Concludia Introduction

Build and explore the reasoning behind conclusions.

Have you ever heard someone make an assertion about the way the world works, or about something that should be done, and doubted whether they were correct? You've wanted to ask them "Why?" but were not able to get a satisfying response. Or perhaps you simply believed they were wrong, either from bad reasoning, or because they might be basing their assertion on something they believe is true, but is actually false.

Or perhaps you yourself have come to a conclusion - one that is counterintuitive. It has a deep argument behind it that is difficult to communicate. You believe it to be convincing, but your audience might disagree with it on a number of different grounds that might vary from person to person. You have answers for each person, but have difficulty reaching them.

Concludia is a way for people to communicate these arguments to each other, fully and completely. It displays conclusions, reasoning, the premises behind them, and the logical relationships between each. It also shows the truth of the premises that the conclusions rest upon, and it propagates truth throughout the arguments to display the provability of each conclusion.

Basic Concepts

Concludia uses three-valued truth. A premise can be True, False, or Unknown.

If you create a box that says "All humans live on Jupiter", it is completely allowable to set it to True.

This is because Concludia has no semantic-level understanding of sentences. Concludia does, however, have syntax-level understanding. If you create two premises and set them to True, and then join them with an AND connector, the connector will forward a True signal, and the output will by definition be Proven (⊢).

If either or both premises are set to False, the connector will forward a False signal, and the output will by definition change to Not Proven (⊬).

Since each output can in turn be an input to another conclusion, the truth values spread throughout the argument. We call this "truth propagation".

Because of this machinery, two things are true:

Users can only adjust truth values on premises; all other truth values propagate from premises.
All arguments are guaranteed valid on a syntax level.

What does Truth mean in Concludia?

With Concludia, these Truth values correspond to provability. If one or more of the premises are False, it does not mean that the conclusion is false. Instead, it means that it is false that the conclusion is proven. In the above example, I might actually be the only soul living on Jupiter, while everyone else is back on Earth. So the statement "I live on Jupiter" might very well be true, even though the argument is "not proven" due to faulty reasoning.

This should match an intuition about long proofs or arguments. If you have a conclusion backed by a lengthy argument, and you believe the conclusion to be true, but then discover one of its underlying premises is false, it does not necessarily mean your conclusion is false. It may still be true; you would just have to find a different way to prove it.

Note, however, that in common usage of the word, if you do successfully prove a conclusion, it is allowable to also say it is True.

Syntax versus Semantics

Just because a sentence is proven on a syntax level does not mean it is actually proven on a semantics level. As discussed above, Concludia's machinery does not understand the semantic meaning of sentences.

We rely on each other as humans to check each other's meanings. So if you come across a premise that is marked True, and believe it is not actually True, Concludia allows this to be contested. This is called an 'undermine': a counterpoint that contests a premise.

Similarly, if you come across a conclusion that is marked proven, but you disagree that its sources justify the conclusion, Concludia allows a way for you to contest the proof. This is called an 'undercut': a counterpoint that contests an inference.

It is also possible to connect LLM models to Concludia to add semantic understanding. A model can help you construct your argument, identify counterpoints, and respond to the counterpoints of others.

Normativity

Concludia supports two styles of premises.

Facts are understood to reflect reality. As such, their truth values are shared for all users. Facts might be wrong, in which case they can be contested, but the truth values are not allowed to vary from person to person.

Values are personal opinions, or moral axioms. I might believe Liberty is more important than Life; you might believe the opposite. As such, we can each assign our own truth values, called "stances".

In either case, truth propagates normally. This means that a normative conclusion might have different truth values from person to person.

Uses

If people use Concludia to fully communicate their arguments, then other people can use Concludia to fully understand these arguments. Additionally, through community engagement, the arguments themselves can be strengthened. The hope is that as usage increases, people will better be able to understand each other and respect each other's points of view.

Alpha notice

Concludia is a work-in-progress prototype. By using it, you acknowledge:

Bugs and downtime are expected.
Features and behavior may change without notice.
Data may be reset or lost as the system evolves.
Please don't enter sensitive personal information. A full privacy policy hasn't been written yet.