Critical Reasoning 1.2 – Recognizing Arguments

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What Counts as an Argument?

• Definition: An argument is a set of statements in which some statements (premises) are claimed to support one other statement (the conclusion).

  • Both premises and conclusion must be statements—i.e., sentences that can be true or false.

  • Premises: supply reasons / evidence.

  • Conclusion: main claim said to be supported or implied.

• Identifying parts

  • Ask: What is the main point being claimed? That statement is the conclusion; all others are premises.

  • Indicator words

  • Premise indicators: since, because, given that, inasmuch as, as shown by, etc.

  • Conclusion indicators: therefore, thus, hence, so, consequently, it follows that, etc.

  • Absence of indicators ⇒ locate conclusion first, then treat remaining statements as premises (there should be only one conclusion).

Argument vs. Non-Argument

• Necessary conditions for a passage to contain an argument

  1. \text{(a)} Some statements claim to provide evidence/reasons.

  2. \text{(b)} There is an inferential claim that the alleged evidence supports something else.

  • Example (argument): Since Dr. Gregg is teaching logic, she deserves to be paid a living wage.

  • Contrast (non-argument conditional): If Dr. Gregg teaches logic, then she deserves to be paid a living wage.

• Inferential claim

  • Explicit: signaled by indicator words.

  • Example: Mad cow disease is spread by feeding parts of infected animals to cows, and this practice has yet to be completely eradicated. Thus, mad cow disease continues to pose a threat to people who eat beef.

  • Implicit: no indicators but the support relation is still present.

  • Example: Genetic modification of food is risky business. Genetic engineering can introduce unintended changes into DNA, and these changes can be toxic to consumers.

• False indicators

  • Indicator words sometimes serve a different grammatical role.

  • Since Edison invented the phonograph, he deserves credit… (premise indicator).

  • Since Edison invented the phonograph, there have been many technological developments. (purely temporal “since,” no argument).

  • Always verify that one statement is claimed to be supported by others.

Simple Non-Inferential Passages

These lack any inferential claim. Five main sub-types:

1. Warnings – "You should never answer your phone in class."

   • No evidence offered; can be converted into an argument by adding premises:

     • Since Dr. Gregg will be very angry, you will miss lecture information, and you’ll annoy classmates, it is a bad idea to answer your phone in class.

     • Formalization:

     • P1: Dr. Gregg will be angry.

     • P2: You will miss valuable information.

     • P3: You will annoy classmates.

     • C: It is a bad idea to answer your phone in class.

2. Statements of belief / opinion – merely report what someone believes.

   • We believe that our company must develop outstanding products…

   • No premise-conclusion relationship.

3. Loosely associated statements – same general topic, no inference.

   • Lao-Tzu quote: Not to honor men of worth… not to value goods… not to display what is desirable…

4. Reports – convey information/events.

   • Example about Yonsei–IBM Quantum Computing Center (July 15, 2022).

5. Expository passages – topic sentence plus elaboration.

   • States of matter example: (a) solid/liquid/gas, then elaborations (b–e). No claim that (b–e) prove (a).

Illustrations vs. Arguments from Example

• Illustration – gives examples of an accepted fact.

  • Chemical elements can be represented by molecular formulas. Thus, O₂, H₂O, NaCl…

  • Here "thus" does not signal a conclusion; examples merely illustrate.

• Argument from example – examples offered to prove a disputed claim.

  • Although most cancers can cause death, not all are life-threatening. For example, basal-cell carcinoma rarely causes death.

  • Example (basal-cell cancer) is intended as evidence for main claim.

Explanations

• Purpose: shed light on a phenomenon already accepted.

• Components

  • Explanandum: statement describing the phenomenon to be explained.

  • Explanans: statements that provide the explanation.

  • The sky appears blue (explanandum) because sunlight is scattered by atmospheric particles (explanans).

• Distinguish from arguments

  • Argument: aims to prove something controversial.

  • Explanation: assumes the main fact is already accepted and explains why.

• Diagnostic test (Mary’s iPhone)

  1. Mary’s iPhone died because she forgot her charger. → Explanation (gives reason why).

  2. Mary’s iPhone died; when she presses the power button, nothing happens. → Argument (second clause is evidence that the first clause is true).

Summary Table

• Argument

  • Main point = conclusion (not accepted at face value).

  • Support = premises (claimed proof).

