Week 3 Philosophy Workshop: The Planetarium and the Sealed Dome

Part 1 — The Big Picture

This week you met Plato's theory of Forms and the allegory of the cave, separated appearance from reality, and put two arguments for the Forms in standard form. In this workshop you take one illustrative packet from a planetarium, reconstruct four short arguments about a projected sky, key each one for validity, and break one invalid form with a counterexample of your own. Then you test the cave with a labelled variation, a sealed dome whose projection is flawless, and ask which way it pulls your intuition. You write a short dialogue between a defender of the Forms and a critic who presses the access objection, each in their strongest form. Last, you check a chatbot's version of the same work and correct its slips by hand. The habit you practice here, stating a view at its strongest before testing it, is the one every later week uses.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: Which of the planetarium's four arguments are valid, how can you show that the invalid ones fail, and does a flawless projection change whether the sealed-dome visitors know the sky, or only how good their appearances are?

Workshop data: Planetarium packet: four illustrative arguments and the sealed-dome variation of the allegory of the cave

Source: An illustrative packet of four short arguments and one variation of a thought experiment written for this course's workshop; it describes no real planetarium or person, and its premises are written for teaching, not claims the course endorses.

• Rows: 4 arguments (A1 to A4) and 1 variation; the reconstruction table has 4 rows and the variation table has 3
• Arguments: A1 the unshifting stars; A2 the visitor who can tell; A3 the smudged star charts; A4 the visitor who leaves
• Variation: a sealed dome whose flawless projection matches the real sky, labelled as a variation of the allegory of the cave

Part 3 — Materials & Procedure

Tools and materials

• A free word processor or note-taking app for arguments in standard form and short dialogues, with the pinned public-domain texts on Project Gutenberg and the Internet Classics Archive open beside it; and one approved chatbot used as a sparring partner whose reconstructions, quotations, and attributions the student checks word for word against the pinned text and record before trusting them
• A free word processor or note-taking app
• One approved chatbot

Ways of working

• reconstruct-the-argument
• test-the-thought-experiment
• write-the-dialogue

Procedure

1. Read the planetarium packet in Part 2 twice. In your notes, copy each of A1 to A4 into standard form: number the premises P1 and P2, and write the conclusion last as C, introduced by So. Tool: A free word processor or note-taking app. Check: Four reconstructions, each with two numbered premises and one conclusion line that begins with So.
2. For each argument, write what P and Q stand for, name the form, and fill in the first table with valid or invalid and a one-sentence reason that uses the definition of validity. Tool: A free word processor or note-taking app. Check: Every row of the first table has letters, a named form, a key, and a reason; no row says sound or unsound.
3. Count the valid and invalid arguments in the second table, showing the subtraction from the 4 arguments in the packet. Then build a counterexample to A2's form with everyday content anyone can check. Check: A count with its subtraction shown, and a counterexample that keeps A2's form line for line with true premises and a false conclusion.
4. Fill in the third table to test the cave with the sealed-dome variation: say what the original case shows, what the variation changes, and which way the variation pulls your intuition about knowledge. Check: Each row names a feature of the case, the variation is labelled as a variation, and the last column says which way the intuition moves.
5. Write a short dialogue of four to six lines between a defender of Plato's theory of Forms and a critic who presses the access objection about the sealed dome. Give each speaker their strongest point, and end with one plain sentence naming where they disagree. Tool: A free word processor or note-taking app. Check: Each speaker answers the other, neither is a weakened version, and a closing sentence names the disagreement.
6. Paste the prompt from Part 6 into one approved chatbot after your completed work, read its reply, and write the critique report. Or, on the equivalent route, mark up the printed flawed analysis instead. Tool: One approved chatbot. Check: A report that quotes at least two slips and corrects each by hand against the packet and Chapter 3.

Fallback route

When to use it: Use this route if you cannot open a word processor or a note-taking app.

Copy the three tables by hand onto paper or into any text file, read the packet from this page, write the four reconstructions, the count, the counterexample, the variation table, and the dialogue by hand, and complete every analysis question and the critique step in the same order. Submit a photo or scan of the paper, or the text file, for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

Lay out each argument's shape before you judge it, so the key rests on form and not on how the conclusion sounds.

Student scaffold table 1

Argument	P and Q stand for	Form	Valid or invalid	Reason from the definition
A1 (the unshifting stars)
A2 (the visitor who can tell)
A3 (the smudged star charts)
A4 (the visitor who leaves)

Count the keys so every number you report traces back to the table above.

