Introduction to Argument Cognitive Development Vocabulary Argument Proposition

Introduction to Argument Cognitive Development

Vocabulary • • • Argument Proposition Premises Statement Conclusion Assumptions Inference Entailment Necessary conditions Sufficient conditions Induction Deduction

To diagram an argument • Number each statement OR label/number each premises/conclusion • Use logical connectives • “Therefore” (conclusion) statement is superlined (opposite of underlined) or beneath brackets

Logical Connectives Symbol Meaning ¬ Not (negation) ʌ And (conjunction) V → ↔ Or (disjunction) ∴ ᵙ= If/then (conditional) ≡ If and only if (bi-conditional) Therefore (used to signal conclusions)

Examples of Argument Diagramming A →B B→C _____ A=C

Sample Argument A Socrates is a man. All men are mortal. Therefore, Socrates is mortal.

Step 1: number statements ① Socrates is a man ② All men are mortal ③ Therefore, Socrates is mortal NB: When numbering statements, always circle the numbers (you’ll see why in a minute. )

Step 2: determine argument parts ① Socrates is a man • Premise ② All men are mortal • Premise ③ Therefore, Socrates is mortal • Conclusion

Step 2 can also be written as… P 1. Socrates is a man • Premise P 2. All men are mortal • Premise C 1. Therefore, Socrates is mortal • Conclusion

Diagram for Sample Argument A P 1, P 2 → C 1 P 1, P 2 C 1

Sample Argument B John didn't get much sleep last night. He has dark circles under his eyes. He looks tired. How would you diagram this argument?

Sample Argument B, Way 1 ① John didn't get much sleep last night. ②He has dark circles under his eyes. ③He looks tired. ②③_ ①

Sample Argument B, Way 2 C 1: John didn’t get much sleep last night P 1: He [John] has dark circles under his eyes P 2: He [John] looks tired Diagram: P 1, P 2 → C 1

Conclusions are tricky… • They can occur anywhere in an argument • Conclusion trigger words Thus therefore consequently hence so it follows that proves that indicates that accordingly implies that for this reason

Sample Argument C ①No one has directly observed a chemical bond, ② so scientists who try to envision such bonds must rely on experimental clues and their own imaginations.

Remember • A statement in logic is not the same thing as a complete sentence. • Often, one sentence will contain multiple statements.

Sample Argument D If students were environmentally aware, they would object to the endangering of any species of animal. The well-known flying squirrel has become endangered as it has disappeared from the LSA Campus because the building of theatre studio destroyed its native habitat. No LSA students objected. Thus, LSA students are not environmentally aware.

Sample Argument D, Way 1 ①If students were environmentally aware, they would object to the endangering of any species of animal. ② The well-known flying squirrel has become endangered ③ as it has disappeared from the LSA Campus ④ because the building of theatre studio destroyed its native habitat. ⑤No LSA students objected. ⑥ Thus, LSA students are not environmentally aware.

Sample Argument D, Way 2 P 1 If students were environmentally aware, they would object to the endangering of any species of animal. P 2 The well-known flying squirrel has become endangered P 3 as it has disappeared from the LSA Campus P 4 because the building of theatre studio destroyed its native habitat. P 5 No LSA students objected. C 1 Thus, LSA students are not environmentally aware.

Diagramming Argument D Way 1 Way 2 P 4 → P 3 → P 2 = P 4(3)(2) P 1, P 5, P 4(3)(2) __________ C 6

• The premise indicators suggest that ② is a subconclusion of ③ since the indicator "as" connects them, and ③, in turn, is a sub-conclusion of ④since the indicator "because" connects those two statements. • Statement ⑥ is the final conclusion since it has the conclusion indicator "thus" and the import of the paragraph indicates that this statement is the main point of the argument. • Intuitively, the structure of the first statement ①together with statement ⑤is a common argument form:

If students were environmentally Aware, they would Object to the endangering of any species of animal. No student Objected (to the endangering of the Greenwood white squirrel). which can be abbreviated as follows: If A then O → Not O and the negation of clause O is logically equivalent to conclusion (6). (this argument structure is termed modus tollens) If A then O Not O______________ Not A which is the same statement as ⑥.

Modus Tollens A→O ¬O ∴ ¬A Latin for “denying the consequent”

Sample Argument E Some cave dwellers use fire. All who use fire have intelligence. Therefore, some cave dwellers have intelligence

Sample Argument F If you overslept, you'll be late. You aren't late. Therefore, you did not oversleep (hint: modus tollens)

Sources • http: //en. wikipedia. org/wiki/Logical_connecti ve • http: //philosophy. lander. edu/logic/diagram. h tml • http: //opencourselibrary. org/phil-120 symbolic-logic/ • http: //www. harryhiker. com/fe/fe-0 -03. htm#4