A true conclusion.
A faulty argument.
One example can agree. Another can undo it.
Build both, and see what really follows.
Aristotle · Prior Analytics · Fourth century BCE
Greek, close English, and teaching Latin.
Your world
Each + places one object. Select its number to remove it.
Inside a circle = belongs to that class; outside = does not.
Inspect this world
Read every object as a sentence
Circles are a modern tool. Only the placed objects exist in this finite world; circle area does not imply an inhabitant.
Try the investigation
A route through this experiment
Aristotle changes the terms: animal / human / horse, then animal / human / stone. These buttons place a small illustrative world for each substitution.
Can a counterexample exist?
An agreeing world is not a proof. Inspect all permitted membership patterns when you are ready to check the inference.
| Pattern class | Count |
|---|
Where could the counterexample’s witness go?
One representative per occupied region is enough. Read the completeness argument.
Which inhabitant does the work?
Compare what follows when different classes must have an object.
Compare all eight inhabitant requirements
Select a requirement to keep the objects. Select object numbers to load a refutation.
How to compare the requirements
Select a requirement in the first column. Every placed object stays where it is. An example can become inadmissible when it lacks a newly required inhabitant.
Select object numbers in the last column to load a smallest refutation and that row’s requirements. Then require more inhabitants: does your example still qualify?
A sufficient setting must permit at least one world. “Weakest” means removing any of its requirements allows a refutation. The rows are modern model comparisons, not historical verdicts on Aristotle.
The highlighted row uses the board’s current requirements.
Inspect the current world on the board. Use the board’s inhabitant checkboxes to return to this comparison.
Put two worlds side by side.
Pin a world to hold it still while you change the live one.
Read the move in Greek.
Back to the experimentClose English
Teaching Latin · a new translation
This Latin is written for the workshop. It is not an ancient or medieval witness.
Edition, transcription, and attribution
Retained-file identities · Source notice · Compare Jenkinson’s public-domain English translation
Keep the reasoning.
Save both worlds, the assumptions, and your explanation. The illustrated notebook carries every reading and complete source page. It opens offline.
Your prose is preserved, not automatically graded. Undo and redo name the action they change. Save a notebook before closing this tab.
Your portable notebook
Files stay on your device. An explicit shared link includes your explanation.
For a PDF, open the saved illustrated notebook and use your browser’s Print command.
What this experiment can tell you.
A modern model beside an ancient text
The circles represent three classes. Every object either belongs or does not belong to each class. “Every” and “no” have no violating instance; “some” and “some not” require an instance. “Some” means at least one, and can include all.
Universal statements here are true when their subject class is empty. Existence is an additional, visible requirement. The checkboxes let you test this convention; they do not reproduce a complete historical theory of Aristotle’s existential assumptions. The third-figure passage actually takes an instance.
The app checks these membership assignments, not the truth of claims about animals, ethics, science, or law. It does not model modality, relations, changing time, or all of ancient logic. A failed proposed conclusion does not imply that no other conclusion follows.
Why eight places are enough
Three memberships, each yes or no, give eight possible regions. All four kinds of statement used here ask only whether certain regions are empty or occupied. They never count objects.
From any counterexample, however large, keep one representative of each occupied region. Every premise, conclusion, and class-existence condition keeps the same truth value. Conversely, each nonempty occupancy pattern is itself a finite world.
There are 28 = 256 patterns. The completely empty universe is excluded, leaving 255. Checking all of them is exhaustive for this defined model, not merely a sample of small examples. The proof would not apply unchanged to sentences about “exactly two”, identity, or relationships.
The pattern of an argument
Greek “A belongs to every B” corresponds to English “Every B is A”. The source’s Γ is our C. In I.6 the source’s Π / Ρ / Σ become A / B / C; Ν is the selected instance. The translated letter names are a reading aid.