Student scaffold table 2

Count	Number	How you got it
Arguments in the packet	4	Given in the packet
Valid arguments
Invalid arguments

Set the original case beside the variation, so you can see exactly what the variation changes.

Student scaffold table 3

Feature	The cave (original case)	The sealed dome (variation)	Which way the intuition pulls
What the viewers see	Shadows on the wall
How close the appearance is to the real thing		A flawless projection
Whether the viewers know the real thing

Part 5 — Analysis Questions

1. How many of the packet's 4 arguments are valid and how many are invalid? Show the subtraction, and name the form of each valid one.
2. Build a counterexample to the form of A2 and explain, in one plain sentence, what it shows about A2.
3. Using your variation table, explain whether a flawless projection would give the sealed-dome visitors knowledge of the sky or only better appearances, and say which of this week's ideas your answer relies on.
4. In your dialogue, what is the strongest point each speaker makes, and where exactly do they disagree? End with one plain sentence.
5. What can a validity check not tell you about A1 or A3, and what can the sealed-dome variation not show about whether the Forms exist?
6. Choose one reflection: (a) which argument in the packet did you first key the wrong way, and what in the definition of validity changed your mind? or (b) which side of your dialogue did you start out agreeing with, and did your view survive writing the other side at its strongest?

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

I've completed my reconstruction table, my tally, my variation table, and my short dialogue above. Here is an illustrative workshop packet from my philosophy course. Planetarium packet (illustrative): in a domed planetarium, a guide and three visitors give four short arguments. A1: If the stars on the dome were the real sky, they would shift as the night goes on. The stars on the dome do not shift as the night goes on. So the stars on the dome are not the real sky. A2: If a visitor has seen the real sky, the visitor can tell the dome is a projection. This visitor can tell the dome is a projection. So this visitor has seen the real sky. A3: If every printed star chart in the gift shop has smudged dots, then no printed chart is a perfect map of the sky. Every printed star chart in the gift shop has smudged dots. So no printed chart is a perfect map of the sky. A4: If a visitor never leaves the dome, the visitor never sees the real sky. This visitor leaves the dome. So this visitor sees the real sky. The sealed dome (a variation of the allegory of the cave, written for this workshop): visitors raised inside the dome have only ever seen its projection, and the projection is flawless, matching the real sky star for star. Please do six things. First, put each of A1 to A4 in standard form, name its form, and say whether it is valid and whether it is sound. Second, tell me who wrote the allegory of the cave, in which book of the Republic it appears, and in what year it was written, and quote its opening lines in Plato's own words. Third, tell me who tells the story of the ring of Gyges, and give me one quotation from Plato about the Forms. Fourth, give me one other famous argument about appearance and reality, with its source, and say whether this idea belongs only to Greek philosophy. Fifth, summarize the debate between a defender of Plato's theory of Forms and a critic who presses the access objection about the sealed dome. Sixth, say which side is right, and end with a balanced summary.

Test the response for these likely failures:

• Chatbots often call A2 valid, reading 'the visitor can tell, so the visitor has seen the sky' as modus ponens, or call A4 valid because leaving the dome sounds like enough to see the sky.
• Chatbots often say A1 is sound, or that it proves the dome is not the sky, without asking whether its first premise is true.
• Chatbots sometimes say Socrates wrote the allegory of the cave, or call it Socrates' own thought experiment.
• Chatbots often place the cave in the wrong book of the Republic, or give an exact year of writing as if it were settled.
• Asked for the opening lines in Plato's own words, chatbots often print an English translation and present it as what Plato wrote.
• Chatbots sometimes supply a quotation from Plato about the Forms, or a line from the ring story, that the course has never pinned.
• Asked for another famous argument about appearance and reality, chatbots often offer 'I think, therefore I am' and place it in Descartes' Meditations.
• Asked whether the idea belongs only to Greek philosophy, chatbots sometimes say that questioning appearances is a Greek invention, or treat the European tradition as the whole of philosophy.
• Chatbots often reduce Plato's view to 'nothing we see is real', or reduce the critic's access objection to 'Plato made it up'.
• Asked which side is right, chatbots often announce that the Forms exist, or that they plainly do not.
• Chatbots often end a 'balanced' summary by saying the critic has the better case and Plato's reply is wishful thinking.

Write 3-5 sentences naming what the chatbot got right and at least two places where it slipped into one of the failures above, quoting its words and correcting each by hand against the packet and Chapter 3.

