P→P
∴Q
Modus Ponens
Modus Ponens, also known as "affirming the antecedent," is a valid form of argument where if a conditional statement ("If P, then Q") is accepted, and the antecedent (P) holds, then the consequent (Q) must also hold.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
It rains.
Premise 3
Therefore, the ground will be wet.
P→P
∴Q
Modus Ponens
Modus Ponens, also known as "affirming the antecedent," is a valid form of argument where if a conditional statement ("If P, then Q") is accepted, and the antecedent (P) holds, then the consequent (Q) must also hold.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
It rains.
Premise 3
Therefore, the ground will be wet.
P→P
∴Q
Modus Ponens
Modus Ponens, also known as "affirming the antecedent," is a valid form of argument where if a conditional statement ("If P, then Q") is accepted, and the antecedent (P) holds, then the consequent (Q) must also hold.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
It rains.
Premise 3
Therefore, the ground will be wet.
P→P
∴Q
Modus Ponens
Modus Ponens, also known as "affirming the antecedent," is a valid form of argument where if a conditional statement ("If P, then Q") is accepted, and the antecedent (P) holds, then the consequent (Q) must also hold.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
It rains.
Premise 3
Therefore, the ground will be wet.
P→Q
¬Q
∴¬P
Modus Tollens
Modus Tollens, also known as "denying the consequent," is a valid form of argument where if a conditional statement ("If P, then Q") is accepted, and the consequent (Q) does not hold, then the antecedent (P) must also not hold.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
The ground is not wet.
Premise 3
Therefore, it did not rain.
P→Q
¬Q
∴¬P
Modus Tollens
Modus Tollens, also known as "denying the consequent," is a valid form of argument where if a conditional statement ("If P, then Q") is accepted, and the consequent (Q) does not hold, then the antecedent (P) must also not hold.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
The ground is not wet.
Premise 3
Therefore, it did not rain.
P→Q
¬Q
∴¬P
Modus Tollens
Modus Tollens, also known as "denying the consequent," is a valid form of argument where if a conditional statement ("If P, then Q") is accepted, and the consequent (Q) does not hold, then the antecedent (P) must also not hold.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
The ground is not wet.
Premise 3
Therefore, it did not rain.
P→Q
¬Q
∴¬P
Modus Tollens
Modus Tollens, also known as "denying the consequent," is a valid form of argument where if a conditional statement ("If P, then Q") is accepted, and the consequent (Q) does not hold, then the antecedent (P) must also not hold.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
The ground is not wet.
Premise 3
Therefore, it did not rain.
P∨Q
¬P
∴Q
Disjunctive Syllogism
Disjunctive Syllogism is a valid form of argument where if one part of a disjunction (an "or" statement) is false, the other part must be true.
EXAMPLE
Premise 1
Either it is raining, or it is sunny.
Premise 2
It is not raining.
Premise 3
Therefore, it is sunny.
P∨Q
¬P
∴Q
Disjunctive Syllogism
Disjunctive Syllogism is a valid form of argument where if one part of a disjunction (an "or" statement) is false, the other part must be true.
EXAMPLE
Premise 1
Either it is raining, or it is sunny.
Premise 2
It is not raining.
Premise 3
Therefore, it is sunny.
P∨Q
¬P
∴Q
Disjunctive Syllogism
Disjunctive Syllogism is a valid form of argument where if one part of a disjunction (an "or" statement) is false, the other part must be true.
EXAMPLE
Premise 1
Either it is raining, or it is sunny.
Premise 2
It is not raining.
Premise 3
Therefore, it is sunny.
P∨Q
¬P
∴Q
Disjunctive Syllogism
Disjunctive Syllogism is a valid form of argument where if one part of a disjunction (an "or" statement) is false, the other part must be true.
EXAMPLE
Premise 1
Either it is raining, or it is sunny.
Premise 2
It is not raining.
Premise 3
Therefore, it is sunny.
P→Q
Q→R
∴P→R
Hypothetical Syllogism
Hypothetical Syllogism is a valid form of argument where if two conditional statements are true ("If P, then Q" and "If Q, then R"), then the conclusion ("If P, then R") must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If the ground is wet, then the flowers will grow.
Premise 3
Therefore, if it rains, the flowers will grow.
P→Q
Q→R
∴P→R
Hypothetical Syllogism
Hypothetical Syllogism is a valid form of argument where if two conditional statements are true ("If P, then Q" and "If Q, then R"), then the conclusion ("If P, then R") must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If the ground is wet, then the flowers will grow.
Premise 3
Therefore, if it rains, the flowers will grow.
P→Q
Q→R
∴P→R
Hypothetical Syllogism
Hypothetical Syllogism is a valid form of argument where if two conditional statements are true ("If P, then Q" and "If Q, then R"), then the conclusion ("If P, then R") must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If the ground is wet, then the flowers will grow.
