# Logical Syllogism: Understanding Logical Reasoning

Learn the basics of logical syllogism with this practical guide. From the structure and types of syllogisms to common fallacies and examples, this resource covers all the essential information you need to understand this fundamental concept in logic and critical thinking.

Modus ponens:

Modus ponens, also known as modus ponendo ponens or the law of detachment, is a logical rule that states that if a conditional statement (if P then Q) is true and the antecedent (P) is also true, then the consequent (Q) must be true.

For example:

If it rains, the streets will be wet. (if P then Q)
It is raining. (P)
Therefore, the streets are wet. (Q)
Modus ponens is a valid form of reasoning because if the conditional statement is true and the antecedent is true, then the consequent must also be true.

References:

Hurley, P. (2010). A concise introduction to logic (12th ed.). Boston, MA: Cengage Learning.
Modus tollens:

Modus tollens, also known as modus tollendo tollens or the law of contraposition, is a logical rule that states that if a conditional statement (if P then Q) is true and the consequent (Q) is false, then the antecedent (P) must also be false.

For example:

If it is Monday, I have class. (if P then Q)
It is not Monday. (not Q)
Therefore, I do not have class. (not P)
Modus tollens is a valid form of reasoning because if the conditional statement is true and the consequent is false, then the antecedent must also be false.

References:

Hurley, P. (2010). A concise introduction to logic (12th ed.). Boston, MA: Cengage Learning.

Hypothetical syllogism:

Hypothetical syllogism is a logical argument in which two conditional statements (if P then Q and if Q then R) are combined to conclude that the final statement (if P then R) must be true.

For example:

If it is raining, the streets will be wet. (if P then Q)
If the streets are wet, the cars will have a hard time driving. (if Q then R)
Therefore, if it is raining, the cars will have a hard time driving. (if P then R)
In this example, the first conditional statement (if it is raining, the streets will be wet) and the second conditional statement (if the streets are wet, the cars will have a hard time driving) are combined to conclude that the final statement (if it is raining, the cars will have a hard time driving) must be true.

References:

Hurley, P. (2010). A concise introduction to logic (12th ed.). Boston, MA: Cengage Learning.
Disjunctive syllogism:

Disjunctive syllogism is a logical argument in which a disjunction (either P or Q) is combined with the negation of one of the disjuncts (not P) to conclude that the other disjunct (Q) must be true.

For example:

Either it is raining or it is not raining. (P or Q)
It is not raining. (not P)
Therefore, it is not raining. (Q)
In this example, the disjunction (either it is raining or it is not raining) is combined with the negation of one of the disjuncts (it is not raining) to conclude that the other disjunct (it is not raining) must be true.

References:

Hurley, P. (2010). A concise introduction to logic (12th ed.). Boston, MA: Cengage Learning.
Constructive dilemma:

Constructive dilemma is a logical argument in which two alternatives (P and Q) are presented, and the choice between them is determined by the truth of one of the conditions (if R then P, if not R then Q). If the condition is true, the first alternative (P) must be chosen, and if the condition is false, the second alternative (Q) must be chosen.

For example:

If it is raining, I will take the bus. (if R then P)
If it is not raining, I will walk. (if not R then Q)
It is raining. (R)
Therefore, I will take the bus. (P)
In this example, the condition (it is raining) is true, so the first alternative (I will take the bus) must be chosen.

References:

Hurley, P. (2010). A concise introduction to logic (12th ed.). Boston, MA: Cengage Learning.
The Stanford Encyclopedia of Philosophy. (n.d.). Constructive dilemma