How to work with this page

This page is the workshop for Lesson 1 of the Logic unit. You work through it alone, in about 45 minutes, with your Lesson 1 handout beside you. It has one job: to make sure that after this lesson you can find the conclusion of any argument, and can tell an argument from an explanation, from a bare claim, and from a performance.

Each part is built the same way:

1. Explanation — short, with the lesson’s own examples.
2. Exercise — you type or choose, then press Check. Nobody sees your mistakes. The page counts your first try; that number is for you.

The page has three stages. Stage 1 puts the lesson’s case on trial and asks you to take a side before you have the tools. Stage 2 gives you the tools: premises and conclusion, argument against explanation and assertion, deductive against inductive, logos against ethos and pathos, and the one distinction the case turns on — a premise against an inference rule. Stage 3 sends you back to your verdict with the tools in hand. Your sheet tells you when each stage is due.

Recall — the Core unit from memory

Before anything new: eight questions on the Core unit, without your notes. Guess first: how many of the eight will you get? …… of 8.

Stage 1 — The case first

On 22 May 2020 The Lancet published a study by Mandeep Mehra and colleagues, built on a registry supplied by the Chicago health-data company Surgisphere: 96,032 COVID-19 patients in 671 hospitals on six continents. After controlling for known confounders, patients given hydroxychloroquine had died in hospital more often; the authors concluded that the drug was associated with increased mortality. The World Health Organization paused the hydroxychloroquine arm of its global trial within days. Within two weeks, James Watson and more than 200 scientists published an open letter. They did not attack the reasoning. They pointed out that the dataset recorded more Australian COVID-19 deaths than Australia had actually had, that African hospitals were credited with electronic records their infrastructure could not have produced, and that Surgisphere refused an independent audit. On 4 June the lead authors asked for retraction, because they could no longer verify the data; The Lancet withdrew the paper the same day.

Mehra et al.’s argument, laid out:

1. The Surgisphere registry records the treatment and outcome of 96,032 COVID-19 patients in 671 hospitals.
2. In that registry, after controlling for known confounders, patients given hydroxychloroquine died in hospital more often than patients who were not.
3. Therefore, hydroxychloroquine is associated with increased in-hospital mortality in COVID-19.

Stage 2 · Part A — Premises and conclusion

A1. The definition

In everyday speech, “argument” means a quarrel. In logic, it means one thing: a set of propositions in which some — the premises — are offered as reasons to believe another — the conclusion. Strip away the rhetoric, the examples and the tone, and what remains is a skeleton: premises, conclusion, and the step between them.

Some words mark the parts:

The lesson’s own example. “We should tax carbon because it damages the atmosphere and damaging the atmosphere is wrong” conceals:

1. (Implied) We should stop things that are wrong.
2. Damaging the atmosphere is wrong.
3. Carbon emissions damage the atmosphere.
4. Therefore, we should stop carbon emissions — that is, tax them.

A2. Argument, explanation, assertion

The definition says the premises are offered as reasons to believe the conclusion. That rules two things out.

An explanation also uses “because” — but it gives the cause of something you already accept. “The pump handle was removed because Snow showed the deaths clustered around it” is not trying to convince you that the handle was removed; nobody doubts it. It tells you why. An assertion is a claim with nothing offered for it at all: “Miasma causes cholera.” It may be true or false; it is not an argument, because it gives you no reason.

The test, in one question: is the “because” there to make me accept the claim, or to tell me why something I already accept came about? If neither — if there is no “because” at all — it is an assertion.

Part B — Two kinds of step, three kinds of appeal

B1. Deductive and inductive

Two fundamentally different kinds of inference:

Deductive: the conclusion is guaranteed by the premises. If the premises are true and the argument is valid, the conclusion cannot be false. The price: the conclusion can only contain what the premises already implicitly contained. Mathematics is deductive.

Inductive: the premises support the conclusion but do not guarantee it. All observed ravens have been black; therefore, probably, all ravens are black. The conclusion goes beyond the premises. This is how science works — and where Hume’s problem of induction will bite, in Lesson 4.

The one question to ask: could the premises all be true and the conclusion still false? If that is impossible, the step is deductive. If it is possible but unlikely, the step is inductive.

B2. Logos, ethos, pathos

Aristotle’s Rhetoric distinguishes three modes of appeal:

• Logos: appeal to reason — an argument.
• Ethos: appeal to the character and credibility of the speaker.
• Pathos: appeal to the emotions of the audience.

Logos is what logic studies. Ethos and pathos are effective — often more effective than logos — but they are not arguments in the logical sense. They can produce belief without justification.

Part C — Premise or inference rule: Carroll’s Tortoise

C1. The distinction

A premise is a claim inside the argument: it can be true or false, and it is what the argument rests on. An inference rule is the pattern that licenses getting from the premises to the conclusion: it is what the argument moves by. “All humans are mortal” is a premise; “from ‘all A are B’ and ‘c is A’, conclude ‘c is B’” is an inference rule.

Lewis Carroll’s Tortoise (1895) accepts every premise Achilles offers and still refuses to move. The argument:

• (A) Things that are equal to the same are equal to each other.
• (B) The two sides of this triangle are things that are equal to the same.
• (Z) Therefore the two sides of this triangle are equal to each other.

The Tortoise accepts (A) and (B) but not (Z). Achilles: “But if you accept A and B, you must accept Z.” The Tortoise agrees — and asks him to write that down as a new premise, (C). Now the Tortoise accepts A, B and C, and still will not accept Z without a further premise saying that A, B and C together entail Z. And so on without end.

Carroll’s point: the rule of inference cannot be justified by adding it as a premise. Any justification of a rule already uses rules. Inference rules are not conclusions of arguments; they are the machinery that produces conclusions, and they have to be accepted as basic.

Part D — Spot the error

D1. How arguments go wrong in this lesson

Seven things students say, and the one mistake in each. Learn to name them: naming is what lets you find them in your own writing.

Stage 3 — Back to the case

Your verdict, with the tools

Take out what you wrote at Stage 1. Now rewrite it in three sentences:

1. Your side: sign — the demand for the dataset is an audit of a premise, methodological hygiene — or decline to read it that way — the demand is Carroll’s regress reaching the data.
2. Your reason — and say what it is about: a premise or an inference rule. A reason that fuses the two (“show us your data” and “justify your inference rule” as one demand) has not signed anything yet.
3. The price your side pays. Audit: what makes the line between premise-audit and rule-justification stable when “verify it” can always be pushed one step further back — and what a reviewer should say if asked to defend modus ponens in the methods section. Regress: how science ever concludes anything if every demand for a further premise sits on one continuum with the Tortoise’s.

Then check your own paragraph:

• Did you keep premise and inference rule apart? “The letter attacked the argument’s logic” is the confusion this lesson exists to end: the form was fine; the data were a premise.
• Did your reason name what the letter demanded (the registry, its audit), not the outcome (the retraction, the WHO pause)?
• Did you say the price in your own words, not the sheet’s?

Only now: compare with the three model paragraphs — two good ones, one bad one.

Done?

You can now:

• find the conclusion of an argument even when it comes first and no marker word is present;
• tell an argument from an explanation and from a bare assertion, by asking what the “because” is for;
• say whether a step guarantees its conclusion or only supports it;
• name an appeal as logos, ethos or pathos — and say which of the three logic studies;
• keep a premise apart from an inference rule, and say why writing the rule in as a premise does not help;
• catch “the argument was refuted” being used for “a premise could not be checked” — in your own essays first.

Go back to your sheet.