Week 3 — Reading the Cave: Mapping, Reconstructing, and Testing the Forms

Assignment 3 of the term — map the allegory of the cave, put the arguments for Plato's theory of Forms in standard form, test the theory against its strongest objection, place the ring of Gyges, and explain the Forms to someone new to philosophy.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into exact, well-reasoned work. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. In Week 1 you learned to name the speaker, the author, and the translator of a line you read, and in Week 2 you learned standard form and validity. This week you met Plato's dialogues, appearance and reality, the theory of Forms, the allegory of the cave, three objections with their replies, and the ring of Gyges. This week's lecture tutorial, quiz, discussion, and Philosophy Workshop practice the same ideas from other angles; this assignment is where you put them together.

The task

You will use this week's shared case, the allegory of the cave, which opens Book VII of Plato's Republic, and the two arguments the chapter reconstructs from it. Those reconstructions, and Dataset B, the argument set, are illustrative: their premises are written for teaching and are not claims the course endorses. The course keys validity, never soundness, because the premises are open questions. You will also use one everyday argument written for this assignment; it is illustrative and describes no real person or place. The course pins no quotation from the Republic, so describe Plato's stories in your own words.

Part A — map and reconstruct. First, map the allegory of the cave in two pairs: say what the shadows on the wall stand for and what the freed prisoner who sees the sun stands for, and say in one sentence why the story is an allegory rather than a history. Then take these four arguments:

1. Argument A (illustrative): "If the things we perceive were the true objects of knowledge, they would be unchanging. The things we perceive are always changing. So the things we perceive are not the true objects of knowledge."
2. Argument B (illustrative): "If you can judge every drawn circle as falling short of a perfect circle, then you grasp a standard that no drawing shows. You can judge every drawn circle as falling short of a perfect circle. So you grasp a standard that no drawing shows."
3. A gallery visitor: "If a painting is a forgery, the museum keeps it in storage. This painting is kept in storage. So this painting is a forgery."
4. Dataset B, argument 2 (illustrative): "If the mind is the brain, then mental states have locations. Mental states have no locations. So the mind is not the brain."

For each one, write it in standard form (P1, P2, then C introduced by "So"), mark any premise the reconstruction adds, say what P and Q stand for, name its form, and say whether it is valid or invalid, with a one-sentence reason that uses the definition of validity. Then work this problem, showing your reasoning:

1. Arguments A and B each have 2 premises. How many premises do the two arguments have in all?

Part B — test the theory. Work this problem first, showing your reasoning:

1. A table that lists the 3 things the Forms explain and the 3 objections to them needs one row for each. How many rows does it need?

Then do three things:

• What the Forms explain. Name the three jobs the Forms do in Plato's theory, each with one example of your own that is not the referee, the whiteboard, or the cave.
• Objection and reply. Choose the access, participation, or regress objection. State it at its strongest, give the strongest reply from Plato's side, and end with one plain sentence naming where the two sides disagree. Do not announce whether the Forms exist.
• Placing the ring of Gyges. Say in which book of the Republic the story appears, who tells it, and what question it raises, and explain in one sentence why crediting it to Socrates as his own argument gets the dialogue backward.

Explain it to a non-expert

A roommate who has never taken philosophy says, "So Plato thought people really live in caves, and the Forms are only ideas in our heads." Write a 3–5 sentence message in everyday words that corrects both misreadings, says what a Form is on Plato's view, and names one honest limit: whether the Forms exist is still an open question. Explain any term your roommate might not know.

For a different, ungraded example, imagine a coworker who asks why the floor plan in a real estate listing is not the apartment. Model answer: "The plan is a guide to the apartment, not the apartment itself. It shows the layout, but not the light, the noise, or the smell of the hallway. Philosophers would call the gap one between appearance and reality: how a thing is presented versus how it is. One limit: a plan can still be accurate about what it shows."

Use that pattern for your message to your roommate, with your own explanation of the cave and the Forms.

Reflect on your revision

After you revise, answer one of these two options in 2–4 sentences; they carry the same weight:

• (a) Which change made your mapping or one of your reconstructions more exact, and which definition showed you it was needed?
• (b) Which change made your objection or Plato's reply stronger, and what had you missed at first?

Part 1 — Student instructions

1. Draft Part A, Part B, and your message to your roommate before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Reply in your own words. Use the coach's feedback to revise at least one part of your mapping, a reconstruction, your objection and reply, or your placement of the ring, even if your first attempt was strong, and then answer reflection option (a) or (b).
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write your mapping, your reconstructions, or your message for you. If it says Socrates wrote the Republic, quotes the cave word for word, credits the ring of Gyges to Socrates, or says the Forms are proved, check that against Chapter 3 before you use it.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach for an introductory philosophy course. Draw out and challenge MY thinking about this week's ideas: Plato's dialogues, with Socrates as the main speaker and Plato as the author; appearance and reality; the theory of Forms (unchanging, perfect Forms such as Justice and Beauty as the true objects of knowledge, not ideas in someone's head); the allegory of the cave, which opens Book VII of Plato's Republic; the access, participation, and regress objections, each with a reply from Plato's side; the ring of Gyges, Glaucon's story in Book II; and standard form with validity. Do not write my assignment for me and do not invent work I did not show. Never quote the cave or the ring story, which the course pins no quotation from; never invent a quotation, a philosopher's view, or a source; never credit an objection to a named philosopher; never call an argument with contested premises sound or unsound; and never announce whether the Forms exist.

