Any sign conforming to the rules of this system which, if it were written placed on the board or sheet of assertion, would assert some intelligible state of things to be true of the universe of discourse, is called a graph. Strictly, I ought to say an existential graph; but for brevity