Part One: Invention (Foundations of Rhetoric)
Invention is concerned with generating material, that is finding something to say and determining how to say it persuasively. The term Latin inventio points at discovery rather than fabrication, so less about creating ideas from "nothing" but sifting and then assembling from already existing means. Classically rhetoric will categorize these into artistic proofs (internal to the speaker like logic or emotion) and inartistic proofs (external like laws, statistics).
Inventing Thinking
So rhetorical invention is yet another method of structured thinking/intelligence. It is a care-ful search for arguments. Factual (precedent, empirics), logical (causal relationships, definitions), anecdotal (narratives, analogies), or affective (sentimental, sensory (this is specific to the classical view)). Children naturally engage in invention when making simple arguments like "we should get a cat because they are soft and my friend has one" Here there is a mix of factual observation (cats are soft) + external precedent (my friend has one). The rhetorical tradition can be viewed and providing systematic techniques for collection of and structuring of thought.
In the Trivium model invention follows grammar and builds toward rhetoric. The important point is when reasoning gets its particular purpose. Logical thinking need not concern itself with persuasion but rhetoric does.
Example of progression:
Grammar: rain (naming)
Logic: rain causes plants to grow (reasoning)
Invention: rain is essential because it nourishes the earth, making life possible (set up for persuasion)
Techniques
Using Classical Topoi (Commonplaces)
Aristotle’s topoi are heuristics for invention (methods of discovering arguments). Examples:
Definition: What is its nature?
Comparison: How does it relate to similar things?
Cause and Effect: What leads to it, and what follows from it?
Testimony: What have others said about it?
Conclusion
Invention is the foundational action of rhetoric. ID'ing relevant material, giving a coherent structuring, and framing it effectively for a given audience are the keys.