ASSIGNMENT: Work through these two problems in order, one at a time. Do not invent, replace, or reorder a problem. Part A: I map the cave in two pairs and say why it is an allegory, then reconstruct four arguments. (1) Argument A (illustrative): "If the things we perceive were the true objects of knowledge, they would be unchanging. The things we perceive are always changing. So the things we perceive are not the true objects of knowledge." (2) Argument B (illustrative): "If you can judge every drawn circle as falling short of a perfect circle, then you grasp a standard that no drawing shows. You can judge every drawn circle as falling short of a perfect circle. So you grasp a standard that no drawing shows." (3) A gallery visitor: "If a painting is a forgery, the museum keeps it in storage. This painting is kept in storage. So this painting is a forgery." (4) Dataset B, argument 2 (illustrative): "If the mind is the brain, then mental states have locations. Mental states have no locations. So the mind is not the brain." I write each in standard form (P1, P2, then C introduced by "So"), mark any added premise, say what P and Q stand for, name the form, and say valid or invalid with a reason from the definition of validity. Part B: the three jobs the Forms do, each with my own example; one objection (access, participation, or regress) at its strongest with the strongest reply from Plato's side, ending in one plain sentence naming the disagreement; and the ring of Gyges placed by book, teller, and question.
PROBLEM P1: Arguments A and B each have 2 premises. How many premises do the two arguments have in all?
PROBLEM P2: A table that lists the 3 things the Forms explain and the 3 objections to them needs one row for each. How many rows does it need?
For P1 I must also write the two-pair mapping, then reconstruct and key all four arguments. For P2 I must also name the three jobs, write the objection and reply, and place the ring; then a 3-5 sentence message in everyday words to a roommate who thinks Plato meant a literal cave and that the Forms are only ideas in our heads. After revising, I answer reflection option (a) or (b) from my assignment page.

SCORING CRITERIA: Score only evidence I supply, out of 100 points. Mapping and reconstruction (P1): 30 if the cave is mapped in two accurate pairs with a sentence on why it is an allegory, all four arguments are in standard form with P and Q identified and added premises marked, each form is named and keyed valid or invalid with a reason from the definition, and the premise count is worked; 20 if the mapping and the count are right but one or two reasons are missing or one reconstruction drops a premise, or three of the four are named and keyed with reasons; 10 if at least two arguments are named and keyed with reasons but others are misnamed or miskeyed, or the mapping or the count is off; 0 otherwise. Objection, reply, and attribution (P2): 35 if the three jobs are named with fresh examples, the objection and the reply are both stated at their strongest and end in a plain sentence naming the disagreement, the ring is placed in Book II with Glaucon as its teller and its question stated, and the row count is worked; 25 if one of those parts is missing; 15 if two or more parts are missing, or the objection is answered in a weakened form, or the ring is credited to Socrates; 0 if no accurate objection, reply, or placement. Plain-language explanation for a non-expert (P2): 20 if the message is in everyday words, corrects both misreadings, says what a Form is, and names the open question as a limit; 10 if it can be followed but corrects only one misreading or omits the limit, or leaves a term unexplained; 0 if missing. Revision and reflection (P2): 15 if I show a before-and-after change plus a reflection on why it is better; 8 if only one of the two; 0 if neither.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my reply. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to check it against the definitions. Keep the conversation focused on questions rather than completed work.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word reply is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied both problems with the mapping, the four reconstructions, the three jobs, the objection and reply, the placement of the ring, and the roommate message AND revised at least one part AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my mapping, my reconstructions, my objection and reply, and my message]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised work, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised work: the two-pair mapping, the four reconstructions with their forms, keys, and reasons, and the premise count; the three jobs, the objection and reply, the placement of the ring, and the row count; your message to your roommate; and your reflection — written, or recorded as audio or video with a transcript; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

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.

Equivalent route (no AI required)

This route assesses the same Week 3 skills — mapping the allegory of the cave, putting the arguments for Plato's theory of Forms in standard form and keying them for validity, stating an objection and Plato's reply at their strongest, placing the ring of Gyges with its teller, and explaining the Forms to someone new to philosophy — for comparable time and effort, about 75 minutes, the same as the coached route. Complete Part A, Part B, the message to your roommate, and one reflection option. Then audit your own first draft against the attached scoring criteria, criterion by criterion: for the mapping, check each pair against the chapter's two pairs; for each reconstruction, underline the premise that matches P and the one that matches Q, check that every added premise carries its mark, and check the form's name against the chapter's list; for the objection, check that you could sign your name to Plato's reply as its defender would state it; and check that your roommate message corrects both misreadings. Write a second draft. Add a 150–200 word revision memo that names one change you made, the definition that prompted it, and one question you still have. Submit the revised work, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The mapping, reconstructions, objection and reply, placement of the ring, message, revision, and reflection must be your own words. Do not ask the chatbot to write any of them or to add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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