Part One: Terms and Propositions

Logic occupies the second stage of the Trivium, following grammar and preceding rhetoric. It takes the terms established in grammar—words or phrases designating objects or concepts—and organizes them into propositions, which are statements asserting something about reality.

Logical Reasoning

In one view, terms can serve as basic units of thought, labeling either concrete entities (table, river) or abstractions (freedom, equality). These have implicit use in everyday language. Propositions emerge when terms are combined into statements, such as "The river flows," linking "river" and "flows" into a testable claim. This shift (from terms to propositions) initiates structured reasoning, enabling evaluation of truth or falsity.

Analysis of (the proposition) "All trees grow" involves isolating its terms (trees, grow) and then assessing the statement’s validity. This process reveals contradictions or overstatements naturally, even in informal settings. Children engage this when they question, "Do all insects bite?"— putting (testing) "insects" against "bite" based on observation and sense.

Examples of Reasoning

- Take a term like "cloud" and form the proposition "Clouds rain." Does this always hold?

- Examine "Fire burns" but consider edge cases: Is it true for all fires?

These rely on intuitive scrutiny/care rather than formal systems, mirroring how reasoning develops organically.

Notes

"This is bad" hinges on "bad," which lacks 'precision' without context—bad how? Vague terms complicate analysis. Overgeneralization, as in "all dogs bark," often collapses under scrutiny, mute breeds disproving that. Precision in terms and care in forming propositions is fundamental.

Conclusion

For this view in this Trivium, the progression terms --> propositions reflects an intellectual shift, as in how children move from naming (cat) to asserting (cats climb) and then questioning (do all cats climb?). This should be the mirror of broader developmental arcs from concrete to abstract thought. Propositions hinge simplistic identification and progressive argumentation, setting the stage for rhetoric.

Logic’s structures thought. The quiet work of connecting and testing ideas is the important thing here, a process that scales from daily decisions to complex ideation, arguments, etc..