Argument Forms

Question 1

What is the difference between a deductive argument and an inductive argument?

Answer 1

A deductive argument: the claims provided prove with absolute certainty that the conclusion must be true (no room for doubt) and the strength of a deductive argument is measured by validity.
An inductive argument makes claims that do not ensure the truth of its conclusions but give us good reason to (measured in strength)

Question 2

P

Answer 2

P is the Antecedent: In the conditional statement “If P then Q,” the part represented by P is called the antecedent. This is the condition or event that is stated to be true or assumed to be true for the consequent to follow.

Question 3

Q

Answer 3

Q is the Consequent: In the same statement, Q represents the consequent. It is the result or outcome that is claimed to occur if the condition P is met.

Question 4

P is a sufficient condition for Q

Answer 4

This means that if P is true, then Q must also be true. In other words, the occurrence of P alone is enough to guarantee the occurrence of Q.

Question 5

Q is a necessary condition for P

Answer 5

This indicates that for P to be true, Q must also be true. Q is essential or required for the occurrence of P.

Question 6

Conditional Statement Example

Answer 6

For example, consider the statement: “If it rains (P), then the ground is wet (Q).”

P (it rains) is the antecedent.
Q (the ground is wet) is the consequent.
If it rains (P), it is sufficient to make the ground wet (Q).
Conversely, if the ground is wet (Q), it is necessary that it has rained (P).

Question 7

Modus Ponens

Answer 7

If P then Q
P
Therefore, Q

Question 8

Modus Tollens

Answer 8

If P then Q
Not-Q
Therefore, Not-P

Question 9

Affirming the Consequent (Fallacy)

Answer 9

If P then Q
Q
Therefore, P

Question 10

Denying the Antecedent

Answer 10

If P then Q
Not-P
Therefore Not-Q

Question 11

Inclusive-or? Exclusive-or?

Answer 11

When in doubt, assume it is an inclusive or

Question 12

Validity

Answer 12

An argument is valid if and only if it is impossible for the premises to be true and the conclusion false. This means that the conclusion follows logically from the premises. However, validity does not necessarily depend on the truth of the premises or the conclusion; it only concerns the structure of the argument.

Question 13

Disjunctive Syllogism

Answer 13

P or Q
Not-P
Therefore Q

Question 14

Eliminative Fallacy/Syllogism

Answer 14

P or Q
P
Therefore, not Q