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.

Facts and values supporting a conclusion
The fact premise and value premise combine through an AND connector. Because both premises are true, the conclusion is proven.

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 contested premise
The counterpoint attacks P1. The premise remains textually true in the base argument, but its effective truth is blocked, so the conclusion is not proven.

A counterpoint that contests an inference is called an undercut.

An undercut
The counterpoint targets the inference into C1 rather than either premise. The conclusion is not proven even though both source premises are true.

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.