Premise 3
Therefore, if it rains, the flowers will grow.
P→Q
Q→R
∴P→R
Hypothetical Syllogism
Hypothetical Syllogism is a valid form of argument where if two conditional statements are true ("If P, then Q" and "If Q, then R"), then the conclusion ("If P, then R") must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If the ground is wet, then the flowers will grow.
Premise 3
Therefore, if it rains, the flowers will grow.
(P→Q)∧(R→S
P∨R
∴Q∨S
Constructive Dilemma
Constructive Dilemma is a valid form of argument where if two conditional statements ("If P, then Q" and "If R, then S") and a disjunction of their antecedents (P or R) are true, then a disjunction of their consequents (Q or S) must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If the ground is wet, then the flowers will grow.
Premise 3
Therefore, if it rains, the flowers will grow.
Conclusion
Therefore, either the ground will be wet, or the flowers will bloom.
(P→Q)∧(R→S
P∨R
∴Q∨S
Constructive Dilemma
Constructive Dilemma is a valid form of argument where if two conditional statements ("If P, then Q" and "If R, then S") and a disjunction of their antecedents (P or R) are true, then a disjunction of their consequents (Q or S) must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If the ground is wet, then the flowers will grow.
Premise 3
Therefore, if it rains, the flowers will grow.
Conclusion
Therefore, either the ground will be wet, or the flowers will bloom.
(P→Q)∧(R→S
P∨R
∴Q∨S
Constructive Dilemma
Constructive Dilemma is a valid form of argument where if two conditional statements ("If P, then Q" and "If R, then S") and a disjunction of their antecedents (P or R) are true, then a disjunction of their consequents (Q or S) must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If the ground is wet, then the flowers will grow.
Premise 3
Therefore, if it rains, the flowers will grow.
Conclusion
Therefore, either the ground will be wet, or the flowers will bloom.
(P→Q)∧(R→S
P∨R
∴Q∨S
Constructive Dilemma
Constructive Dilemma is a valid form of argument where if two conditional statements ("If P, then Q" and "If R, then S") and a disjunction of their antecedents (P or R) are true, then a disjunction of their consequents (Q or S) must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If the ground is wet, then the flowers will grow.
Premise 3
Therefore, if it rains, the flowers will grow.
Conclusion
Therefore, either the ground will be wet, or the flowers will bloom.
(P→Q)∧(R→S)
¬Q∨¬S
∴¬P∨¬R
Destructive Dilemma
Destructive Dilemma is a valid form of argument where if two conditional statements ("If P, then Q" and "If R, then S") and a disjunction of the negations of their consequents (not Q or not S) are true, then a disjunction of the negations of their antecedents (not P or not R) must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If it is sunny, then the flowers will bloom.
Premise 3
Either the ground is not wet, or the flowers do not bloom.
Conclusion
Therefore, either it does not rain, or it is not sunny.
(P→Q)∧(R→S)
¬Q∨¬S
∴¬P∨¬R
Destructive Dilemma
Destructive Dilemma is a valid form of argument where if two conditional statements ("If P, then Q" and "If R, then S") and a disjunction of the negations of their consequents (not Q or not S) are true, then a disjunction of the negations of their antecedents (not P or not R) must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If it is sunny, then the flowers will bloom.
Premise 3
Either the ground is not wet, or the flowers do not bloom.
Conclusion
Therefore, either it does not rain, or it is not sunny.
(P→Q)∧(R→S)
¬Q∨¬S
∴¬P∨¬R
Destructive Dilemma
Destructive Dilemma is a valid form of argument where if two conditional statements ("If P, then Q" and "If R, then S") and a disjunction of the negations of their consequents (not Q or not S) are true, then a disjunction of the negations of their antecedents (not P or not R) must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If it is sunny, then the flowers will bloom.
Premise 3
Either the ground is not wet, or the flowers do not bloom.
Conclusion
Therefore, either it does not rain, or it is not sunny.
(P→Q)∧(R→S)
¬Q∨¬S
∴¬P∨¬R
Destructive Dilemma
Destructive Dilemma is a valid form of argument where if two conditional statements ("If P, then Q" and "If R, then S") and a disjunction of the negations of their consequents (not Q or not S) are true, then a disjunction of the negations of their antecedents (not P or not R) must also be true.
EXAMPLE
Premise 1
If it rains, then the ground will be wet.
Premise 2
If it is sunny, then the flowers will bloom.
Premise 3
Either the ground is not wet, or the flowers do not bloom.
Conclusion
Therefore, either it does not rain, or it is not sunny.
ARGUMENT
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Truth tools for critical thinking.
