p.3-4 Peirce repeated on numerous occasions throughout his many works that diagrams illustrate the general course of thought (cf. "Prolegomena to an Apology for Pragmaticism", CP 4.530, 1906). This idea corresponds to his belief that reasoning is not a mechanical function, nor a closed mental faculty. Peirce's notion of reason, very distinct from the isolated and exclusionary conception of reason derived from rationalism, may be called "reasonableness". Reasonableness is an ideal to be incarnated in a creative way, and implies the human ability to introduce new intelligibility, to make sense of one’s own life and to try to make it reasonable, together with what surrounds it. Reasonable beings are creative beings, growing, seeking to expand their ideas, generating new meanings, seeking truth through science and developing habits that help them to live and communicate better.

p.4 Around 1902, Peirce wrote: "The essence of rationality lies in the fact that the rational being will act so as to attain certain ends. Prevent his doing so in one way, and he will act in some utterly different way which will produce the same result. Rationality is being governed by final causes" (CP 2.66, c.1902). Reason is not something separated which dissects problems, nor is it merely consciousness. The essence of reason is thirdness, allowing us to connect things together, allowing us to compose (cf. CP 6.343, 1908). 

p.5 Diagrams are, according to Peirce, an essential part of certain types of reasoning, for example, of mathematical reasoning, which "consists in constructing a diagram according to a general precept, in observing certain relations between parts of that diagram not explicitly required by the precept, showing that these relations will hold for all such diagrams, and in formulating this conclusion in general terms" (CP 1.54, c.1896). The diagram expresses the abstract relationships between the premises from which a hypothesis emerges. In order to test it, experiments are made on the diagram, which is changed in various ways until the right one is found (cf. CP 2.778, 1901).

In short, according to Peirce, thought is illustrated, and drawings and diagrams, built with the help of the imagination, are a central part of the activity of our mind.