Student Workbook

This sample includes the full workbook introduction and contents list, plus the complete Lab 1 and Lab 18. Section navigation: About This Workbook · Lab 1 · Lab 18.

About This Workbook

This workbook provides one extra practice lab per chapter of the main text—fresh problems, in the same style and at a similar difficulty level as each chapter’s own exercises, meant for additional practice after working through a chapter. These problems do not duplicate anything in the main text or in the Teacher & Parent Supplement.

This is a student edition: it contains no answer key. Check your work against the reasoning patterns and worked examples in the chapter itself, or with a teacher or parent.

Workbook Contents

• Lab 1 — Introduction to Philalethic Logic
• Lab 2 — Simple Ideas, Clauses, and Symbols
• Lab 3 — Quantified Claims, Abstraction, and Letter Order
• Lab 4 — Negating Claims
• Lab 5 — Restating Negated Claims
• Lab 6 — Visualizing Clauses and Circumstances
• Lab 7 — Simple Implications and Inferences
• Lab 8 — Validity, Soundness, and the Anatomy of an Argument
• Lab 9 — Contradiction: The Engine of Validation
• Lab 10 — The Validation Process
• Lab 11 — Decomposition Rules and Ordering
• Lab 12 — Worked Validation Examples I: Clause Arguments
• Lab 13 — Worked Validation Examples II: Portional and Multi-Premise Arguments
• Lab 14 — Modality: Necessity, Potential, and Possibility
• Lab 15 — Compound Claims: Conjunction and Disjunction
• Lab 16 — Compound Claims: Implication and Equivalence
• Lab 17 — Validating Compound Arguments
• Lab 18 — Special Problems, Common Mistakes, and Informal Fallacies
• Lab 19 — Bracketed Notation (Bonus Chapter)

Lab 1: Introduction to Philalethic Logic

Extra practice for Chapter 1. No answer key — check your reasoning with a teacher or parent, or against the chapter’s own worked examples.

Exercise: Belief, Doubt, or Denial?

For each, decide whether the speaker is judging the claim true, judging it false, or withholding judgment—and note if they seem to be confusing two of these.

1. “I’m not saying the rumor is true, but I’m not saying it’s false either.”
2. A witness tells police, “I never said I saw him leave—I said I didn’t see him arrive.”
3. “Honestly, I have no idea if the bridge is safe, so I’m taking the long way around.”
4. “I doubt the weather report is right, but I packed the umbrella just in case.”
5. Asked whether she trusts the new manager, an employee says, “I haven’t decided yet.”

Exercise: Apply the Axioms

For each scenario, name which of the three axioms from this chapter (non-contradiction, excluded middle, or identity) is being violated or misapplied, and explain briefly.

1. “The package is both fully delivered and not yet delivered at the same time, in the same sense.”
2. “That question is just unanswerable—it isn’t true, and it isn’t false either, and there’s no third option needed here.”
3. “Clark Kent and Superman can’t possibly be the same person, since Clark wears glasses and Superman doesn’t.”
4. “My favorite band is the best band—that’s just true for me, though it might not be true for you.”
5. “The witness testified the light was red. The witness also testified the light was not red. Both statements are accurate as given.”

Exercise: True, False, or Not Yet Verifiable?

Classify each claim, and briefly explain your reasoning. Remember: a claim’s truth doesn’t depend on whether anyone can currently confirm it.

1. “There is a planet somewhere in the universe with exactly two moons the same size.”
2. “The author of this book has a favorite color.”
3. “It will rain in this city exactly one year from today.”
4. “Two plus two equals four.”
5. “Somewhere, right now, someone is thinking about the number seven.”
6. The 10,000th digit of pi is a 7.
7. A specific stranger you’ve never met is, at this exact moment, telling a lie.
8. If this coin is flipped once, right now, it will land on heads.
9. There is a language spoken today that has no word at all for “yesterday.”

Discussion Questions

1. Is it possible to sincerely believe something false without being dishonest? What separates the two?
2. Why might “I don’t know” sometimes be a more honest answer than a confident yes or no?
3. Can wisdom exist without love, as this chapter defines the terms? Why or why not?
4. Describe a time your own understanding of something changed. What moved it from belief to knowledge, or corrected a false belief?
5. Why might treating “I don’t believe that” as the same as “that’s false” cause real problems in a disagreement?

Lab 18: Special Problems, Common Mistakes, and Informal Fallacies

Extra practice for Chapter 18.

Exercise: Name the Fallacy

Identify the fallacy (or fallacies) at work in each passage below.

1. “I don’t need to walk you through the numbers—every economist worth listening to already agrees with my forecast.”
2. “Councilwoman, you want to add a bike lane? So you want to ban cars from downtown entirely?”
3. “If we let one student turn in a late assignment, pretty soon nobody will ever meet a deadline again and the whole system falls apart.”
4. “This cream must work—my coworker used it for a week and her skin cleared right up.”
5. “Don’t listen to his critique of the budget—he got fired from his last accounting job.”
6. “You’re either fully on board with the merger, or you’re actively trying to sink the company.”
7. “This restaurant has to be the best in town—my whole book club raves about it every time we meet there.”
8. “Before we discuss the delayed shipment, let’s talk about how much revenue this product line brings in.”

Exercise: More Fallacies in the Wild

1. “My financial advisor recommended this fund, and he’s been doing this for twenty years, so it has to be a safe bet.”
2. “If we let staff work from home one day a week, next thing you know nobody will ever come into the office again.”
3. “You’re questioning the new curriculum? Typical—you probably think kids shouldn’t learn anything challenging at all.”
4. “This training program works—anyone who truly commits to it gets promoted, and if you didn’t get promoted, you obviously didn’t truly commit.”
5. “Two neighbors on my street had their packages stolen last week. Package theft is clearly out of control around here.”

Exercise: When Is It Even a Claim?

1. Is it true or false, right now, that “Sears is a great place to buy appliances”? Discuss why this is an awkward claim to evaluate in the present tense, and how rephrasing it resolves the discomfort.
2. Pick a company, product, or trend from your own lifetime that has since faded or changed dramatically. Write a present-tense claim about it that no longer sits well, then restate it correctly in the past tense.

Exercise: How Do You Actually Know That?

For each claim, identify what evidence (if any) the speaker actually has, and whether it’s really enough to justify how confident they sound.

1. “I read the first three pages and the writing was clunky, so the whole book is bad.”
2. “My grandfather smoked a pack a day and lived to 95, so the health warnings must be overblown.”
3. “The last two times I called customer service, I got a rude rep—that company clearly doesn’t care about its customers.”
4. “Every time I’ve worn my lucky socks, my team has won. I’m wearing them Sunday.”