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Reading and Literature Studies · Reading Informational and Graphic Texts

Evaluating Reasoning: Validity, Hidden Premises and Subtler Fallacies

1.7About 70 minutes
Learning goals
  • I can distinguish a valid argument from a sound one.
  • I can reconstruct an argument's hidden premise (enthymeme) and judge whether it is acceptable.
  • I can identify subtler fallacies: equivocation, begging the question, appeal to tradition, tu quoque, red herring, moving the goalposts and loaded questions.
  • I can evaluate an argument fairly, using the principle of charity and avoiding the fallacy fallacy.

Words to know

premise
A statement offered as a reason for a conclusion.
valid
Describes a deductive argument whose conclusion must be true if its premises are true.
sound
Valid, with all premises actually true.
enthymeme
An argument with an unstated premise that the reader is expected to supply.
fallacy
A flaw in reasoning that makes an argument seem stronger than it is.
principle of charity
Interpreting an argument in its strongest reasonable form before evaluating it.
fallacy fallacy
Concluding that a claim is false just because someone argued for it badly.

Hook: right answer, wrong reasoning

All birds can fly. Penguins are birds. So penguins can fly. The logic is perfect: if the first two statements were true, the third would have to be. The problem is the first statement. Some Canadians like snow. Mei is Canadian. So Mei likes snow. Mei might well like snow, but the reasoning does not show it.

Evaluating an argument means asking two different questions: Are the reasons true? and Do the reasons actually support the conclusion? This lesson gives you the vocabulary of logic used in first-year philosophy and law courses, applied to the arguments you meet in editorials, letters and speeches.

Remember from Grade 11

In ENG3U you learned to find and fix eight common fallacies in your own writing: straw man, false dilemma, hasty generalization, slippery slope, post hoc, ad hominem, bandwagon and appeal to questionable authority, and you used the Toulmin warrant to find unstated assumptions. Watch for them in the letter below too. This lesson adds subtler fallacies and the tools of validity, soundness and the enthymeme.

Validity and soundness

A deductive argument claims that its conclusion follows necessarily.

  • It is valid if the conclusion must be true whenever the premises are true. Validity is about structure, not facts.
  • It is sound if it is valid and all its premises are actually true.

The penguin argument is valid but unsound (a false premise). The Mei argument is invalid (some Canadians does not lead to Mei), even if its conclusion happens to be true.

Inductive arguments (from examples or data) are judged differently: not valid or invalid, but strong or weak, depending on how well the evidence supports a probable conclusion.

Evaluating a deductive argument: two separate questionsPremises TRUEA premise FALSEVALID(follows)INVALID(does not follow)SOUNDconclusion must be truevalid but unsoundlogic works, a fact failsinvalidtrue facts, broken logicinvalid and unsoundfails both testsOnly the top-left cell guarantees the conclusion.
Two questions, four outcomes. A critic who says your premise is false and a critic who says that doesn't follow are making different objections; precise evaluation names which one.

Hidden premises: the enthymeme

Most real arguments leave a premise unstated. Aristotle called this an enthymeme. It has worked for sixty years, so it should not change hides the premise what has worked before will keep working (or will keep being the best option). Spelling out the hidden premise is often the fastest way to evaluate an argument, because hidden premises are where weak assumptions live. (This is the same move as finding a warrant in the Toulmin model.)

statedpremise + claimHIDDEN PREMISE(unstated assumption)"It has worked for sixty years,so it should not change."Assumes: whateverworked before willkeep working.surface of the textbelow the surface
An enthymeme is like an iceberg: the stated reason and claim sit above the surface, and the premise holding them up sits below. Bring it to the surface and ask: Is this acceptable?

A text to practise on

Letter to the editor: Keep the Carnival on the Lake

(An invented letter written for this lesson.)

(1) The town's plan to move the Winter Carnival from Mill Lake to Riverside Park is a mistake. The carnival has been held on the lake for sixty years, and what has worked for sixty years should not be changed.

(2) The council says the ice has become unsafe in some recent winters. But every outdoor activity carries some risk; walking to the arena carries risk. If we cancelled everything with a risk, we would never leave the house, and nobody wants that.

(3) Councillor Ross, who now says the lake ice is too risky, skated on Mill Lake herself last winter. If she trusted the ice then, why should anyone listen to her now?

(4) The council promised that a park carnival would cost no more than the lake carnival. When the budget showed it would cost the same, supporters of the move were satisfied. But now that costs are equal, I ask: why should taxpayers pay the same for a worse carnival?

(5) A carnival on a lake is the real carnival, because the real Winter Carnival is the one held on the lake. Besides, the town still has not fixed the potholes on Queen Street.

FallacyWhat it doesWhere in the letter
Appeal to traditiontreats we have always done it as a reason in itselfpara. 1: sixty years
Equivocationuses one word in two senses so the argument seems to workpara. 2: risk shifts from small everyday risk to serious danger
Tu quoque / attacking consistencydismisses a view because the speaker has not acted consistently with it (a cousin of ad hominem)para. 3: Councillor Ross skated on the lake herself
Moving the goalpostschanges the standard after it has been metpara. 4: cost was the test; now it is a worse carnival
Begging the question (circular)assumes the conclusion in a premisepara. 5: the real carnival is on the lake because the real one is on the lake
Red herringchanges the subject to distractpara. 5: potholes on Queen Street
Loaded (complex) questiona question that presupposes a disputed claimpara. 4: a worse carnival is assumed, not shown
Seven subtler fallacies, all in one invented letter.
Worked example

Let's evaluate paragraph 2 precisely

Evaluate the reasoning in paragraph 2 of the letter.