Equivalent route (no AI required)

No AI account is required for this workshop. This route assesses the same objectives, Objective 3 (explain central positions in metaphysics and epistemology — Plato's Forms, rationalism and empiricism, skepticism, and the analysis of knowledge — and evaluate the arguments for them) and Objective 2 (identify arguments, put them in standard form, judge whether they are valid, sound, or inductively strong, and test claims with counterexamples and thought experiments), takes comparable effort of about the same 90 minutes, uses the same rubric, and earns the same credit. Instead of the chatbot, critique this flawed analysis of the planetarium packet, printed here in full: "All four arguments are valid, because each conclusion sounds likely, and A2 is modus ponens. A1 is sound, so the dome is definitely not the sky. Socrates wrote the allegory of the cave in Book I of the Republic in the year 375, and his opening words in Plato's own language were: 'Imagine a dark room where people watch a screen.' Socrates also tells the story of the ring of Gyges, and Plato wrote, 'The Forms are only ideas in the mind.' Another famous argument about appearance is Descartes' 'I think, therefore I am,' from his Meditations. Questioning appearances is a Greek invention, so philosophy outside Europe never takes it up. Plato thought nothing we see is real, and the critic only says Plato made the Forms up. The sealed dome proves the Forms do not exist. To sum up fairly, the critic is right and Plato's reply is wishful thinking." Mark every error you find, name the failure it shows, and correct it by hand against the packet and Chapter 3; find at least two. Submit the marked-up analysis with your corrections in place of the chatbot report and share link.

Part 7 — What to Submit

• The three completed tables from Part 4, including the count with its subtraction
• The counterexample to A2's form and the four-to-six-line dialogue
• Written answers to all six analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Philosophy Workshop report on one illustrative planetarium packet: three completed tables (four arguments reconstructed and keyed for validity with reasons; the count of valid and invalid arguments with its subtraction; and the sealed-dome variation set beside the cave), a counterexample to A2's form, a four-to-six-line dialogue between a defender of the Forms and a critic ending in a plain sentence, written answers to six analysis questions, and a critique of a chatbot's version of the same work, or, on the equivalent route, a marked-up correction of the printed flawed analysis. Choose how you show it: written answers, a recorded explanation with a transcript, or labelled tables with short notes; every form is graded by the same scoring criteria. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Accurate reconstruction and validity judgment	All four arguments are in standard form with letters identified, each form is named, each is keyed valid or invalid with a reason from the definition, and the count is worked with its subtraction.	Most arguments are reconstructed and keyed with reasons, but one or two are misnamed or miskeyed, a reason is missing, or the count is missing or off.	The reconstructions are missing, or the keys rest on whether conclusions sound true rather than on form.
Counterexample and thought-experiment test	The counterexample keeps A2's form exactly with checkably true premises and a false conclusion, and the variation table sets the sealed dome beside the cave, labels it a variation, and says which way it pulls the intuition about knowledge.	Either the counterexample or the variation test is complete, but the other changes the form, leaves a row empty, or never says which way the intuition pulls.	No counterexample and no variation test appear.
Two positions stated fairly in dialogue	The dialogue gives the defender of the Forms and the critic each their strongest point, has each answer the other, and ends in one plain sentence naming where they disagree.	Both positions appear, but one is weakened, the speakers talk past each other, or the closing sentence is missing.	No dialogue, or only one side is stated.
Caught-and-corrected AI slip, on either route	The chatbot critique report, or the equivalent route's marked-up flawed analysis, quotes at least two errors, names the failure each shows, and corrects each by hand against the packet and Chapter 3; either route earns this band equally.	One error is quoted and corrected on either route, or errors are named without a correction.	No critique on either route, or chatbot output is pasted without checking it.
Accurate sourcing and reflection	The allegory and the theory of Forms are credited to Plato, the cave appears only in paraphrase, the sealed dome is labelled as a variation, nothing is invented, and the reflection answers option (a) or (b) with a reason.	The sourcing is accurate but the reflection is thin, or the reflection is strong but one attribution goes beyond the pinned record.	An invented quotation, work, or date appears, and there is no reflection.

Quality Gate

• Every argument is in standard form, with numbered premises and a conclusion line introduced by So, and any added premise is marked as added.
• Every key says valid or invalid with a reason from the definition, and no argument in the packet is called sound or unsound.
• The counterexample keeps A2's form line for line, with premises that are plainly true and a conclusion that is plainly false.
• The sealed dome is labelled as a variation of the allegory of the cave, and the allegory and the theory of Forms are credited to Plato, the author.
• No quotation, work, date, or philosopher's view is invented anywhere in the submission, and the cave is described only in paraphrase.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors by hand.