Polysyllogisms & Aristotelian Sorites
All scholars are careful readers.
All careful readers annotate.
All who annotate catch key claims.
Final conclusion?
All scholars catch key claims.
If draft is peer-reviewed (D), feedback occurs (F). If feedback occurs (F), revision happens (R).
D → R
Major: All students with active IDs may access the database, because the library license grants access to current ID holders.
Minor: All seniors have active IDs, because most seniors had them last year.
Major valid; minor invalid (past ≠ present status).
(Grasp a horn)
If we take the bus, we’ll arrive on time (B→A). If we drive, we’ll arrive on time (D→A). Either B or D. Therefore, A.
Show B→A fails today due to a bus strike.
If we take a practice exam, confidence rises (E→C).
If we join a study group, confidence rises (G→C).
Either E or G. Therefore, C.
Best escape?
Show a third option: an independent study plan with weekly check-ins also raises confidence (¬E ∧ ¬G but still C).
All debate finalists publish drafts.
All who publish drafts get feedback.
All who get feedback revise.
All debate finalists revise.
If students outline (O), they see structure (S). If they see structure (S), they spot fallacies (F). If they spot fallacies (F), they improve arguments (I).
O → I
Major: All qualifying submissions receive extra credit, because the rubric awards points for qualifying work.
Minor: All annotated bibliographies are qualifying submissions, because they look impressive.
Best eval
Major valid; minor invalid (appearance ≠ policy/definition).
(Escape between the horns)
If we eat in the cafeteria, we save money (C→M). If we pack lunch, we save money (P→M). Either C or P. Therefore, M.
Student forgets lunch; buys off-campus discount (third option).
Who is my favorite Sonic character?
Shadow the Hedgehog
All team captains attend leadership training.
All who attend leadership training submit a plan.
Some juniors are team captains.
Some juniors submit a plan.
If enrolled (E), fees are paid (F). If fees are paid (F), an ID is issued (I).
What follows?
E → I
Major: All items on the approved list are classroom-appropriate, because the curriculum committee vetted them.
Minor: All Unit 4 documentaries are on the approved list, because the committee’s minutes list them by title.
Major valid; minor valid.
(Escape between the horns)
If we practice scales, musicianship improves (S→M). If we practice repertoire, musicianship improves (R→M). Either S or R. Therefore, M.
Best escape:
Show a third option (ear-training/ensemble rehearsal) that also leads to M.
(Evaluate the reasons)
Major: All students with lab clearance may borrow goggles, because the safety policy states cleared users may check out PPE.
Minor: All Biology II students have lab clearance, because most had it last semester.
Major valid; minor invalid (past status ≠ current clearance).
All honors students take calculus.
All who take calculus study limits.
All who study limits understand continuity.
All honors students understand continuity.
If training is completed (T), the test is passed (P). If the test is passed (P), clearance is granted (C). If clearance is granted (C), equipment may be used (E).
T -> E
Major: All tasks on the safety list require goggles, because policy §4 states eye protection is required for listed tasks.
Minor: All acid-handling tasks are on the safety list, because the teacher said so.
Major valid; minor invalid (needs documented policy/list, not authority alone).
(Grasp a horn)
If we use wipes, surfaces are sanitized (W→Z). If we use spray, surfaces are sanitized (R→Z). Either W or R. Therefore, Z.
Show that the wipes used are expired/ineffective (W ∧ ¬Z).
Who is my favorite MLP FiM Character?
The Great and Powerful Trixie Lulamoon
All AP students outline.
All who outline see structure.
All who see structure spot fallacies.
All who spot fallacies write stronger essays.
All AP students write stronger essays.
If attendance is ≥90% (A), then eligible for final (L). If eligible for final (L), then can sit exam (X). If can sit exam (X), then course grade is issued (G).
A → G
Major (needs repair): All seniors may park on campus, because parking is fun.
Which rewrite makes the major reason valid?
Answer Vary
If we use a rubric, feedback quality improves (U→Q).
If we conference, feedback quality improves (C→Q).
Either U or C. Therefore, Q.
Best Grasp to Deny
Show U→Q fails: the rubric is vague and yields inconsistent scores (U ∧ ¬Q).
Major (needs repair): All independent researchers may use the archive, because archives are inspiring.
Make a valid major reason.
because the access policy grants permits to registered independent researchers with government-issued ID.
Example