Habits of reasoning: On the grammar and critics of logical habits

We explain the grammar and the critics of the habits of reasoning, using Peirce’s 1903 Lowell Lectures and the related Syllabus as the key textual source. We establish what Peirce took sound reasoning to be, and derive a major soundness result concerning his logic as semeiotic: an argument is valid if for any object that the premises represent, the conclusion represents it as well, which in semeiotic terms translates to a sign being a valid argument if for any object that the sign represents, the interpretant sign represents it as well. The perfect adherence of the grammar to the critics is evidenced by the un-eliminability of leading principles. Just as a logical leading principle is an un-eliminable element of reasoning, because any attempt to use it as a premise engenders an infinite regress, so a logical representative interpretant is a habit that cannot be rendered a sign. The logical representative interpretant is a principle not itself a premise, a rule not itself subject to rules, a habit not itself a sign.