Topic 6: Basic Forms of Deductive Reasoning

Question 1

What is Syllogism?

Answer 1

A syllogism is an argument that consists of three sentences, each of which expresses a relation of predication between two terms.

In a syllogism, there must only be three different terms and each term must appear twice in the argument.

Question 2

Express the Syllogism Form

Answer 2

All A are B
All A are C
————-
Some B are C

Question 3

What is a Conditional arguement?

Answer 3

“if..then” relationship expresses a particular kind of relationship (hypothetical relationship) between two sentences.

If the antecedent is true, then the consequent must also be true.

Question 4

What is the Modus Ponendo Ponens Form?

Answer 4

It is a valid form of conditional form, whereby it is affirming the antecedent.

If P, then Q
P
————–
Q

Question 5

What is Modus Tollendo Tonens?

Answer 5

It is a valid form of conditional form, whereby it is denying the consequent.

If P, then Q
Not Q
————–
Not P

Question 6

What are the fallacy of a conditional form?

Answer 6

The fallacy of Denying the antecedent

If P, then Q
Not P
————–
Not Q

The fallacy of Affirming the consequent

If P, then Q
Q
—————
P

Question 7

Derive “Only if..”

Answer 7

P only if Q
= “If not Q, then not P”
= “If P, then Q”

Question 8

“… If and Only if…”

Answer 8

P if and only if Q
= “P, if Q” and “P only if Q”
= “If Q, then P” and “If P, then Q”
Bidirectional Relationship

Question 9

How is “Not” expressed

Answer 9

Not is a negation it is often used as ‘it is not the case that’ is used to express the negation

Question 10

What would be a double negation?

Answer 10

Double negation would cancel the negation and return the statement back to its original form.

Question 11

How is “And” expressed

Answer 11

A sentence formed by “and” is called conjunction: we are assuming that both statements is true.

Question 12

What is the form of Conjunction Introduction (CI)?

Answer 12

We can affirm independently two separate sentences, we can always affirm the conjunction of the two sentences

P
Q
———–
P and Q

Question 13

What is the form of Conjunction Elimination (CE)?

Answer 13

We can always derive anyone of the conjuncts from the conjunction

P

and vice versa

Q

Question 14

What are the form of a Negation of a Conjuction Arguement?

Answer 14

Not both (P and Q)
P
————————-
Not Q

and vice versa

Not both (P and Q)
Q
—————————
Not P

Question 15

Give an example of an invalid form of a Negation of a Conjunction Arguement?

Answer 15

Not both (P and Q)
Not P
————————-
Q

and vice versa

Not both (P and Q)
Note Q
—————————
P

Question 16

How is “Or” Expressed

Answer 16

Each component sentence of ‘or’ is a disjunct whereby there is a choice between two things.

Question 17

Describe the inclusive sense of ‘Or’

Answer 17

At least one of the disjunct is true which doesn’t exclude the possibility that both disjuncts can be true. In other words, the disjunct is false when both disjuncts are false.

Question 18

Describe the exclusive sense of ‘Or’

Answer 18

At least one of the disjunct is true but not both sentences are true. In other words, the disjunct is false when both are false or both are true.

Question 19

How would you determine in the statement is an inclusive sense or exclusive sense?

Answer 19

It would depend on the speaker … If we mean it in the exclusive sense we would say “P or Q, but not both”

Question 20

What is the form of Disjunction Introduction?

Answer 20

Any unit can be derived.

P or Q

and vice versa

Q or P

Question 21

Give an example of an invalid form of Disjunction Introduction?

Answer 21

P

Question 22

What is the form of Disjunction Elimination?

Answer 22

P or Q
Not P
——–
Q

and vice versa

P or Q
Not Q
——–
P

Question 23

Give an example of an invalid form of Disjunction Elimination?

Answer 23

P or Q
P
——–
Not Q

and vice versa

P or Q
Q
———
Not P

Question 24

Give an example of a valid Disjunction Elimination in an exclusive sense

Answer 24

P or Q
Not both (P and Q)
P
------------------------
Not Q

Question 25

Derive “Unless…”

Answer 25

“Unless P, Q
= “If not P, than Q”
=”P or Q”

Question 26

Derive “Neither …Nor”

Answer 26

Neither P Nor Q
= “Not P And Not Q”
= “Not Both (P And Q)”