• Explanation

  • Main point = explanandum (accepted fact).

  • Support = explanans (shed light on the fact).

Conditional Statements

• Form: If P, then Q.

  • Antecedent = P (follows "if").

  • Consequent = Q (follows "then").

  • Symbolizations: P \rightarrow Q or P \supset Q (not to be confused with set-theoretic A \supset B meaning "A is a superset of B").

• Not an argument by itself

  • "If sugary drinks cause heart disease, then they should be regulated" makes no claim that either clause is true—merely establishes a conditional link.

• Contrast with an argument

  • Sugary drinks cause heart disease; therefore they should be regulated. – two separate statements + inference.

• Conditional in arguments

  • Modus ponens (valid):

  • P1: If sugary drinks cause heart disease, they should be regulated.

  • P2: Sugary drinks cause heart disease.

  • C: Therefore, they should be regulated.

  • Pure hypothetical syllogism (valid):

  • P1: If Tom wins the lottery, Tom will be happy.

  • P2: If Tom is happy, Jane will be happy.

  • C: If Tom wins the lottery, Jane will be happy.

Necessary vs. Sufficient Conditions

• Sufficient condition (A ⇒ B): Whenever A occurs, B must occur.

  • \text{If }A,\text{ then }B.

  • Being a dog is sufficient for being an animal.

• Necessary condition (¬A ⇒ ¬B): B cannot occur without A.

  • \text{If not }A,\text{ then not }B.

  • Being an animal is necessary for being a dog.

• Dog in a box thought-experiment

  • Told "there is a dog" → you can infer "there is an animal" (sufficient).

  • Told "there is no animal" → infer "there is no dog" (necessary).

• Four logical relations between A and B

  1. A necessary but not sufficient for B (being an animal for being a dog).

  2. A sufficient but not necessary for B (being a dog for being an animal).

  3. A both necessary & sufficient for B ("being July 4" ⇔ "being Independence Day (US)").

  4. A neither necessary nor sufficient for B (being a mammal vs. being a bird).

Deciding: Argument or Non-Argument?

• Core question: Does the passage contain an inferential relationship?

  • If yes → argument.

  • If no → non-argument (expository, illustration, explanation, report, etc.).

• Controversy heuristic: If the main claim is generally accepted, passage is likely non-argument. If it’s controversial, evidence is probably being offered ⇒ argument.

• Context sensitivity

  • Some passages can function as explanations in one context but arguments in another (depends on audience background knowledge & dispute level).

  • Political or social contexts may mask inferential structures (e.g., climate-change facts treated as controversial by some audiences).

Practical Implications & Pitfalls

• Commands & normative sentences

  • Not obviously statements (lack truth value), yet sometimes treated as conclusions (contested in Hurley’s text).

• Belief reports

  • Structure "I believe X because Y" might be a mere report or an argument depending on whether Y is claimed evidence.

  • Example hierarchy:

  • I believe in unicorns because I read it in a book. → statement of belief.

  • I have good reason to believe in unicorns because I read about them in _The Lion, the Witch and the Wardrobe_ → begins to look like an argument (claims source reliability).

• Indicator word fallacy

  • Do not mechanically treat every "since," "thus," etc., as indicating premises/conclusion. Verify the inferential claim.

Formal Logic Connections

• Conditional statements map directly onto logical rules (modus ponens, modus tollens, hypothetical syllogism).

• Understanding necessary / sufficient language is foundational for advanced proof techniques, validity testing, and building complex arguments.

Ethical & Epistemic Notes

• Epistemic entitlement: Widespread expert acceptance of a claim often removes the need for argument (e.g., "Edison invented the phonograph").

• Scientific paradigm shifts (Copernicus) show that disagreement can sometimes signal conceptual progress—but most denials of well-established facts stem from incomplete information or misconceptions.

• Logicians must analyze arguments and navigate sociopolitical contexts where the status of "fact" is contested.

Quick Reference Cheat-Sheet

• Argument: premises + conclusion, inferential claim present.

• Explanation: explanans + explanandum, inferential claim absent; goal = understanding.

• Illustration: examples clarify accepted statement.

• Report: neutral information dump.

• Conditional alone: not an argument.

• Indicators: helpful but fallible; always test for real support.

• Necessary: must‐have for B.

• Sufficient: all-that-is-needed for B.

End of structured notes.