1. Introduction to Argument
Cognitive Development

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

3. 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

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

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

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

7. 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.)

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

9. Step 2 can also be written as…
P1. Socrates is a man P2. All men are mortal C1. Therefore, Socrates is mortal
Premise
Conclusion

10. Diagram for Sample Argument A
P1, P2 → C1
P1, P2 C1

11. How would you diagram this argument?
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?

12. ②③_ ① 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

13. Sample Argument B, Way 2
C1: John didn’t get much sleep last night P1: He [John] has dark circles under his eyes P2: He [John] looks tired Diagram: P1, P2 → C1

14. 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

15. 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.

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

17. 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 the theatre studio destroyed its native habitat. No LSA students objected. Thus, LSA students are not environmentally aware.

18. 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 the theatre studio destroyed its native habitat. ⑤No LSA students objected. ⑥ Thus, LSA students are not environmentally aware.

19. Sample Argument D, Way 2
P1 If students were environmentally aware, they would object to the endangering of any species of animal. P2 The well-known flying squirrel has become endangered P3 as it has disappeared from the LSA Campus P4 because the building of the theatre studio destroyed its native habitat. P5 No LSA students objected. C1 Thus, LSA students are not environmentally aware.

20. P4 → P3 → P2 = P4(3)(2) P1, P5, P4(3)(2) ___________________ C6

21. Diagramming Argument D
Way 1
Way 2
P4 → P3 → P2 = P4(3)(2) P1, P5, P4(3)(2) ___________________ C6

22. The premise indicators suggest that ② is a sub-conclusion 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:

23. 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.

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

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

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

27. Sources http://en.wikipedia.org/wiki/Logical_connective