  1. Charitable reconstruction: Some risk is a normal part of life; the risk of the lake carnival is small; so the risk is not a good reason to move it. This is the strongest version.
  2. Spot the shift: every outdoor activity carries some risk uses risk to mean small everyday risk. But the council's concern is unsafe ice, a serious danger to hundreds of people at once. The word risk covers both, so the argument equivocates.
  3. Spot the second flaw: If we cancelled everything with a risk, we would never leave the house is a straw man (no one proposed cancelling everything) and has a slippery-slope flavour.
  4. Find what is missing: the key premise, the risk of the lake carnival is small, is never supported. The council says the opposite, and the letter offers no ice data.
  5. Verdict: the paragraph is weak: it never engages with the actual evidence about ice.

Precise evaluation reconstructs the argument charitably, names the flaw and explains it with the text, then says what evidence would be needed. Name-calling (this is a fallacy!) without explanation earns little credit.

Worked example

Let's avoid the fallacy fallacy

A student concludes: The letter is full of fallacies, so the carnival should definitely move to the park. Evaluate the student's reasoning.

  1. Name it: this is the fallacy fallacy: concluding a claim is false (or its opposite is true) because the argument for it was bad.
  2. Explain: a badly argued position can still be right. There might be good reasons to keep the carnival on the lake (tradition as a value the community chooses, cost of park setup, ice-testing programs) that the letter simply did not give.
  3. Better conclusion: The letter gives no good reason to keep the carnival on the lake; the decision should rest on evidence about ice safety, cost and what residents value.

Evaluating an argument is not the same as deciding the issue. A fair reader separates the two.

Just for fun

Riddle: What is the real carnival?

The one on the lake. How do we know? Because it's the real carnival. (This riddle has been reviewed and found to be going in circles.)

Hands-on activity

Fallacy hunt in the letters page

You need: the letters to the editor or comment section of a newspaper (print or online), a pencil, and about 30 minutes.

  1. Choose two letters that take opposite sides of the same issue.
  2. For each, write the main argument in premise, premise, conclusion form, adding any hidden premise.
  3. Mark each argument valid or invalid (deductive) or strong or weak (inductive), and say whether the premises are true or unsupported.
  4. Name and explain any fallacies, with a quotation.
  5. Write a fair conclusion that avoids the fallacy fallacy.

What to look for: charitable reconstructions; fallacies explained, not just named; equal scrutiny of both sides (it is easy to find fallacies only in the side you disagree with).

Your turn

1

Is this argument valid? All provincial parks in this list allow winter camping. Algonquin is on the list. So Algonquin allows winter camping.

2

What is the difference between a valid and a sound argument?

3

Find the hidden premise: She is the team captain, so she should speak for the team at the meeting.

4

Which fallacy is in paragraph 5's first sentence? Explain.

5

Why is the potholes sentence a red herring?

6

Explain how paragraph 4 moves the goalposts.

7

What is the principle of charity?

More practice: warm-up

1

Is the penguins can fly argument valid, sound, both or neither?

2

What do we call an argument with an unstated premise?

3

Name the fallacy: Why do you keep wasting money on that car?

4

Name the fallacy: We've always held exams in June, so we should keep doing it.

5

Are inductive arguments judged valid or strong?

More practice: on your own

1

Identify the equivocation: The law says all people are equal. But people are obviously not equal in height or talent. So the law is wrong.

2

Is paragraph 3 an ad hominem? Explain carefully.

3

Reconstruct paragraph 1's argument charitably and state its hidden premise.

4

Write a valid argument with a false premise, and say which premise is false.

5

A columnist says: My opponent's study was funded by a company, so its findings are false. Evaluate.

Challenge

1

Rewrite the letter's argument so that it is free of fallacies but still argues to keep the carnival on the lake.

2

Explain why an argument can be valid, have true premises, and still fail to persuade a reasonable reader.

3

Evaluate this claim: Spotting fallacies is the most important part of evaluating an argument.

Check your understanding

Quiz

1.

An argument is sound when...

2.

Every outdoor activity carries some risk, used to dismiss a serious ice-safety concern, is an example of...

3.

The real carnival is on the lake because the real carnival is the one on the lake is...

4.

When cost was the test and costs turned out equal, the writer switched to quality. This is...

5.

Which statement avoids the fallacy fallacy?

6.

The hidden premise in It has worked for sixty years, so it should not change is...

7.

Inductive arguments are evaluated as...

For parents and teachers

What this lesson teaches: ENG4U Reading and Literature Studies 1.7: evaluating the effectiveness of complex texts using evidence, here focused on the quality of reasoning (validity, soundness, hidden premises and fallacies).

How to help at home:

  • Pick a letter to the editor or a social media argument and ask: What's the hidden assumption?
  • Play steel man: before criticizing an argument, state its best version.
  • Model fairness: look for fallacies on your own side of an issue too.

Common difficulties:

  • Labelling without explaining. Naming a fallacy is only the start; ask why it fails here.
  • Confusing valid with true. Valid is about structure; the premises can still be false.
  • The fallacy fallacy. A badly argued view can still be right.

Facts used: the letter is invented for teaching. The term enthymeme comes from Aristotle's Rhetoric.