# Unit 1 Deductive Arguments

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1. Name the 12 deductive argument forms
• 1.    Argument based on mathematics
• 2.    Argument from definition
• 3.    Categorical syllogism
• 4.    Hypothetical syllogism
• 5.    Modus ponens
• 6.    Modus tollens
• 7.    Denying the antecedent
• 8.    Affirming the consequent
• 9.    Disjunctive syllogism
• 10.  Constructive dilemma
• 11.  Destructive dilemma
• 12.   Logical relationships
2. Argument based on mathematics
an argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement.
3. Argument from definition
an argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion
4. Categorical syllogism
deductive argument syllogism in which each statement begins with one of the words “all,” “no,” or “some.”
5. Hypothetical syllogism
deductive argument syllogism in which there are three conditional statements, two conditional premises and one conditional conclusion

• If p, then q
• If q, then r
• If p, then r
6. Modus ponens
"affirming mode" - deductive argument syllogism in which there are three statements, with one premise as a conditional statement, the second premise, and the conclusion

• If p, then q
• P
• Q
7. Modus tollens
"denying mode" - deductive argument syllogism in which the first premise is a conditional statement, the second premise negates the first premise, and the conclusion negates the first premise

• If p, then q
• Not q
• Not p
8. Denying the antecedent
• deductive argument syllogism in which the first premise is a conditional statement, the second premise negates the first premise's
• antecedent , and the conclusion negates the first premise's consequent

• If p, then q
• Not p
• Not q
9. Affirming the consequent
• deductive argument syllogism in which the first premise is a conditional statement, the second premise confirms the first premise's
• consequent, and the conclusion states the antecedent of the first premise

• If p, then q
• q
• p
10. Disjunctive syllogism
deductive argument with "either/or "statement. there are two disjunctive statements in a disjunctive syllogism, which state a truth value relationship

• Either p or q
• Not p
• q

• Either p, or q
• Not q
• P
11. Constructive dilemma
• deductive argument which has three premises, the first being a conditional statement of one type, the second being a conditional statement of another type, the third being a disjunctive statement of
• the first two premise, and the conclusion being a disjunctive statement of the second type.

• If p, then q
• If r, then s
• Either p or r
• Either q or s
12. Destructive dilemma
• deductive argument which has three premises, the first being a conditional statement of one type, the second being a conditional statement of another type, the third being a disjunctive statement of
• the first two premise, and the conclusion being a disjunctive statement of the second type negating the premises.

• If p, then q
• If r, then s
• Either not q, or not s
• Either not p, or not r
13. Logical relationships (5)
• Comparison
• Temporal relations
• Spatial relations
• Family relations
• Identity
14. Identity formats (2)
• A = B
• Pa
• Pb

• Pa
• Not Pb
• A =/ B
15. Which argument types are always valid? (5)
• hypothetical syllogism
• modus ponens
• modus tollens
• constructive dilemma
• destructive dilemma
16. What deductive argument type is always predicate logic?
Categorical syllogism
17. What is a deductive argument?
group of sentences in which one or more (premises) claim to support one of the others (conclusion) with logical necessity
18. What is a valid argument?
An argument in which it is impossible for the conclusion to be false given that the premises are true
19. How do we prove invalidity?
Counterexample where the two premises are true and the conclusion is outrageously false
20. What is an invalid argument?
deductive argument in which it is possible for the conclusion to be false given that the premises are true
21. Sound argument
deductive argument that is valid and has all true premises.
 Author: ceilingmoth ID: 308364 Card Set: Unit 1 Deductive Arguments Updated: 2015-10-06 22:15:09 Tags: logic Folders: logic Description: x Show Answers: