Reconstruct an argument: Logic, Round 1

1 Learn

You will be able to

Write each premise and the conclusion as a single declarative sentence.
Add at least one hidden premise and show that the argument needs it.
Judge validity by asking whether the premises could be true while the conclusion is false.
Mark the weakest premise and state the strongest objection.

LibraryProof and Precise Reasoning: From Arguments to Theorems · Anatomy of an argumentPremises, conclusion and hidden assumptions, with the steps for evaluating any argument.2 min glance · 6 min
LibraryProof and Precise Reasoning: From Arguments to Theorems · Validity, soundness, consistency and truthValidity is about form, soundness adds true premises, and affirming the consequent is invalid.2 min glance · 6 min
LibraryProof and Precise Reasoning: From Arguments to Theorems · Propositional logic and truth tablesWhen a conditional is false, and why its converse is a different claim.2 min glance · 6 min
LibraryPeirce on the Fixation of Belief · Worked reconstructionA model reconstruction with hidden premises, weakest premise and strongest objection marked.2 min glance · 4 min
LibraryThe Weekly Loop: Read, Reconstruct, Make, Defend, Log · The five stepsA reusable six-line template for the Reconstruct step: thesis, premises, hidden premises, weakest premise, objection, verdict.2 min glance · 4 min
LibraryThe Seven Liberal Arts, Hands-On: Logic, Proof and the Quadrivium · The trivium in practiceThe logic practice and its made thing: numbered premises, a conclusion and an argument map.2 min glance · 7 min
LibraryHow to Read a Great Book: Levels, Modes and the Completion Standard · Reconstruct before you criticizeWhat makes a reconstruction fair, and why it comes before any objection.2 min glance · 6 min

2 Practise

Answer each card from memory, then grade yourself honestly. The cards join your review deck and come back just before you would forget them.

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

Show answer
A valid argument is one where, if the premises were true, the conclusion would have to be true; validity concerns form only. A sound argument is valid and also has premises that are in fact true.
recall
When is a conditional "if P then Q" false, and which statement always shares its truth value: its converse or its contrapositive?

Show answer
It is false only when P is true and Q is false. Its contrapositive, "if not Q then not P", always has the same truth value; its converse, "if Q then P", need not.
explain
Why is affirming the consequent ("If it rained, the road is wet; the road is wet; so it rained") an invalid form?

Show answer
Both premises can be true while the conclusion is false, because the road could be wet for other reasons. The argument treats "if it rained, the road is wet" as if it meant its converse, "if the road is wet, it rained", which it does not.
apply
A classmate checks a formula for n = 1, 2, 3 and 4 and concludes it holds for every positive integer n. Why is that not a proof, and which proof form on the page is built to cover every n?

Show answer
Checking particular cases can refute a universal claim but cannot establish it; the next case could fail, as "every odd number is prime" fails at 9. Induction can cover every n: prove a base case, then prove that if the formula holds for n, it holds for n + 1.
connect
The logic practice asks you to reconstruct an argument as numbered premises and a conclusion, then mark the weakest premise. How do validity and soundness, as covered in 'Proof and Precise Reasoning: From Arguments to Theorems', sharpen that exercise?

Show answer
Validity asks whether the conclusion would have to be true if the premises were; soundness adds that the premises are in fact true. Marking the weakest premise is a soundness check: a valid argument with a false premise can still reach a false conclusion.
connect
"The Weekly Loop: Read, Reconstruct, Make, Defend, Log" builds this page's rule "reconstruct before you criticize" into a weekly routine. What makes a reconstruction fair, and why must it come before you object?

Show answer
A fair reconstruction is one the author would accept: a person who holds the view could read your summary and say, "yes, that is what I think." Without that, any objection you make is aimed at a stand-in rather than at the author's actual argument.
connect
The Weekly Loop points to 'Peirce on the Fixation of Belief' as a worked example. Which step of the loop does that guide illustrate, and what does the step ask you to write?

Show answer
It illustrates Reconstruct. You write a one-sentence thesis in your own words, the argument as numbered premises leading to a conclusion, its hidden premises, the weakest premise and why, the strongest objection with the author's likely reply, and your verdict.

3 Prove it: the mastery check

5 questions drawn from a pool of 12. The pass mark is 80%. There is no time limit, and you can retake it with new questions; your best result counts.

4 Prove it: the performance task

Reconstruct and grade a published argument

Choose a paragraph of 80 to 250 words from a published editorial, essay or technical report that argues for a conclusion. Do not use your own writing, a private message, or Peirce's essay, which the site has already reconstructed. Write a one-page reconstruction with these parts: (1) the conclusion in one sentence; (2) the premises, numbered; (3) at least one hidden premise, marked as hidden; (4) a verdict on validity, with a scenario in which the premises are true and the conclusion is false if you judge the argument invalid; (5) a verdict on soundness, saying which premises you accept and why; (6) the weakest premise and the strongest objection. Allow about 30 to 45 minutes, then reread your premises and reword any the author would not accept.

What to hand in: A one-page written reconstruction with the source paragraph quoted at the top, or a link to it. Save it on the page or download it.

Check your work against the rubric The conclusion is stated as one declarative sentence that appears in, or is clearly implied by, the source paragraph. Each premise is numbered and is a single declarative sentence, and each one is something the author asserts or is marked as hidden. At least one hidden premise is added and shown to be needed: without it, the premises could be true while the conclusion is false. Validity and soundness are judged separately: the write-up says whether the premises, if true, would guarantee the conclusion, and which premises are actually true. The weakest premise is named with a reason, and the strongest objection is worded so that a person who holds the view would accept it as fair.

Your work Or a link to it (optional)

Saved only in this browser. To keep a copy, download it or export your progress.

5 Discuss: the seminar

Read the text, then think, write or talk through the question with someone. There is no answer key: the aim is a better question.

Logic or dialectic · Round 1

Plato, Euthyphro, 2a-16a (the whole dialogue)Read the whole dialogue in one sitting. Give most attention to 5d-6e (Socrates asks for the one form that makes every pious act pious), 10a-11b (is the pious loved by the gods because it is pious?) and 15c-16a (the ending). The link is H. N. Fowler's translation on Perseus, which renders the key word (hosion) as 'holy'; many other translations say 'pious'. Benjamin Jowett's translation is also free at Project Gutenberg (ebook 1642).

Euthyphro is certain he knows what piety is, yet each answer he gives fails under Socrates' questions. What does the questioning accomplish, and would you call the ending a failure?

At 6d-e Socrates asks for the one form that makes every pious act pious, not a list of pious acts. Why is a list of examples not a definition?
At 10a Socrates asks whether the gods love the pious because it is pious, or whether it is pious because they love it. Why does the order of the explanation matter for the definition?
At 11b-d Euthyphro complains that whatever they propose moves about and will not stay where they put it, and each speaker suggests the other is the Daedalus who sets it moving. Whose fault is it: the definitions', the speaker's or the questioner's?

Keep notes on the seminars page →

Reconstruct an argument