In "How to Makes Our Ideas Clear" spends most his time clarifying the concept of force by working on what seem like an a priori explication of the a diagram, a "parallelogram of forces." However, concept of force is tied to our existential experiences of acceleration. This "purpose" guides the applications of the diagram to experience, the structuring of the diagram itself, and the testing of inferred consequences from it.
He then goes on to say, given his understanding of the concept of force, that:
Whether we ought to say that a force is an acceleration, or that it causes an acceleration, is a mere question of propriety of language, which has no more to do with our real meaning than the difference between the French idiom "Il fait froid" and its English equivalent "It is cold."But this is doesn't ring true. A mathematical diagram of forces is one thing, and a categorical diagram of causes is another. In fact, it would seem that modern science, among other things, was precisely this turning away from the Aristotelian causes for a mathematical renditions of forces. It was, thus, not a major shift when modern science shifted from causal explanations to statistical ones. It was simply a continuation of the mathematical manipulations of a very different concept, namely force.
Peirce describes this concept functioning as the basis for modern science:
This leads us to undertake an account of the idea of Force in general. This is the great conception which, developed in the early part of the seventeenth century from the rude idea of a cause, and constantly improved upon since, has shown us how to explain all the changes of motion which bodies experience, and how to think about all physical phenomena; which has given birth to modern science, and changed the face of the globe; and which, aside from its more special uses, has played a principal part in directing the course of modern thought, and in furthering modern social development.The rudeness of "idea of a cause" is apparently it's more rudimentary diagrammatic representation as Aristotle's four kinds of causes and what can be done with it compared to the mathematical representation of forces.