Reading Graphs
Premises, values, lemmas, conclusions, truth, proof, and counterpoints.
The Smallest Useful Argument
A Concludia graph starts with statements. Premises sit at the bottom of a reasoning branch. Conclusions and lemmas sit above their sources. A connector between sources and a target means the sources are being offered as sufficient support for the target.
Premises
A premise is a statement whose truth is set directly. Concludia does not decide whether a sentence is semantically true. People do that work. The graph records what truth value is currently being used by the argument.
Factual premises are claims about how the world is. Value premises are claims about what should matter. Value premises are important because an ought-claim cannot be derived from facts alone.
Lemmas And Conclusions
A lemma is an intermediate result. It lets an argument build in stages instead of forcing every premise to point directly at the final conclusion. A conclusion is the statement the argument is trying to establish.
Both lemmas and conclusions get their proof status from their sources. If a lemma becomes not proven, anything that depends on it can also become not proven.
Counterpoints
Counterpoints are targeted objections. A counterpoint that contests a premise is called an undermine.
A counterpoint that contests an inference is called an undercut.
Reading Disagreement
When you disagree with a proven conclusion, move downward through the sources until you find the first place you stop agreeing. That place might be a factual premise, a value premise, or the inference that says the sources are sufficient.
When you see a not-proven conclusion, move downward through the contested source path until you find the premise or counterpoint responsible for the break.