Inference from particulars to particulars is also called analogy.
Peirce gave a fair account of the logic behind statistical inference, as used in the research sciences from before his time to the present day. That logic depends on a fair amount of probability theory, which Boole had already begun to cast as a generalization of classical logic, but a lot of the underlying logic of inquiry is already visible in the infrastructure at the level of propositional and predicate logic. And that much of the basic structure was more or less roughly outlined by Aristotle himself.
Here’s a set of notes on the role of abduction, deduction, induction, and analogy in inquiry, as seen in the works of Aristotle and Peirce.
More discussion of these topics can be found on the following pages.
- Prospects for Inquiry Driven Systems
- Introduction to Inquiry Driven Systems
- Inquiry Driven Systems • Inquiry Into Inquiry